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How to solve Logical Reasoning part in elitmus pH test?

Logical Reasoning is always the toughest part of eLitmus. In elitmus LR questions usually comes with 2/3 bits . A paragraph is given with full of information followed by 2/3 questions. You have to read it and use your logic to answer the questions. In 3 sections CAT paper there is no special section on LR but one can expect LR questions to be present in any section.

“The main idea behind LR is to is use the information and preconditions to make a conclusion”

Most problems give a variety of conditions and you must use an "if"-"then" approach. It's important that you read the whole problem, and choose the best hint or clue before starting to solve the problem. When practicing logic with reasoning making a chart or drawing a picture are good strategies. Before starting any LR problem it s advised to keep few points in mind.

Important Tips for Logical Reasoning

Before you try to answer a few sample questions, here are some general test-taking tips that should help you with the Logical Reasoning section.

1.Study the question carefully. A brief explanation of why each choice is correct or incorrect follows each practice question. If you understand this reasoning for the practice items, you will do well on the actual assessment.

2.NEVER assume or use any information that the question fails to give you. This is NOT an assessment of how much you know about economics in general! Consider ONLY the information given in each reading passage when choosing among the alternative responses.

3.Read both the factual passage and the sentence completion instruction carefully. Both must be considered in making your choice.

4.Be sure to read all the response choices carefully before choosing one.

5.In questions that ask you to select a valid conclusion, always choose the one conclusion that must definitely follow from the information you are given. In questions that ask you to find the invalid alternative, choose the one conclusion that does not definitely follow from the information.

6.Pay special attention to words like "all," "some," or "none" when you read the factual information each question gives you. Other qualifying words such as "other than," "only" or "unless" are important, too. These words can play a critical part in precisely specifying the facts to be used in your reasoning.

7.Pay attention to negative prefixes also, such as non-, un-, or dis-. These can be crucial to specifying the basic facts in the paragraph.

8."Test-taking" courses or your college instructors may have advised you to avoid any response choices that contain the quantifiers "all" or "none." In both the practice questions here and in the actual economist assessment, these words are NOT signs of

1

incorrect response choices. They will appear in both correct and incorrect response choices.

9.Pay close attention to the word "ONLY" and to the phrase "IF AND ONLY IF." Saying "The door will open IF AND ONLY IF both keys are used" sets up a highly specific condition that must be met. There is exactly one way to open the door-you must use both keys. By contrast, if the sentence says, "The door will open if the key is used," there may be several ways to open the door besides by using the key.

10.The questions in the assessment will vary in difficulty level, and difficult questions will be mixed in with easier ones throughout the assessment. When you encounter a question that is difficult for you, try drawing diagrams or other schematic notes on the "scratch" paper provided to support and confirm your thought processes. Also, bear in mind that you can stop working on a difficult question temporarily and return to it later.

Solving elitmus Cryptarithmetic Questions in Logical Reasioning Section-Method-I eLitmus Guru

05:10 cryptarithmeticLogical

In elitmus test you will be getting 3 questions(30 marks) on cryptic multiplication...

This tutorial will be very helpful in solving those questions.I myself solved those 3 questions just by reading this tutorial. you won't find any help regarding this topic anywhere else so please read this tutorial.

HOW TO SOLVE A PUZZLE

1. Preparation

Rewrite the problem, expanding the interlinear space to make room for trial numbers that will be written under the letters.

For example, the puzzle SEND + MORE = MONEY, after solving, will appear like this:

 

S

E

N

D

 

9

5

6

7

+

M

O

R

E

 

1

0

8

5

---------------

 

 

M

O

N

E

Y

1

0

6

5

2

Also Read:Data Sufficiency Part in eLitmus

2

2.Remember cryptarithmetic conventions

Each letter or symbol represents only one digit throughout the problem;

When letters are replaced by their digits, the resultant arithmetical operation must be correct;

The numerical base, unless specifically stated, is 10;

Numbers must not begin with a zero;

There must be only one solution to the problem.

3.See subtractions as "upside-down" additions

Ease the analysis of subtractions by reading them as upside-down additions. Remember that you can check a subtraction by adding the difference and the subtracter to get the subtrahend: it's the same thing. This subtraction:

C O U N T

- C O I N

---------

S N U B

must be read from the bottom to the top and from the right to the left, as if it were this series of additions:

B + N = T + C1

U + I = N + C2

N + O = U + C3

S + C = O + C4

C1, C2, C3 and C4 are the carry-overs of "0" or "1" that are to be added to the next column to the left.

4. Search for "0" and "9" in additions or subtractions

A good hint to find zero or 9 is to look for columns containing two or three identical letters. Look at these additions:

* * * A

* * * B

+ * * * A

+ * * * A

-------

-------

* * * A

* * * B

The columns A+A=A and B+A=B indicate that A=zero. In math this is called the "additive identity property of zero"; it says that you add "0" to anything and it doesn't change, therefore it stays the same. Now look at those same additions in the body of the cryptarithm:

* A * *

* B * *

+ * A * *

+ * A * *

-------

-------

* A * *

* B * *

In these cases, we may have A=zero or A=9. It depends whether or not "carry 1" is received from the previous column. In other words, the "9" mimics zero every time it gets a carry-over of "1".

5. Search for "1" in additions or subtractions

3

Look for left hand digits. If single, they are probably "1". Take the world's most famous cryptarithm:

S E N D

+ M O R E

---------

M O N E Y

"M" can only equal 1, because it is the "carry 1" from the column S+M=O (+10). In other words, every time an addition of "n" digits gives a total of "n+1" digits, the left hand digit of the total must be "1". In this Madachy's subtraction problem, "C" stands for the digit "1":

C O U N T

- C O I N

---------

S N U B

Also Read : Verbal Section in eLitmus

6. Search for "1" in multiplications or divisions

In this multiplication:

M A D

B E

-------

M A D R A E

-------

A M I D

The first partial product is E x MAD = MAD. Hence "E" must equal "1". In math jargon this is called the "identity" property of "1" in multiplication; you multiply anything by "1" and it doesn't change, therefore it remains the same.Look this division:

K T

--------

N E T / L I N K N E T

----------

K E K K

K T E C

----------

K E Y

In the first subtraction, we see K x NET = NET. Then K=1.

7. Search for "1" and "6" in multiplications or divisions

Any number multiplied by "1" is the number itself. Also, any even number multiplied by "6" is the number itself:

4 x 1 = 4

7 x 1 = 7

2 x 6 = 2 (+10)

8 x 6 = 8 (+40)

Looking at right hand digits of multiplications and divisions, can help you spot digits "1" and "6". Those findings will show like these ones:

4

 

C B

 

-------

* * A

* * A / * * * * *

B C

* * * C

--------

------

* * * C

* * * *

* * * B

* * * B

---------

-------

* * * * *

* * *

The logic is: if

 

C x * * A = * * * C B x * * A = * * * B

then A=1 or A=6.

8. Search for "0" and "5" in multiplications or divisions

Any number multiplied by zero is zero. Also, any odd number multiplied by "5" is "5":

3 x 0 = 0

6 x 0 = 0

7 x 5 = 5 (+30)

9 x 5 = 5 (+40)

Looking at right hand digits of multiplications and divisions, can help you spot digits "0" and "5". Those findings will show like these ones:

 

C B

 

----------

* * A

* * A / * * * * *

B C

* * * A

-------

---------

* * * A

* * * *

* * * A

* * * A

---------

-------

* * * * *

* * *

The logic is: if

 

C x * * A = * * * A B x * * A = * * * A

then A=0 or A=5

9. Match to make progress

Matching is the process of assigning potential values to a variable and testing whether they match the current state of the problem.

To see how this works, let's attack this long-hand division:

K M

----------

A K A / D A D D Y D Y N A

---------

A R M Y

A R K A

-------

5

R A

To facilitate the analysis, let's break it down to its basic components, i.e., 2 multiplications and 2 subtractions:

I.K x A K A = D Y N A

II.M x A K A = A R K A

III.D A D D

-D Y N A

---------

A R M

IV.

A R M Y

 

- A R K A

 

---------

 

R A

From I and II we get:

K x * * A = * * * A M x * * A = * * * A

This pattern suggests A=0 or A=5. But a look at the divisor "A K A" reveals that A=0 is impossible, because leading letters cannot be zero. Hence A=5.Replacing all A's with "5", subtraction IV becomes:

5 R M Y - 5 R K 5

---------

R 5

From column Y-5=5 we get Y=0. Replacing all Y's with zero, multiplication I will be:

K x 5 K 5 = D 0 N 5

Now, matching can help us make some progress. Digits 1, 2, 3, 4, 6, 7, 8 and 9 are still unidentified. Let's assign all these values to the variable K, one by one, and check which of them matches the above pattern. Tabulating all data, we would come to:

K x 5K5 = D0N5

----------------------

1

515

515

2

525

1050

3

535

1605

4

545

2180

6

565

3390

SOLUTION --> 7

575

4025 <-- SOLUTION

8

585

4680

9

595

5355

----------------------

You can see that K=7 is the only viable solution that matches the current pattern of multiplication I, yielding:

K x A K A

= D Y N A

7

5 7 5

4

0 2 5

This solution also identifies two other variables: D=4 and N=2.

6

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10. When stuck, generate-and-test

Usually we start solving a cryptarithm by searching for 0, 1, and 9. Then if we are dealing with an easy problem there is enough material to proceed decoding the other digits until a solution is found.

This is the exception and not the rule. Most frequently after decoding 1 or 2 letters (and sometimes none) you get stuck. To make progress we must apply the generate-and- test method, which consists of the following procedures:

1. List all digits still unidentified;

2. Select a base variable (letter) to start generation;

3. Do a cycle of generation and testing: from the list of still unidentified digits (procedure 1) get one and assign it to

the base variable; eliminate it from the list; proceed guessing values for the other variables; test consistency; if not consistent, go to perform the next cycle (procedure 3); if consistent, stop: you have found the solution to the problem.

To demonstrate how this method works, let's tackle this J. A. H. Hunter's addition:

T A K E

A

+ C A K E

----------

K A T E

The column AAA suggests A=0 or A=9. But column EAEE indicates that A+E=10, hence the only acceptable value for "A" is 9, with E=1. Replacing all "A's" with 9 and all "E's" with 1, we get

T 9 K 1 9

+ C 9 K 1

----------

K 9 T 1

Letter repetition in columns KKT and TCK allows us to set up the following algebraic system of equations:

C1 + K + K = T + 10

C3 + T + C = K

Obviously C1=1 and C3=1. Solving the equation system we get K+C=8: not much, but we discovered a relationship between the values of "K" and "C" that will help us later. But now we are stuck! It's time to use the"generate-and-test" method. Procedure 1: digits 2,3,4,5,6,7 and 8 are still unidentified;

Procedure 2: we select "K" as the base variable;

CYCLE #1, procedure 3: column TCK shows that T+C=K and no carry, hence "K" must be a high valued digit. So we enter the list obtained through procedure 1 from the high side, assigning "8" to the base variable "K".

Knowing that K+C=8, if K=8 then C=0. But this is an unacceptable value for "C", because the addend "CAKE" would become "0981" and cryptarithmetic conventions say that no

7

number can start with zero. So, we must close this cycle and begin cycle #2.

By now, the addition layout and the table summarizing current variable data would look like this:

T 9 8 1

CYCLE A

E

K C T

9

========================

+ 0 9 8 1

#1

9

1

8

[0]

----------

 

 

 

 

 

 

8 9 T 1

Conflicting values for variables are noted within square brackets.

CYCLE #2, procedure 3: assigning "7" to the letter "K" we get C=1 because K+C=8. This is an unacceptable value for "C" considering that we have already fixed E=1. Again we have to close the current cycle and go to cycle #3, with the setup and table showing:

T 9 7 1

CYCLE A E K C T

9

========================

+ 1 9 7 1

#1

9

1

8

[0]

---------- #2

9

1

7

[1]

 

7 9 T 1

 

 

 

 

 

CYCLE #3, procedure 3: assigning "6" to the letter "K" we get C=2 because K+C=8. Testing these values for "K" and "C" in the column TCK, we get C3+T+2+=6 making T=3.Now, testing T in column KKT, we would obtain C1+K+K=T+10 or 1+6+6=T+10, making T=3. This is an acceptable value for T, confirming the previous value T=3 we had already found. So, we have got the final solution to the problem, stopping the routine "generate-and-test". The final layout and table would read

 

3 9 6 1

CYCLE

A

E

K

 

C T

 

9

 

========================

+

2 9 6 1

 

#1

9

1

8 [0]

 

 

----------

#2

9

1

7[1]

 

 

 

6 9 3

1

 

#3

9

1

6

2

3

Solving elitmus Cryptarithmetic Questions in Logical Reasioning Section-Method-II eLitmus Guru

05:16

cryptarithmeticLogical

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8

EXAMPLES WORKED OUT IN DETAIL BY MASTER PUZZLISTS

1. Geoffrey Mott-Smith In "Mathematical Puzzles for Beginners & Enthusiasts"©

S E N D + M O R E

------------

M O N E Y

We see at once that M in the total must be 1, since the total of the column SM cannot reach as high as 20. Now if M in this column is replaced by 1, how can we make this column total as much as 10 to provide the 1 carried over to the left below? Only by making S very large: 9 or 8. In either case the letter O must stand for zero: the summation of SM could produce only 10 or 11, but we cannot use 1 for letter O as we have already used it for M. If letter O is zero, then in column EO we cannot reach a total as high as 10, so that there will be no 1 to carryover from this column to SM. Hence S must positively be 9. Since the summation EO gives N, and letter O is zero, N must be 1 greater than E and the column NR must total over 10. To put it into an equation: E + 1 = N From the NR column we can derive the equation: N + R + (+ 1) = E + 10 We have to insert the expression (+ 1) because we don’t know yet whether 1 is carried over from column DE. But we do know that 1 has to be carried over from column NR to EO. Subtract the first equation from the second: R + (+1) = 9 We cannot let R equal 9, since we already have S equal to 9. Therefore we will have to make R equal to 8; hence we know that 1 has to be carried over from column DE. Column DE must total at least 12, since Y cannot be 1 or zero. What values can we give D and E to reach this total? We have already used 9 and 8 elsewhere. The only digits left that are high enough are 7, 6 and 7, 5. But remember that one of these has to be E, and N is 1 greater than E. Hence E must be 5, N must be 6, while D is 7. Then Y turns out to be 2, and the puzzle is completely solved. © Copyright Dover Publications, Inc., New York, 1954, ISBN 0-486-20198-8.

2. Steven Kahan In "Take a Look at a Good Book"©

E A T

+ T H A T

------------

A P P L E

Since every four-digit number is less than 10,000 and every three-digit number is less than 1,000, the sum of two such numbers is necessarily less than 11,000. This sum, though, is a

9

five-digit number, hence is greater than 10,000. Consequently, A must be 1 and P must be 0. Further, we can conclude that T = 9. Otherwise, we would be adding a number less than 1,000 to one less than 9,000, leaving us short of the requisite total. The units column then produces E = 8 while generating a carryover of 1 into the tens column. Together with the previously found value of A, we learn from the tens column that L = 3. Finally, the hundreds column yields the equation E + H = P + 10, where the "10" is required to accommodate the needed carryover into the thousands column. When the values of E and P are substituted into this relationship, we get 8 + H = 10, from which it follows that H = 2. Therefore, the unique solution of the puzzle turns out to be 819 + 9219 = 10038. © Copyright Baywood Publishing Company, Inc., Amityville, New York, 1996, ISBN 0-89503-142-6.

3. J. A. H. Hunter In "Entertaining Mathematical Teasers and How to Solve Them"©

N O

G U N + N O

----------

H U N T

Obviously H = 1. From the NUNN column we must have "carry 1," so G = 9, U = zero. Since we have "carry" zero or 1 or 2 from the ONOT column, correspondingly we have N + U = 10 or 9 or 8. But duplication is not allowed, so N = 8 with "carry 2" from ONOT. Hence, O + O = T + 20 - 8 = T + 12. Testing for T = 2, 4 or 6, we find only T = 2 acceptable, O = 7. So we have 87 + 908 + 87 = 1082. © Copyright Dover Publications, Inc., New York, 1983, ISBN 0-486-24500-4.

4. Maxey Brooke In "150 Puzzles In Crypt-Arithmetic"©

A B C x D E

----------

F E C

D E C

----------

H G B C

In the second partial product we see D x A = D, hence A = 1. D x C and E x C both end in C, hence C = 5. D and E must be odd. Since both partial products have only three digits, neither can be 9. This leaves only 3 and 7. In the first partial product E x B is a number of two digits

10

while in the second partial product D x B is a number of only one digit. Thus E is larger than D, so E = 7 and D = 3. Since D x B has only one digit, B must be 3 or less. The only two possibilities are 0 and 2. B cannot be zero because 7B is a two-digit number. Thus B = 2. By completing the multiplication, F = 8, E = 7, and G = 6. The answer is 125 x 37 =

4625 ©Copyright Dover Publications, Inc., New York, 1963.

5. Joseph S. Madachy In "Madachy´s Mathematical Recreations"©

(B E) (B E) = M O B

Here a 3-digit number is the product of a 2-digit number multiplied by itself. Basic knowledge of the laws of multiplication will immediately force the conclusion that B cannot be greater than 3. For if B is 4, and the lowest possible value, 0, is assigned to E then BE = 40. However, (40)(40) = 1,600, a 4-digit number, and the product in the puzzle to be solved has but 3 digits. Convention demands that the initial letters or symbols of alphametics cannot be 0, so B is either 1, 2, or 3. Another convention demands that 2 different letters cannot be substituted for the same digit. That is, if B turns out to be 3, then no other letter in this alphametic could stand for 3. Attention can be directed to E since much can be deduced from the fact that (E)(E) ends in B. If E equals 0, 1, 5, or 6, then the product would be a number ending in 0, 1, 5, or 6, respectively. Since the product, MOB, does not end in E, these numbers for E are eliminated. 2, 3, 4, 7, and 8 can also be eliminated as values for E, since they would yield the terminal digits of 4, 6, or 9 for MOB, and B has been established as being 1, 2, or 3. Only one value for E, 9, remains: (9) (9) = 81 so B = 1, and the alphametic is solved: (BE) (BE) = MOB is (19) (19) = 361. © Copyright Dover Publications, Inc., New York, 1979, ISBN 0-486-23762-1.

6. C. R. Wylie Jr. In "101 Puzzles in Thought & Logic"©

A L E x R U M

----------

W I N E

W U W L

E W W E

-------------

E R M P N E

11

To systematize our work we first write in a row the different letters appearing in the problem:

A L E R U M W I N P

Over each letter we will write its numerical equivalent when we discover it. In the columns under the various letters we will record clues and tentative hypotheses, being careful to put all related inferences on the same horizontal line. In problems of this sort the digits 0 and 1 can often be found, or at least restricted to a very few possibilities, by simple inspection. For instance, 0 can never occur as the leftmost digit of an integer, and when any number is multiplied by zero the result consists exclusively of zeros. Moreover when any number is multiplied by 1 the result is that number itself. In the present problem, however, we can identify 0 by an even simpler observation. For in the second column from the right, N plus L equals N, with nothing carried over from the column on the right. Hence L must be zero. In our search for 1 we can eliminate R, U, and M at once, since none of these, as multipliers in the second row, reproduces A L E. Moreover E cannot be 1 since U times E does not yield a product ending in U. At present, however, we have no further clues as to whether 1 is A, I, N, P, or W. Now the partial product W U W L ends in L, which we know to be 0. Hence one of the two letters U and E must be 5. Looking at the units digits of the other partial products, we see that both M x E and R x E are numbers ending in E. A moment’s reflection (or a glance at a multiplication table) shows that E must therefore be 5. But if E is 5, then both R and M must be odd, since an even number multiplied by 5 would yield a product ending in 0, which is not the case in either the first or third partial product. Moreover, by similar reasoning it is clear that U is an even number. At this point it is convenient to return to our array and list under U the various possibilities, namely 2, 4, 6, and 8. Opposite each of these we record the corresponding value of W as read from the partial product W U W L, whose last two digits are now determined since the factor A L E is known to be _05. These values of W are easily seen to be 1, 2, 3, and 4. From an inspection of the second column from the left we can now deduce the corresponding possibilities for R. As we have already noted, R must be odd; hence its value is twice W plus 1 (the 1 being necessarily carried over from the column on the right). The possible values for R are then 3, 5, 7, and 9, and our array looks like this:

0 5

A L E R U M W I N P 3 2 1

12

5 4 2

7 6 3

9 8 4

Now in the third column from the left in the example the sum of the digits W, U, and W must be more than 9, since 1 had to be carried over from this column into the column on the left. The values in the first two rows of the array are too low for this, however, hence we can cross out both of these lines. A further consideration of the sum of the digits W, U, and W in the third column from the left, coupled with the fact that M is known to be odd, shows that in the third row of the array M must be 3 while in the fourth row it must be 7. This permits us to reject the third row of the array also, for it contains 3 for both M and W, which is impossible. The correct solution must therefore be the one contained in the fourth row. Hence R is 9, U is 8, M is 7, and W is 4. Substituting these into the problem it is a simple matter to determine that A is 6, I is 2, N is 3, and P is 1. This completes the solution.

How to solve Data Sufficiency questions in elitmus pH Test? eLitmus Guru

03:22

DILogical

Elitmus test writers use data sufficiency questions to test your ability to "reason quantitatively." This stands in sharp contrast to the problem solving section, which is designed to test how well you manipulate numbers. If you find yourself doing a lot of number crunching on the data sufficiency questions, you are doing something wrong.

Math Concepts You Should Know

The data sufficiency questions cover math that nearly any college-bound high school student will know. In addition to basic arithmetic, you can expect questions testing your knowledge of averages, fractions, decimals, algebra, factoring, and basic principles of geometry such as triangles, circles, and how to determine the areas and volumes of simple geometric shapes.

The Answer Choices

Elitmus data sufficiency questions will all have the exact same answer choices. Memorize these answer choices before you take the exam. It will help you better utilize your time in the quantitative section. The answer choices are summarized below as you will see them on the

13

pH exam.

A.Statement 1 alone is sufficient but statement 2 alone is not sufficient to answer the question asked.

B.Statement 2 alone is sufficient but statement 1 alone is not sufficient to answer the question asked.

C.Both statements 1 and 2 together are sufficient to answer the question but neither statement is sufficient alone.

D.Each statement alone is sufficient to answer the question.

E.Statements 1 and 2 are not sufficient to answer the question asked and additional data is needed to answer the statements.

Use Process of Elimination

If statement 1 is insufficient, then choices A and D can immediately be eliminated. Similarly, if statement 2 is insufficient, then choices B and D can immediately be eliminated. If either statement 1 or 2 is sufficient on its own, then choices C and E can be eliminated.

A Simple 4 Step Process for Answering These Questions

Many test takers make the mistake of not arming themselves with a systematic method for analyzing the answer choices for these questions. Overlooking even one step in the process outlined below can make a big difference in the final quantitative score you will be reporting to your selected business schools.

1.) Study the questions carefully. The questions generally ask for one of 3 things: 1) a specific value, 2) a range of numbers, or 3) a true/false value. Make sure you know what the question is asking.

2.) Determine what information is needed to solve the problem. This will, obviously, vary depending on what type of question is being asked. For example, to determine the area of a circle, you need to know the circle's diameter, radius, or circumference. Whether or not statements 1 and/or 2 provide that information will determine which answer you choose for a data sufficiency question about the area of a circle.

3.) Look at each of the two statements independently of the other. Follow the process of elimination rules covered above to consider each statement individually.

4.) If step 3 did not produce an answer, then combine the two statements. If the two statements combined can answer the question, then the answer choice is C. Otherwise, E.

Data Sufficiency Tips and Strategies

Use only the information given in the questions. The elitmus seeks to measure your ability to distinguish facts from careless assumptions. Do not rely on a visual assessment of a diagram accompanying a geometry question to determine angle sizes, parallel lines, etc. In

14

addition, do not carry any information over from one question to the next. Each question in the data sufficiency section of the CAT stands on its own. You can count on seeing at least a few questions where a wrong answer choice tries to capitalize on this common fallacy.

Do not get bogged down with complicated or lengthy calculations. As we stated before, these questions are designed to test your ability to think conceptually, not to solve math problems.

Use process of elimination. This Elitmus section lends itself perfectly to using the process of elimination. If time becomes an issue, you can always look at the 2 statements in either order. Remember, the order you analyze the two statements in doesn't matter, so long as you begin by looking at them individually. If you find statement 1 confusing, you can save time by skipping to statement 2 and seeing whether it can help you eliminate incorrect answer choices.

Be on the lookout for statements that tell you the same thing in different words. When the 2 statements convey the same exact information, you will know, through process of elimination, that the correct answer choice is either D or E. A favorite ploy of CAT testers is to mix ratios and percentages. Here is an example where Statement 2 simply states backwards the exact same information provided by Statement 1.

1.x is 50% of y

2.the ratio of y:x is 2:1

Make real-world assumptions where necessary. You must assume that, in certain abstract questions such as "What is the value of x?", that x might be a fraction and/or a negative number.

Practice, practice, practice. The more time you spend practicing data sufficiency questions, the better able you will be to internalize the tips and strategies given above. You will also become very comfortable with the type of questions from this portion of the test, and will quickly realize if there are any math areas, such as geometry or algebra where you need to brush up your skills. When it comes time to sit for the CAT, you will want to know key math

formulas and data relationships off the top of your head How to solve Parajumbles in Verbal Section?

eLitmus Guru

01:46

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EnglishParajumbles

Para jumbles are jumbled sentences. Basically, you are given a paragraph, but the sentences are not in the right order. It’s up to you to untie this knot and rearrange the sentences so that they logically make sense. Normally instructions for this type of questions will read "Choose the most logical order of sentences from among the given choices to construct a coherent paragraph". Given below would be 4 or 5 perplexing sentences which he would need to sort and arrange like a jigsaw puzzle.

Establish Link Between Two Sentences and Then Examine The Options

Suppose you establish the link 'BA'. The given options are:

(a) DABC

(b) ACDB

(c) CBAD

(d) DBAC.

Now you are left with option (c) and (d) to examine. You read the sentences in the order given by these two options and use your methods again to determine which one is correct. Is establishing links between two sentences easy?

Not ALWAYS!!! However, easy or not, you can certainly establish links between two or more sentences with the help of some friends found in the sentences. These friends are:

TRANSITION WORDS

Transition words make the shift from one idea to another very smooth. They organize and connect the sentences logically. Observing the transition words found in a sentence can often give you a clue about the sentence that will come before/after that particular sentence. Given below are some commonly used transition words:

also, again, as well as, besides, furthermore, in addition, likewise, moreover, similarly, consequently, hence, otherwise, subsequently, therefore, thus, as a rule, generally, for instance, for example, for one thing, above all, aside from, barring, besides, in other words, in short, instead, likewise, on one hand, on the other hand, rather, similarly, yet, but, however, still, nevertheless, first of all, to begin with, at the same time, for now, for the time

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being, in time, later on, meanwhile, next, then, soon, the meantime, later, while, earlier, simultaneously, afterward, in conclusion, with this in mind, after all, all in all to sum-up.

Transition Words: Example from ELITMUS

So how does knowledge of transition words helps us in parajumbles? Try out this ELITMUS question:

A.But in the industrial era destroying the enemy's productive capacity means bombing the factories which are loelitmused in the cities.

B.So in the agrarian era, if you need to destroy the enemy's productive capacity, what you want to do is bum his fields, or if you're really vicious, salt them.

C.Now in the information era, destroying the enemy's productive capacity means destroying the information infrastructure.

D.How do you do battle with your enemy?

E.The idea is to destroy the enemy's productive capacity, and depending upon the economic foundation, that productive capacity is different in each case F. With regard to defence, the purpose of the military is to defend the nation and be prepared to do battle with its enemy.

1. FDEBAC

2. FCABED

3. DEBACF

4. DFEBAC

Answer:

Look at the transition word "but" in the first sentence. It signifies that the sentence is expressing an idea contrary to an idea expressed in some previous sentence. Now we need to find that previous sentence. If we further look at the beginning of the first sentence, it says "but in the industrial era..." which suggests that the contrariness is with respect to eras. Looking further, we see that sentence B and C are also starting with statement about eras. But the transition word at the start of C is "now" which expresses present era and hence it cannot chronologically come before any other past era. That is, if information era is the present era, talk about any other era will come before this. So sentence B is the correct sentence to come before the first sentence.

Likewise, sentence C is the correct sentence to come after the first sentence (sentence C is continuing the idea). Therefore, we have the link BAC.

We see that option 1, 3 and 4 all have the link BAC. Furthermore, all the three options have the link EBAC. Therefore, we only need to arrange D and F. The sentence F states that "The purpose is...to battle with the enemy" and D questions "how do you battle with the enemy?" Therefore, D will come after F.

Hence FDEBAC is the correct arrangement.

PERSONAL PRONOUNS

Personal pronouns are he, she, it, him, her, they, you, your etc. Remember that personal pronouns always refer to a person, place or thing etc. Therefore, if a sentence contains a personal pronoun without mentioning the person, place or object it is referring to, the person, place or object must have come in the previous sentence. Often, this is a good lead to identify a link.

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Personal Pronouns: Example from ELITMUS:

A.Although there are large regional variations, it is not infrequent to find a large number of people sitting here and there and doing nothing.

B.Once in office, they receive friends and relatives who feel free to call any time without prior appointment.

C.While working, one is struck by the slow and clumsy actions and reactions, indifferent attitudes, procedure rather than outcome orientation, and the lack of consideration for others.

D.Even those who are employed often come late to the office and leave early unless they are forced to be punctual.

E.Work is not intrinsically valued in India.

F.Quite often people visit ailing friends and relatives or go out of their way to help them in their personal matters even during office hours.

1. ECADBF

2. EADCFB

3. EADBFC

4. ABFCBE

Answer:

Look at the personal pronoun "they" in sentence B: Once in office, they receive friends and relatives who feel free to call any time without prior appointment. This they must be referring to some people. The reference to some people only comes in sentences A, D, and F. Therefore, one of the sentences will come before sentence B. Let's see the link AB, DB,

and FB;

Link AB- Although there are large regional variations, it is not infrequent to find a large number of people sitting here and there and doing nothing. Once in office, they receive friends and relatives who feel free to call any time without prior appointment.

Link DB- Even those who are employed often come late to the office and leave early unless they are forced to be punctual. Once in office, they receive friends and relatives who feel free to call any time without prior appointment.

Link FB- Quite often people visit ailing friends and relatives or go out of their way to help them in their personal matters even during office hours. Once in office, they receive friends and relatives who feel free to call any time without prior appointment.

Which of these links makes sense? Only link DB seems coherent. Now, we examine the options with link DB. We see that options 1 and 3 have link DB in them. Also, both the options have link ADBF. Therefore, ADBF is a link. Now we only need to place sentences E and C. We can do that by reading the sentences in the order given in options 1 and 3.

Option 1: Link ECADBF- Work is not intrinsically valued in India. While working, one is struck by the slow and clumsy actions and reactions, indifferent attitudes, procedure rather than outcome orientation, and the lack of consideration for others. Although there are large regional variations, it is not infrequent to find a large number of people sitting here and there and doing nothing. Even those who are employed often come late to the office and leave early unless they are forced to be punctual. Once in office, they receive friends and relatives who feel free to call any time without prior appointment. Quite often people visit ailing

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friends and relatives or go out of their way to help them in their personal matters even during office hours.

Option 3: Link EADBFC- Work is not intrinsically valued in India. Although there are large regional variations, it is not infrequent to find a large number of people sitting here and there and doing nothing. Even those who are employed often come late to the office and leave early unless they are forced to be punctual. Once in office, they receive friends and relatives who feel free to call any time without prior appointment. Quite often people visit ailing friends and relatives or go out of their way to help them in their personal matters even during office hours. While working, one is struck by the slow and clumsy actions and reactions, indifferent attitudes, procedure rather than outcome orientation, and the lack of consideration for others.

Both the options seem plausible. We have to determine which one of the links EC and EA is better. Here is the thumb rule when trying to determine plausibility of a link

THE FLOW OF AUTHORS IDEA SHOULD BE COMPLETELY LOGICAL; THE AUTHOR DOES NOT JUMP FROM ONE IDEA TO OTHER SUDDENLY.

In link EC, sentence E is talking about work not being valued whereas sentence C is talking about people being clumsy, indifferent, inconsiderate etc. Sentence C is NOT talking about value of work. It is talking about people's behavior. Therefore, EC cannot be a logical flow.

In link EA, sentence E is talking about work not being valued and sentence A is talking about people sitting idle. This certainly says that people do not value work. Therefore, EA is the correct link. Hence, option 3 is correct.

Personal Pronouns: Example from Elitmus

Here is another elitmus question that seems tough but can be solved in a matter of seconds. See if you can do it:

A.Passivity is not, of course, universal.

B.In areas where there are no lords or laws, or in frontier zones where all men go armed, the attitude of the peasantry may well be different.

C.So indeed it may be on the fringe of the un-submissive.

D.However, for most of the soil-bound peasants the problem is not whether to be normally passive or active, but when to pass from one state to another.

E.This depends on an assessment of the political situation.

1. EDAC

2. CDABE

3. EDBAC

4. ABCDE

Answer:

It cannot get easier than this. Look at the personal pronoun "it" in sentence C: So

indeed it may be on the fringe of the un-submissive. What is "it" here referring to? And it says that "it may be... un-submissive." What can be un-submissive? It cannot be "political situation" (sentence E), "passivity" (sentence A), or "problem" (sentence D). Only "attitude" (sentence B) can be un-submissive. Therefore, BC is a link.

The link BC is only present in option 4 and we need not look any further.

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DEMONSTRATIVE PRONOUNS

The demonstrative pronouns are "this," "that," "these," and "those." "This" and "that" are used to refer to singular nouns or noun phrases and "these" and "those" are used to refer to plural nouns and noun phrases. Whenever a sentence contains a demonstrative pronoun without mentioning the noun or the noun phrase, it means that the previous sentence must be mentioning that noun or noun phrase. Finding that noun or noun phrase helps us connect two sentences.

Demonstrative Pronouns: Example from ELITMUS

A.Michael Hofman, a poet and translator, accepts this sorry fact without approval or complaint.

B.But thanklessness and impossibility do not daunt him.

C.He acknowledges too "in fact he returns to the point often " that best translators of poetry always fail at some level.

D.Hofman feels passionately about his work, and this is clear from his writings.

E.In terms of the gap between worth and rewards, translators come somewhere near nurses and street-cleaners.

1. EACDB

2. ADEBC

3. EACBD

4. DCEAB

Answer:

Again an easy one. Notice the demonstrative pronoun "this" in sentence A: Michael Hofman, a poet and translator, accepts this sorry fact without approval or complaint. Also note that sentence A is introducing Michael Hofman (Michael Hofman, a poet and translator,...) and will thereby come before every sentence containing the personal pronoun he or him. So which sorry fact is sentence A referring to? It can only be the fact found in sentence E. Also, other sentences contain "he" or "him".

Therefore, EA is a link. Link EA is contained in option 1, 3 and 4. But in 4, sentence D is coming before sentence A, and this cannot happen because sentence A should be before any other sentence referring to Hofman as sentence A is introducing Hofman. Therefore, we are left with options 1 and 3. The difference between options 1 and 3 is the order of

sentence D and B. Let's examine the link DB:

Option 1: Link DB- Hofman feels passionately about his work, and this is clear from his writings.

But thanklessness and impossibility do not daunt him.

Does this sound like a plausible flow? Certainly NOT. Therefore, link DB is incorrect and the correct answer is option 3.

COMBINING IT ALL WITH LOGIC

Sometimes using logic to decide the order of sentences can yield high dividends. In the previous example, we had used logic to determine that sentence A would come before any other sentence referring Hofman. Keep your eyes open for clues such as these. Here's is the last ELITMUS question that I cracked, using logic; see if you can do the same:

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Example from ELITMUS

A.The situations in which violence occurs and the nature of that violence tends to be clearly defined at least in theory, as in the proverbial Irishman's question: "Is this a private fight or can anyone join in?"

B.So the actual risk to outsiders, though no doubt higher than our societies, is calculable.

C.Probably the only uncontrolled applielitmusions of force are those of social superiors to social inferiors and even here there are probably some rules.

D.However binding the obligation to kill, members of feuding families engaged in mutual massacre will be genuinely appalled if by some mischance a bystander or outsider is killed.

1. DABC

2. ACDB

3. CBAD

4. DBAC

Answer:

The clue to this question came to me from the word "calculable" in sentence B: So the actual risk to outsiders, though no doubt higher than our societies, is calculable. How does something become "calculable"? Then I noticed sentence A and the phrase "clearly defined in theory..." Something becomes calculable when it is clearly defined in theory. No other sentence could give answers to "calculable". Therefore, the link AB was clearly marked. The link AB was present in option 1 only. Easy, no?

Notice that I have been going to the option again and again to eliminate one or two options. Form this habit sedulously. It will pay you rich dividends.

Acronym Approach

Full form vs. short form: In PJ we encounter full and short names sometimes acronyms of some term or institution.

Ex-World Trade Organization – WTO

Dr. Manmohan Singh - Dr. Singh

Karl Marx – Marx

President George W. Bush - President bush or the president

The rule is that if both full form as well as short form is present in different sentences, then the sentence containing full form will come before the sentence containing short form.

Example:

1.If you are used to having your stimulation come in from outside, your mind never develops its own habits of thinking and reflecting

2.Marx thought that religion was the opiate, because it soothed people's pain and suffering and prevented them from rising in rebellion

3.If Karl Marx was alive today, he would say that television is the opiate of the people.

4.Television and similar entertainments are even more of an opiate because of their addictive tendencies.

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A. 2134

B. 1423 C. 2431

D. 3241

Answer:

Sentence 2 has Marx (short Form) and sentence 3 has Karl Marx (Full form). So 3 will come before 2. Now look at the options. In A, B and C, 2 is placed before C3-hence rejected. D is the right answer.

Time Sequence Approach (TSA)

Either dates or time sequence indielitmusing words:

Be aware of the time indielitmusion either by giving years - or by using time indielitmusing words. Arrange the sentences using their proper time sequence. Here are a few time sequence indielitmusing words -Before after later when

Example 1:

1.Then two astronomers—the German, Johannes Kepler, and the Italian, Galileo Galilei- started publicly to support the Copernican theory, despite the fact that the orbits it predicted did not quite match the ones observed.

2.His idea was that the sun was stationary at the centre and that the earth and the planets move in circular orbits around the sun.

3.A simple model was proposed in 1514 by a Polish priest, Nicholas Copernicus.

4.Nearly a century passed before this idea was taken seriously.

A. 3421

B. 3241

C. 2314

D. 3142

Solution:

Answer is 3241

The 3rd sentence talks about the time event and other time vents follow it in a chronological order. So option A is Best choice

Example 2:

1.By the time he got to Linjeflug four years later, he had learned many lessons; in fact, he began his second stint as top dog by calling the entire company together in a hanger and asking for help, a far cry from his barking out commands just 48months back.

2.At SAS, he arrived at a time crisis.

3.This book is chock-a-block full of intrusive stories and practical advice, describing Carton's activities at Vingresor (where he assumed his first presidency at age 32), Linjeflug, and SAS in particular.

4.He began at Vingresor as an order giver, not a listener - neither to his people nor to his customers and made every mistake in the book.

A. 2143

B. 2134

C. 3214

D. 3412

Solution:

4 will come before 1 and 2. Hence 3412.

Alternate: In 3, order is given - Vingressor, Linjeflug, SAS - arrange according to this.

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Alternate: 3 will be the opening sentence because only 3 has noun (NAME) for he.

Hypothesis or Theory Approach

If any sentence is working as an example - place it after the sentence for which it is working as an example, not necessarily just after – because one has to explain the idea, it is hypothesis/ theory. It should not be before the idea that it explains.

Example:

1.The potential exchanges between the officials of IBBF and the Maharashtra Body-Building Association has all the trappings of a drama we are accustomed to.

2.In the case of sports persons, there is room for some sympathy, but the apathy of the administrators, which has even led to sanctions from international bodies, is unpardonable.

3.A case in the point is the hefty penalty of US $10,000 slapped on the Indian Body-Building Federation for not fulfilling its commitment for holding the Asian Championships in Mumbai in October.

4.It is a matter of deep regret and concern that the sports administrators often cause more harm to the image of the country than sportsmen and sportswomen do through their dismal performances.

A. CABD

B. DBCA

C. DABC

D. CDBA

Solution:

Here sentence 3 is an example of sentence 4. So it will come after 4. So now only option B and C remain. Now go by ACRONYM Method discussed earlier. (IBBF in 1 and Indian Body-Building Federation in 3) 3 will come before 1.

So only option B remains, which is the right option.

Articles Approach

Articles can be divided into two elitmusegories –

1.Definite (the) and

2.Indefinite (a and an).

When the author uses 'a / an' - he wants to make a general statement - wants to introduce the noun followed by a/an for the first time but when he uses 'the' he wants to refer back to some previously discussed noun. It means having 'the' is very unlikely in the opening sentence. If 'a/an' and 'the' both are used for the same noun then the sentence containing 'the' will come after the sentence containing a/an.

Noun, Pronoun and Adjective (NPA) Approach

1. Pronoun – Whenever pronoun comes – it will come in the immediate sentence containing the respective noun.

i. e. A sequence can be like this Noun

Pronoun

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Pronoun

Pronoun or like

Noun Pronoun

.............. no pronoun Noun

Pronoun

i.e. the pronoun sequence will continue till it is halted by a break (i.e. a sentence containing no pronoun) then if necessary it will start with the noun again. We can't write pronoun after a break. It is not a correct form of writing.

Opening – Closing sentence (OCS) Approach

Supported or free, general or need previous explanation

OCS is particularly useful in 4 sentence parajumble (where opening sentence is not given) Let's see the characteristics of an opening sentence

It will introduce an idea in the first hand.

In most of the cases it will use indefinite article a/an. i.e. if both definite and indefinite articles are used for the same noun then the sentence containing noun with indefinite article a/an will come first (may be opening sentence).

The sentence can stand alone

It will not have pronouns (exception: if respective noun is not mentioned anywhere). It will not have contrast words/or words indielitmusing continuation/or words like - hence , therefore, so- etc.

Key Words Approach - KWA

Some words will be repeated in two consecutive sentences.

In most of the cases we repeat some important words of one sentence in the sentence that follows.

Hence if you are seeing any important (not like he, she, that, is, are type) then chances are that these two sentences will be consecutive. Remember it gives you an idea that which sentences can be consecutive for example 23 or 32 but for exact order you have to look for some other clue or meaning.

Structure Approach - SA

Link sentences logically i.e.

Link the sentences logically i.e. see what is the role played by a specific sentence Premise

Conclusion Support Example Continuation

and then search for some proper sentence that should come before or the one which will follow.

Indielitmusing Words Approach - IWA

Take care of words that indielitmuse something helpful to decide sequence.

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Some words indielitmuses some specific nature of sentences that will come before or that will

follow.

Look for the words like But

So Therefore And However

think what they are indielitmusing.

Signal/Indielitmusing Word List

Writers use transitions to link their ideas logically. These transitions or signal words are clues that can help you figure out what the sentence actually means and its sequence. Para-jumble sentences often contain several signal words, combining them in complex ways.

NOTE: The list given below is not a comprehensive list. You must collect the signal words while reading.

Cause and Effect Signals

Look for words or phrases explicitly indielitmusing that one thing causes another or logically determines another.

Accordingly in order to because so...that consequently therefore given

thus hence

when...then if...then

Support Signal Words

Look for the words or phrases supporting a given sentences. These words containing sentences will not be the opening sentence. These sentences will follow immediately the sentence supported.

Furthermore

Additionally Also

And

Too as well besides

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indeed likewise moreover

Contrast Signals (Explicit)

Precisely and clearly expressed or readily observable; leaving nothing to implielitmusion.

Look for function words or phrases (conjunctions, sentence adverbs, etc.) that explicitly indielitmuse a contrast between one idea and another, setting up a reversal of a thought. Albeit

Nevertheless Although Nonetheless But Notwithstanding Despite

on the contrary even though

on the other hand however

rather than In contrast Still

In spite of While Instead of yet

Contrast Signals (Implicit)

Implied though not directly expressed; inherent in the nature of something

Look out for words which indielitmuse contrast or turn a situation or something unexpected possibly even unwanted, has occurred.

Anomaly

Anomalous

Anomalously Illogic Illogical Illogically Incongruity Incongruous Incongruously Irony

Ironic Ironically Paradox

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Paradoxical

Paradoxically

Surprise

Surprising

Surprisingly

Unexpected

Unexpectedly

Time sequence indielitmusing words

Before

After

Later

When

All the Rules in Brief

The approaches for PARAJUMBLE

Acronym Approach – full form vs. short form

Time Sequence Approach – TSA – either dates or time sequence indielitmusing words

Examples Approach – EA – after an hypothesis or theory

Articles – definite and indefinite

Noun, Pronoun, and Demonstrative Adjective – NPDA Approach – limited to not just noun

Opening – Closing Sentence Approach – OCSA – supported or free, general or need previous explanation

Key Words Approach – KWA – words repeated in two consecutive sentences

Structure Approach – SA – link sentences logically.

Indielitmusing Words Approach – IWA – take care of words that indielitmuse something helpful to decide the sequence.

How to solve Reading Comprehension part in elitmus pH Test eLitmus Guru

06:48

EnglishReading Comprehension

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The purpose of reading is to connect the ideas on the page to what you already know. If you don't know anything about a subject, then pouring words of text into your mind is like pouring water into your hand. You don't retain much.

For example, try reading these numbers:

7516324 This is hard to read and remember.

751-6324 This is easier because of chunking.

123-4567 This is easy to read because of prior knowledge and structure.

Similarly, if you like sports, then reading the sports page is easy. You have a framework in your mind for reading, understanding and storing information.

Also Read: How to solve Logical reasoning part in Elitmus?

Improving Comprehension.

Reading comprehension requires motivation, mental frameworks for holding ideas, concentration and good study techniques. Here are some suggestions.

Develop a broad background.

Broaden your background knowledge by reading newspapers, magazines and books. Become interested in world events.

Know the structure of paragraphs.

Good writers construct paragraphs that have a beginning, middle and end. Often, the first sentence will give an overview that helps provide a framework for adding details. Also, look for transitional words, phrases or paragraphs that change the topic.

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Identify the type of reasoning.

Does the author use cause and effect reasoning, hypothesis, model building, induction or deduction, systems thinking.

Anticipate and predict.

Really smart readers try to anticipate the author and predict future ideas and questions. If you're right, this reinforces your understanding. If you're wrong, you make adjustments quicker.

Look for the method of organization.

Is the material organized chronologically, serially, logically, functionally, spatially or

hierarchical? See section 10 for more examples on organization.

Also Read: How to solve Data Interpretation part in Elitmus?

Create motivation and interest.

Preview material, ask questions, discuss ideas with classmates. The stronger your interest, the greater your comprehension.

Pay attention to supporting cues.

Study pictures, graphs and headings. Read the first and last paragraph in a chapter, or the first sentence in each section.

Highlight, summarize and review.

Just reading a book once is not enough. To develop a deeper understanding, you have to highlight, summarize and review important ideas.

Build a good vocabulary.

For most educated people, this is a lifetime project. The best way to improve your vocabulary is to use a dictionary regularly. You might carry around a pocket dictionary and use it to look up new words. Or, you can keep a list of words to look up at the end of the day. Concentrate on roots, prefixes and endings. Going through word-of-the-day of elitmusguru will definitely help you in this regard.

Use a systematic reading technique like SQR3.

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Develop a systematic reading style, like the SQR3 method and make adjustments to it, depending on priorities and purpose. The SQR3 steps include Survey, Question, Read, Recite and Review.

Monitor effectiveness.

Good readers monitor their attention, concentration and effectiveness. They quickly recognize if they've missed an idea and backup to reread it.

Should You Vocalize Words? Yes, although it is faster to form words in your mind rather than on your lips or throat. Eye motion is also important. Frequent backtracking slows you down considerably

Rules for deriving conclution from two given premises

eLitmus Guru

00:27 EnglishPreposition

In our previous post we discussed about the concept of proposition and logical deduction techniques. Here we discuss about the important rules for deriving conclusion from two given premises.

RULES FOR DERIVING CONCLUSION FROM TWO GIVEN PREMISES:

1. The conclusion does not contain the middle term.

Example

Statements:

1.All men are girls.

2.Some girls are students.

Conclusions:

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1.All girls are men.

2.Some girls are not students.

Since both the conclusions 1 and 2 contain the middle term 'girls', so neither of them can follow

2. No term can be distributed in the conclusion unless it is distributed in the premises.

Example

Statements:

1.Some dogs are goats.

2.All goats are cows.

Conclusions:

1.All cows are goats.

2.Some dogs are cows.

Statement 1 is an I-type proposition which distributes neither the subject nor the predicate. Statement 2 is an A type proposition which distributes the subject i.e. 'goats' only. Conclusion 1 is an A-type proposition which distributes the subject 'cow' only since the term 'cows' is distributed in conclusion 1 without being distributed in the premises, so conclusion 1 cannot follow.

3. The middle term (M) should he distribute at least once in the premises. Otherwise, the conclusion cannot follow.

For the middle term to be distributed in a premise

(i)M must be the subject if premise is an A proposition.

(ii)M must be subject or predicate if premise is an E proposition.

(iii)M must be predicate if premise is an O proposition.

Note that in an I proposition, which distributes neither the subject nor the predicate, the middle term cannot be distributed.

Example

Statements:

1.All fans are watches.

2.Some watches are black.

Conclusions:

1. All watches are fans.

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2. Some fans are black.

In the premises, the middle term is 'watches'. Clearly, it is not distributed in the first premise which is an A proposition as it does not form its subject. Also, it is not distributed in the second premise which is an I proposition. Since the middle term is not distributed even once in the premises, so no conclusion follows.

4. No conclusion follows

(a) if both the premises are particular

Example

Statements:

1.Some books are pens.

2.Some pens are erasers.

Conclusions:

1.All books are erasers.

2.Some erasers are books.

Since both the premises are particular, so no definite conclusion follows.

(b) If both the premises are negative.

Example

Statements:

1.No flower is mango.

2.No mango is cherry.

Conclusions:

1.No flower is cherry.

2.Some cherries are mangoes. Since both the premises are negative, neither conclusion follows.

(c) If the major premise is particular and the minor premise is negative.

Example

Statements:

1. Some dogs are bulls.

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2. No tigers are dogs.

Conclusions:

1.No dogs are tigers.

2.Some bulls are tigers.

Here, the first premise containing the middle term 'dogs' as the subject is the major premise and the second premise containing the middle term 'dogs' as the predicate is the minor premise. Since the major premise is particular and the minor premise is negative, so no conclusion follows.

5. If the middle term is distributed twice, the conclusion cannot be universal.

Example

Statements:

1.All fans are chairs.

2.No tables are fans.

Conclusions:

1.No tables are chairs.

2.Some tables are chairs.

Here, the first premise is an A proposition and so, the middle term 'fans' forming the subject is distributed. The second premise is an E proposition and so, the middle term 'fans' forming the predicate is distributed. Since the middle term is distributed twice, so the conclusion cannot be universal.

6. If one premise is negative, the conclusion must be negative.

Example

Statements:

1.All grasses are trees.

2.No tree is shrub.

Conclusions:

1.No grasses are shrubs.

2.Some shrubs are grasses.

Since one premise is negative, the conclusion must be negative. So, conclusion 2 cannot follow.

7. If one premise is particular, the conclusion must be particular.

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Example

Statements:

1.Some boys are thieves.

2.All thieves are dacoits.

Conclusions:

1.Some boys are dacoits.

2.All dacoits are boys.

Since one premise is particular, the conclusion must be particular. So, conclusion 2 cannot follow.

8. If both the premises are affirmative, the conclusion must be affirmative.

Example

Statements:

1.All women are mothers.

2.All mothers are sisters.

Conclusions:

1.All women are sisters.

2.Some women are not sisters.

Since both the premises are affirmative, the conclusion must be affirmative. So, conclusion 2 cannot follow.

9. If both the premises are universal, the conclusion must be universal.

Complementary pair:

A pair of contradictory statements i.e. a pair of statements such that if one is true, the other is false and when no definite conclusion can be drawn, either of them is bound to follow, is called a complementary pair. E and I-type propositions together form a complementary pair and usually either of them follows, in a case where we cannot arrive at a definite conclusion, using the rules of syllogism.

What is Proposition and Logical Deduction in elitmus?

eLitmus Guru

23:36 EnglishPreposition

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Proposition is one of the important part in Elitmus pH test, in verbal section contains more than three questions are asked from proposition part. Proposition is easiest one in verbal section. In this post you find more details about Proposition and logical deduction questions and important rules for handling those questions.

Proposition

In Logic, any categorical statement is termed as the Proposition.

A Proposition is a statement that asserts that either a part of, or the whole of, one set of objects - the set identified by the subject term in the sentence expressing that statement - either is included in, or is excluded from, another set - the set identified by the predicate term in that sentence.

The standard form of a proposition is:

Quantifier + Subject + Copula + Predicate

Thus, the proposition consists of four parts:

1)Quantifier: The words 'all', 'no' and 'some' are called quantifiers because they specify a quantity 'All' and 'no' are universal quantifiers because they refer to every object in a certain set, while the quantifier 'some' is a particular quantifier because it refers to at least one existing object in a certain set.

2)Subject (denoted by 'S'): The subject is that about which something is said.

3)Predicate (denoted by 'P'): The predicate is the part of the proposition denoting that which is affirmed or denied about the subject.

4)Copula: The copula is that part of the proposition which denotes the relation between the subject and the predicate.

Four-Fold Classification of Propositions:

A proposition is said to have a universal quantity if it begins with a universal quantifier and a particular quantity if it begins with a particular quantifier. Besides, propositions which assert

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something about the inclusion of the whole or a part of one set in the other are said to have affirmative quality, while those which deny the inclusion of the whole or a part of one set in the other are said to have a negative quality. Also, a term is distributed in a proposition if it refers to all members of the set of objects denoted by that term. Otherwise, it is said to be undistributed. Based on the above facts, propositions can be classified into four types:

1)Universal Affirmative Proposition (denoted by A): It distributes only the subject i.e. the predicate is not interchangeable with the subject while maintaining the validity of the proposition.

2)Universal Negative Proposition (denoted by E): It distributes both the subject and the predicate i.e. an entire class of predicate term is denied to the entire class of the subject term, as in the proposition.

3)Particular Affirmative Proposition (denoted by I): It distributes neither the subject nor the predicate.

4) Particular Negative Proposition (denoted by O): It distributes only the predicate. e.g., Someanimals are not wild. Here, the subject term 'animals' is used only for a part of its class and hence is undistributed while the predicate term 'wild' is denied in entirety to the subject term and hence is distributed. These facts can be summarized as follows:

 

Statement Form

 

Quantity

 

Quality

 

Distributed

 

 

 

 

 

(A): All S is P.

Universal

Affirmative

S only

 

(E): No S is P.

Universal

Negative

Both S and P

 

(I): Some S is P.

Particular

Affirmative

Neither S nor P

 

(O): Some S is not P Particular

Negative

P only

 

 

 

 

 

 

 

 

Logical Deduction:

The phenomenon of deriving a conclusion from a single proposition or a set of given propositions, is known as logical deduction. The given propositions are also referred to as the premises.

Two Inferential Processes of Deduction:

I. Immediate Deductive Inference:

Here, conclusion is deduced from one of the given propositions, by any of the three ways - conversion, obversion and contraposition.

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1) Conversion: The Conversion proceeds with interchanging the subject term and the predicate term i.e. the subject term of the premise becomes the predicate term of the conclusion and the predicate term of the premise becomes the subject of the conclusion.

The given proposition is called converted, whereas the conclusion drawn from it is called its converse.

Table of Valid Conversions

 

Converted

 

Converse

 

 

 

A: All S is P

I: Some P is S

 

Ex. All pins are tops.

Some tops are pins.

 

E: No S is P.

E: No P is S.

 

Ex. No fish is whale.

No whale is fish.

 

I: Some S is P.

I: Some P is S.

 

Ex. Some boys are poets.

Some poets are boys.

 

O: Some S is not P.

No valid conversion

 

 

 

 

Note that in a conversion, the quality remains the same and the quantity may change.

2) Obversion: In obversion, we change the quality of the proposition and replace the predicate term by its complement.

Table of Valid Obversions

 

 

 

 

 

 

Obverted

 

Obverse

 

 

A: All birds are mammals.

E: No birds are non-mammals.

 

E: No poets are singers.

A: All poets are non-singers.

 

I: Some nurses are doctors.

O: Some nurses are not non-doctors.

O: some politicians are not statesmen. I: Some politicians are non-statesmen

Contraposition: To obtain the contra positive of a statement, we first replace the subject and predicate terms in the proposition and then exchange both these terms with their complements.

Table of Valid Contrapositions

 

 

Proposition

 

Contra positive

 

 

 

 

A: All birds are mammals.

A: All non-mammals are non-birds.

 

I: Some birds are mammals. I: Some non-mammals are non-birds.

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Note: The valid converse, obverse or contra positive of a given proposition always logically follows from the proposition.

II. Mediate Deductive Inference (SYLLOGISM): First introduced by Aristotle, a Syllogism is a deductive argument in which conclusion has to be drawn from two propositions referred to as the premises.

Example:

1.All lotus are flowers.

2.All flowers are beautiful.

3.All lotus are beautiful.

Clearly, the propositions 1 and 2 are the premises and the proposition 3, which follows from the first two propositions, is called the conclusion.

Term: In Logic, a term is a word or a combination of words, which by itself can be used as a subject or predicate of a proposition.

Syllogism is concerned with three terms:

1.Major Term: It is the predicate of the conclusion and is denoted by P (first letter of 'Predicate').

2.Minor Term: It is the subject of the conclusion and is denoted by S (first letter of 'Subject').

3.Middle Term: It is the term common to both the premises and is denoted by M (first letter of 'Middle').

Tips to solve word fitting questions in Verbal section eLitmus Guru

09:10

EnglishWord Fitting

Word fitting is one of the part of verbal section. In Elitmus paper nearly three to five questions are from word fitting .Here you will find some tips and examples for solving those questions.

Example: Crestfallen by having done poorly on the GRE, Susan began to question her

abilities. Her self-confidence was ..........

A. appeased

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B.destroyed

C.placated

D.elevated

E.sustained

If somebody is crestfallen (despairing) and has begun to question herself, then her self- confidence would be destroyed. Hence, the answer is (B).

Also Read: How to solve Logical reasoning part in Elitmus?

Transitional Words:

Be alert to transitional words. Transitional words tell you what is coming up. They indicate that the author is now going to draw a contrast with something stated previously, or support something stated previously.

i. Contrast Indicators:

To contrast two things is to point out how they differ. In this type of sentence completion problem, we look for a word that has the opposite meaning (an antonym) of some key word or phrase in the sentence.

Following are some of the most common contrast indicators:

But

Yet

Despite

Although

However

Nevertheless

Also Read: How to solve Probability in Aptitude Section?

Example: Although the warring parties had settled a number of disputes, past experience made them .......... to express optimism that the talks would be a success.

A.rash

B.ambivalent

C.scornful

D.overjoyed

E.reticent

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"Although" sets up a contrast between what has occurred--success on some issues--and what can be expected to occur--success for the whole talks. Hence, the parties are reluctant to express optimism. The common word "reluctant" is not offered as an answer-choice, but a synonym--reticent--is. The answer is (E).

ii. Support Indicators:

Supporting words support or further explain what has already been said. These words often introduce synonyms for words elsewhere in the sentence.

Following are some common supporting words:

And

Also

Furthermore

Likewise

In Addition

For

Also Read: How to solve Parajumbles in Verbal Section?

Example: Davis is an opprobrious and ..........

speaker, equally caustic toward friend or foe--a

true curmudgeon.

 

A. lofty

B. vituperative

C. unstinting

D. retiring

E. laudatory

"And" in the sentence indicates that the missing adjective is similar in meaning to "opprobrious," which is very negative. Now, vituperative--the only negative word--means "abusive." Hence, the answer is (B).

iii. Cause And Effect Indicators:

These words indicate that one thing causes another to occur.

Some of the most common cause and effect indicators are

Because

For

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Thus

Hence

Therefore

If , Then .

Example: Because the House has the votes to override a presidential veto, the President has

no choice but to ..........

A.object

B.abdicate

C.abstain

D.capitulate

E.compromise

Since the House has the votes to pass the bill or motion, the President would be wise to compromise and make the best of the situation. The answer is (E).

Also Read:How to solve Data Sufficiency questions in elitmus pH Test?

Apposition:

This rather advanced grammatical structure is very common on the GRE. (Don't confuse "apposition" with "opposition": they have opposite meanings.)

Words or phrases in apposition are placed next to each other, and the second word or phrase defines, clarifies, or gives evidence to the first word or phrase.

The second word or phrase will be set off from the first by a comma, semicolon, hyphen, or parentheses.

Note: If a comma is not followed by a linking word--such as and, for, yet--then the following phrase is probably appositional.

Identifying an appositional structure, can greatly simplify a sentence completion problem since the appositional word, phrase, or clause will define the missing word.

Example: His novels are .......... ; he uses a long circumlocution when a direct coupling of a simple subject and verb would be best.

A.prolix

B.pedestrian

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C.succinct

D.vapid

E.risque

The sentence has no linking words (such as because, although, etc.). Hence, the phrase following the semicolon is in apposition to the missing word--it defines or further clarifies the missing word. Now, writing filled with circumlocutions is aptly described as prolix. The answer is (A).

Also Read:How to solve Logical Reasoning part in elitmus pH test?

Punctuation:

Whenever the punctuation "," (comma) appears, followed by a blank in between two sentences, then it means that the synonym of the phrase/word before "," is the meaning of the blank. In simple words, when you find ',' followed by a blank then find the synonym of the word before ',' and check the options to match the synonym of the word.

In the same way, when you find ":"( colon) or ";"( semi-colon) in the sentence, they will indicate that the idea coming up is merely an explanation of the earlier idea. So, simply find the synonym of the word/phrase before the punctuation and fill in the blank with the synonym from the options given.

Positive/Negative Flow:

When you read the sentence, you have to look out for adjectives/adverbs which tell you the idea of the sentence. After finding these adjectives/adverbs, you need to find out if the idea of the sentence is positive/negative. All the negative ideas may be a "bad word/bad phrase" or any term which has no/none/not... in it.

You need to just go on marking the words with +/- and keep on doing till the end of the sentence. Then you need to use the punctuations/conjunctions clue which would break the sentence into 2/3 parts. After that you need to compare the +/- signs on both sides and enter the desired sign in the blank. In simple words, if the flow of the first part of the sentence is positive and the second part is negative, then the blank must be negative to even the flow of the sentence. This would solve the sentence completion question without even understanding the question.

Example: Because he did not want to appear_______, the junior executive refused to dispute the board's decision, in spite of his belief that the decision would impair employee morale.

A.contentious

B.indecisive

C.solicitous

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D.overzealous

E.steadfast

Explanation: (C) and (E) are gone because they're positive words. .(B)doesn't work because the clue is "refused to dispute." That doesn't work with indecisive. For the same reason,(D) doesn't work either. So the best answer is option A.

Process of Elimination(POE):

You can easily eliminate all the options that are definitely wrong or are eliminated through the positive/negative flow. Suppose if you have a blank in the sentence for which the answer is positive, then you can eliminate all the options which are negative. In this way you can eliminate options and have very less options remaining. The probability of you getting right answer from 2 options is much higher than you getting right from 5 options.

Important Formula: Time and Distance,Problem on Trains,Boats & Streams eLitmus Guru

22:13 AptitudeFormula

Quantum Aptitude is the first section in pH test. It Contains 20 questions from various Aptitude topics. All the important formulas are printed in the question paper. But you need to study more topics to crack the test. In this post covers some important topics and tips to solve Aptitude question.

Important Formula:

Speed

=

Distance / Time

Time

=

Distance / speed

Distance

=

speed * time

1 km/hr

=

518ms

1 m/s

=

185Kmhr

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If the ratio of the speed of A and B is a:b,then the ratio of the time taken by them to cover the same distance is 1a:1b or b:a

Suppose a man covers a distance at x km/hr and an equal distance at y km/hr, then the AVERAGE SPEED during the whole journey is (2xy/x+y) km/hr

Out of time, speed and distance we can compute any one of the quantities when we happen to know the other two. For example, suppose we drive for 2 hours at 30 miles per hour, for a total of 60 miles.

If we know the time and the speed, we can find the distance: 2 hour * 30 mileshour=60 miles

If we know the time and the distance, we can find the speed: 60 miles2 hours=30mileshour

Distance is directly proportional to Velocity when time is constant:

Train Problems:

The basic equation in train problem is the same

Speed=Distance/Time

The following things need to be kept in mind while solving the train related problems.

When the train is crossing a moving object, the speed has to be taken as the relative speed of the train with respect to the object.

The distance to be covered when crossing an object, whenever trains crosses an object will be equal to: Length of the train + Length of the object

Boats & Streams:

Let U= Velocity of the boat in still water

V=Velocity of the stream.

While moving in upstream, distance covered, S=(U−V)T

In case of downstream, distance covered , S=(U+V)T

Clock:

For clock problems consider the clock as a circular track of 60km.

Min. hand moves at the speed of 60km/hr (think min. hand as a point on the track) and hour hand moves at 5km/hr and second hand at the speed of 3600 km/hr.

Relative speed between HOUR hand and MINUTE hand = 55

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What is Probability and How to solve Probability in Aptitute Section

eLitmus Guru

21:13 AptitudeProbability

1. What is Probability

Probability deals with the analysis of random phenomena. It is a way of assigning every event a value between zero and one, with the requirement that the event made up of all possible results is assigned a value of one.

2. Experiment

An operation which results in some well-defined outcomes is called an experiment.

Also Read: How to solve Logical reasoning part in Elitmus?

2.1. Random Experiment

An experiment whose outcome cannot be predicted with certainty is called a random experiment. In other words, if an experiment is performed many times under similar conditions and the outcome of each time is not the same, then this experiment is called a random experiment.

Example:

A). Tossing of a fair coin

B). Throwing of an unbiased die

C). Drawing of a card from a well shuffled pack of 52 playing cards

3. Sample Space

The set of all possible outcomes of a random experiment is called the sample space for that experiment. It is usually denoted by S.

Example:

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A). When a die is thrown, any one of the numbers 1, 2, 3, 4, 5, 6 can come up. Therefore, sample space:

S = {1, 2, 3, 4, 5, 6}

B). When a coin is tossed either a head or tail will come up, then the sample space w.r.t. the tossing of the coin is:

S = {H, T}

C). When two coins are tossed, then the sample space is

3.1 Sample Point or Event Point

Each element of the sample spaces is called a sample point or an event point.

Example:

When a die is thrown, the sample space is S = {1, 2, 3, 4, 5, 6} where 1, 2, 3, 4, 5 and 6 are the sample points.

3.2 Discrete Sample Space

A sample space S is called a discrete sample if S is a finite set.

4. Event

A subset of the sample space is called an event.

Also Read: How to solve Logical reasoning part in Elitmus?

4.1. Problem of Events

Sample space S plays the same role as universal set for all problems related to the particular experiment.

(i). is also the subset of S and is an impossible Event.

(ii). S is also a subset of S which is called a sure event or a certain event.

5. Types of Events

A. Simple Event or Elementary Event

An event is called a Simple Event if it is a singleton subset of the sample space S.

Example:

A). When a coin is tossed, then the sample space is S = {H, T}

Then A = {H} occurrence of head and

B = {T} occurrence of tail are called Simple events. B). When two coins are tossed, then the sample space is S = {(H,H); (H,T); (T,H); (T,T)}

Then A = {(H,T)} is the occurrence of head on 1st and tail on 2nd is called a Simple event.

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B. Mixed Event or Compound Event or Composite Event

A subset of the sample space S which contains more than one element is called a mixed event or when two or more events occur together, their joint occurrence is called a Compound Event.

Example:

When a dice is thrown, then the sample space is S = {1, 2, 3, 4, 5, 6}

Then let A = {2, 4 6} is the event of occurrence of even and B = {1, 2, 4} is the event of occurrence of exponent of 2 are Mixed events.

Compound events are of two type:

(i). Independent Events, and (ii). Dependent Events

C. Equally likely events

Outcomes are said to be equally likely when we have no reason to believe that one is more likely to occur than the other.

Example:

When an unbiased die is thrown all the six faces 1, 2, 3, 4, 5, 6 are equally likely to come up.

D. Exhaustive Events

A set of events is said to be exhaustive if one of them must necessarily happen every time the experiments is performed.

Example:

When a die is thrown events 1, 2, 3, 4, 5, 6 form an exhaustive set of events.

Important: We can say that the total number of elementary events of a random experiment is called the exhaustive number of cases.

E. Mutually Exclusive Events

Two or more events are said to be mutually exclusive if one of them occurs, others cannot

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occur. Thus if two or more events are said to be mutually exclusive, if not two of them can

occur together.

Hence, A1,A2,A3,…,An are mutually exclusive if and only if Ai∩Aj= , for i≠j

Example:

A). When a coin is tossed the event of occurrence of a head and the event of occurrence of a tail are mutually exclusive events because we cannot have both head and tail at the same time.

B). When a die is thrown, the sample space is S = {1, 2, 3, 4, 5, 6} Let A is an event of occurrence of number greater than 4 i.e., {5, 6} B is an event of occurrence of an odd number {1, 3, 5}

C is an event of occurrence of an even number {2, 4, 6}

Here, events B and C are Mutually Exclusive but the event A and B or A and C are not Mutually Exclusive.

F. Independent Events or Mutually Independent events

Two or more event are said to be independent if occurrence or non-occurrence of any of them does not affect the probability of occurrence of or non-occurrence of their events.

Thus, two or more events are said to be independent if occurrence or non-occurrence of any of them does not influence the occurrence or non-occurrence of the other events.

Example:

Let bag contains 3 Red and 2 Black balls. Two balls are drawn one by one with replacement.

Let A is the event of occurrence of a red ball in first draw. B is the event of occurrence of a black ball in second draw.

Then probability of occurrence of B has not been affected if A occurs before B. As the ball has been replaced in the bag and once again we have to select one ball out of 5(3R + 2B) given balls for event B.

Also Read: How to solve Logical reasoning part in Elitmus?

6. Occurrence of an Event

For a random experiment, let E be an event

Let E = {a, b, c}. If the outcome of the experiment is either a or b or c then we say the event has occurred.

Sample Space: The outcomes of any type

Event: The outcomes of particular type

6.1. Probability of Occurrence of an event

Let S be the same space, then the probability of occurrence of an event E is denoted by P(E) and is defined as

P(E)=n(E)n(S)= number of elements in E number of elements in S P(E)= number of favourable/particular cases total number of cases

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Example:

A). When a coin is tossed, then the sample space is S = {H, T} Let E is the event of occurrence of a head

E = {H}

B). When a die is tossed, sample space S = {1, 2, 3, 4, 5, 6} Let A is an event of occurrence of an odd number

And B is an event of occurrence of a number greater than 4 A = {1, 3, 5} and B = {5, 6}

P(A) = Probability of occurrence of an odd number =n(A)n(S) =36=12 and

P(B) = Probability of occurrence of a number greater than 4 =n(B)n(S) =26=13

7. Basic Axioms of Probability

Let S denote the sample space of a random experiment.

1.For any event E, P(E)≥0

2.P(S)=1

3.For a finite or infinite sequence of disjoint events E1,E2,… P(E1 E2 E3 …)=∑iP(Ei)

Class10 NCERTMaths,Ex15.1,Probability

POSTED BY ABHIJIT KUMAR DEY ON 0 COMMENTS

Question 1:

Complete the following statements:

(i)Probability of an event E + Probability of the event ‘not E’ = _______.

(ii)The probability of an event that cannot happen is _________. Such as event is called

_________.

(iii)The probability of an event that is certain to happen is _________. Such as event is called ________.

(iv)The sum of the probabilities of all the elementary events of an experiment is

_________.

(v)The probability of an event is greater than or equal to _______ and less than or equal to _______.

Answer

(i)1

(ii)0, impossible event

(iii)1, sure event or certain event

(iv)1

(v)0, 1

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Question 2:

Which of the following experiments have equally likely outcomes? Explain.

(i)A driver attempts to start a car. The car starts or does not start.

(ii)A player attempts to shoot a basketball. She/he shoots or misses the shot.

(iii)A trial is made to answer a true-false question. The answer is right or wrong.

(iv)A baby is born. It is a boy or a girl.

SOL.

(i)It is not an equally likely event, as it depends on various factors such as whether the car will start or not. And factors for both the conditions are not the same.

(ii)It is not an equally likely event, as it depends on the player’s ability and there is no information given about that.

(iii)It is an equally likely event.

(iv)It is an equally likely event.

Question 3:

Why is tossing a coin considered to be a fair way of deciding which team should get the ball at the beginning of a football game?

SOL.

When we toss a coin, the possible outcomes are only two, head or tail, which are equally likely outcomes. Therefore, the result of an individual toss is completely unpredictable.

Question 4:

Which of the following cannot be the probability of an event?

SOL.

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Question 6:

A bag contains lemon flavoured candies only. Malini takes out one candy without looking into the bag. What is the probability that she takes out

(i)an orange flavoured candy?

(ii)a lemon flavoured candy?

SOL.

(i) The bag contains lemon flavoured candies only. It does not contain any orange flavoured candies. This implies that every time, she will take out only lemon flavoured candies. Therefore, event that Malini will take out an orange flavoured candy is an impossible event.

Hence, P (an orange flavoured candy) = 0

(ii)As the bag has lemon flavoured candies, Malini will take out only lemon flavoured candies. Therefore, event that Malini will take out a lemon flavoured candy is a sure event.

P (a lemon flavoured candy) = 1

Question 7:

It is given that in a group of 3 students, the probability of 2 students not having the same birthday is 0.992. What is the probability that the 2 students have the same birthday?

SOL.

=1 − 0.992

=0.008

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Question 8:

A bag contains 3 red balls and 5 black balls. A ball is drawn at random from the bag. What is the probability that the ball drawn is (i) red? (ii) not red?

(i) Total number of balls in the bag = 8

Question 9:

A box contains 5 red marbles, 8 white marbles and 4 green marbles. One marble is taken out of the box at random. What is the probability that the marble taken out will be (i) red? (ii) white? (iii) not green?

SOL.

Total number of marbles = 5 + 8 + 4 = 17

Question 10:

A piggy bank contains hundred 50 p coins, fifty Rs 1 coins, twenty Rs 2 coins and ten Rs 5 coins. If it is equally likely that one of the coins will fall out when the bank is turned upside down, what is the probability that the coin

(i)Will be a 50 p coin?

(ii)Will not be a Rs.5 coin?

Total number of coins in a piggy bank = 100 + 50 + 20 + 10

= 180

(i) Number of 50 p coins = 100

Question 11:

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Gopi buys a fish from a shop for his aquarium. The shopkeeper takes out one fish at random from a tank containing 5 male fish and 8 female fish (see the given figure). What is the probability that the fish taken out is a male fish?

Total number of fishes in a tank

=Number of male fishes + Number of female fishes

=5 + 8 = 13

SOL.

Question 12:

A game of chance consists of spinning an arrow which comes to rest pointing at one of the numbers 1, 2, 3, 4, 5, 6, 7, 8 (see the given figure), and these are equally likely outcomes. What is the probability that it will point at

(i)8?

(ii)an odd number?

(iii)a number greater than 2?

(iv)a number less than 9? SOL.

Question 13:

A die is thrown once. Find the probability of getting

(i)a prime number;

(ii)a number lying between 2 and 6;

(iii)an odd number.

SOL.

The possible outcomes when a dice is thrown = {1, 2, 3, 4, 5, 6}

Number of possible outcomes of a dice = 6

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(i) Prime numbers on a dice are 2, 3, and 5.

Total prime numbers on a dice = 3

Question 14:

One card is drawn from a well-shuffled deck of 52 cards. Find the probability of getting

(i)a king of red colour

(ii)a face card

(iii)a red face card

(iv)the jack of hearts

(v)a spade

(vi)the queen of diamonds

SOL.

Total number of cards in a well-shuffled deck = 52

(i) Total number of kings of red colour = 2

Question 15:

Five cards−−the ten, jack, queen, king and ace of diamonds, are well-shuffled with their face downwards. One card is then picked up at random.

(i)What is the probability that the card is the queen?

(ii)If the queen is drawn and put aside, what is the probability that the second card picked up is (a) an ace? (b) a queen?

(i) Total number of cards = 5

54

Total number of queens = 1

SOL.

Question 16:

12 defective pens are accidentally mixed with 132 good ones. It is not possible to just look at a pen and tell whether or not it is defective. One pen is taken out at random from this lot. Determine the probability that the pen taken out is a good one.

SOL.

Total number of pens = 12 + 132 = 144

Total number of good pens = 132

Question 17:

(i)A lot of 20 bulbs contain 4 defective ones. One bulb is drawn at random from the lot. What is the probability that this bulb is defective?

(ii)Suppose the bulb drawn in (i) is not defective and is not replaced. Now one bulb is drawn at random from the rest. What is the probability that this bulb is not defective?

SOL.

(i) Total number of bulbs = 20

Total number of defective bulbs = 4

Question 18:

A box contains 90 discs which are numbered from 1 to 90. If one disc is drawn at random from the box, find the probability that it bears

(i)a two-digit number

(ii)a perfect square number

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(iii) a number divisible by 5.

SOL.

Total number of discs = 90

(i) Total number of two-digit numbers between 1 and 90 = 81

Question 20:

Suppose you drop a die at random on the rectangular region shown in the given figure. What is the probability that it will land inside the circle with diameter 1 m?

SOL.

Question 21:

A lot consists of 144 ball pens of which 20 are defective and the others are good. Nuri will buy a pen if it is good, but will not buy if it is defective. The shopkeeper draws one pen at random and gives it to her. What is the probability that

(i)She will buy it?

(ii)She will not buy it? Sol.

Total number of pens = 144

Total number of defective pens = 20

Total number of good pens = 144 − 20 = 124

Question 22:

Two dice, one blue and one grey, are thrown at the same time.

(i) Write down all the possible outcomes and complete the following table:

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(ii) A student argues that ‘there are 11 possible outcomes 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 and 12.

(i) It can be observed that,

To get the sum as 2, possible outcomes = (1, 1)

To get the sum as 3, possible outcomes = (2, 1) and (1, 2)

To get the sum as 4, possible outcomes = (3, 1), (1, 3), (2, 2)

To get the sum as 5, possible outcomes = (4, 1), (1, 4), (2, 3), (3, 2)

To get the sum as 6, possible outcomes = (5, 1), (1, 5), (2, 4), (4, 2), (3, 3) To get the sum as 7, possible outcomes = (6, 1), (1, 6), (2, 5), (5, 2),

(3, 4), (4, 3)

To get the sum as 8, possible outcomes = (6, 2), (2, 6), (3, 5), (5, 3), (4, 4) To get the sum as 9, possible outcomes = (3, 6), (6, 3), (4, 5), (5, 4)

To get the sum as 10, possible outcomes = (4, 6), (6, 4), (5, 5)

To get the sum as 11, possible outcomes = (5, 6), (6, 5)

To get the sum as 12, possible outcomes = (6, 6)

(ii)Probability of each of these sums will not be 1/2 as these sums are not equally likely. Question 23:

A game consists of tossing a one rupee coin 3 times and noting its outcome each time. Hanif wins if all the tosses give the same result i.e., three heads or three tails, and loses otherwise. Calculate the probability that Hanif will lose the game.

SOL.

The possible outcomes are

{HHH, TTT, HHT, HTH, THH, TTH, THT, HTT} Number of total possible outcomes = 8

Number of favourable outcomes = 2 {i.e., TTT and HHH}

Question 24:

A die is thrown twice. What is the probability that

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(i)5 will not come up either time?

(ii)5 will come up at least once?

[Hint: Throwinga die twice and throwing two dice simultaneously are treated as the same experiment].

SOL.

Total number of outcomes = 6 × 6

= 36

(i)Total number of outcomes when 5 comes up on either time are (5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6), (1, 5), (2, 5), (3, 5), (4, 5), (6, 5)

Hence, total number of favourable cases = 11

Question 25:

Which of the following arguments are correct and which are not correct? Give reasons for your answer.

(i)If two coins are tossed simultaneously there are three possible outcomes−−two heads, two tails or one of each. Therefore, for each of these outcomes, the probability is 1/3.

(ii)If a die is thrown, there are two possible outcomes- an odd number or an even number. Therefore, the probability of getting an odd number is 1/2.

SOL.

(i) Incorrect

When two coins are tossed, the possible outcomes are (H, H), (H, T), (T, H), and (T, T). It can be observed that there can be one of each in two possible ways − (H, T), (T, H).

Therefore, the probability of getting two heads is 1/4, the probability of getting two tails is 1/4, and the probability of getting one of each is1/2.

It can be observed that for each outcome, the probability is not1/3.

(ii) Correct

When a dice is thrown, the possible outcomes are 1, 2, 3, 4, 5, and 6. Out of these, 1, 3, 5 are odd and 2, 4, 6 are even numbers.

Therefore, the probability of getting an odd number is 1/2.

ClassXNCERTMathsSolution,Ex-15.2Probablity.

POSTED BY ABHIJIT KUMAR DEY ON 0 COMMENTS

Exercise 15.2

Question 1:

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Two customers Shyam and Ekta are visiting a particular shop in the same week (Tuesday to Saturday). Each is equally likely to visit the shop on any day as on another day. What is the probability that both will visit the shop on

(i) the same day? (ii) consecutive days? (iii) different days?

There are a total of 5 days. Shyam can go to the shop in 5 ways and Ekta can go to the shop in 5 ways.

SOL.

Therefore, total number of outcomes = 5 × 5 = 25

(i) They can reach on the same day in 5 ways.

i.e., (t, t), (w, w), (th, th), (f, f), (s, s)

Question 2:

A die is numbered in such a way that its faces show the number 1, 2, 2, 3, 3, 6. It is thrown two

times and the total score in two throws is noted. Complete the following table which gives a few values of the total score on the two throws:

What is the probability that the total score is

(i)even? (ii) 6? (iii) at least 6?

+

1 2 2 3 3 6

 

 

1

2 3 3 4 4 7

 

 

2

3 4 4 5 5 8

 

 

2

3 4 4 5 5 8

 

 

3

4 5 5 6 6 9

 

 

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3

4 5 5 6 6 9

 

 

6

7 8 8 9 9 12

 

 

SOL.

Total number of possible outcomes when two dice are thrown = 6 × 6 = 36

(i)Total times when the sum is even = 18

P (getting an even number) = 18/36 =1/2

(ii)Total times when the sum is 6 = 4

P (getting sum as 6) = 4/36 = 1/9

(iii) Total times when the sum is at least 6 (i.e., greater than 5) = 15

P (getting sum at least 6) = 15/36 =5/12

Question 3:

A bag contains 5 red balls and some blue balls. If the probability of drawing a blue ball isdouble that of a red ball, determine the number of blue balls in the bag.

SOL.

Let the number of blue balls be x.

Number of red balls = 5

Total number of balls = x + 5

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However, the number of balls cannot be negative.

Hence, number of blue balls = 10

Question 4:

A box contains 12 balls out of which x are black. If one ball is drawn at random from the box, what is the probability that it will be a black ball?

If 6 more black balls are put in the box, the probability of drawing a black ball is now double of what it was before. Find x.

SOL.

Total number of balls = 12

Total number of black balls = x

If 6 more black balls are put in the box, then

Total number of balls = 12 + 6 = 18

Total number of black balls = x + 6

According to the condition given in the question,

Question 5:

A jar contains 24 marbles, some are green and others are blue. If a marble is drawn at random from the jar, the probability that it is green is 2/3. Find the number of blue balls in the jar.

SOL.

Total number of marbles = 24

Let the total number of green marbles be x.

Then, total number of blue marbles = 24 − x

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According to the condition given in the question, Therefore, total number of green marbles in the jar = 16

Hence, total number of blue marbles = 24 − x = 24 − 16 = 8

Section 1:

Quant Section ( 20 Questions) (Major topics)

permutation geometry Probability Number System work and time Section 2:

DI and Logical Reasoning ( 20 Questions) (major questions)

DI- tabular data with conditions 5 questions Arrangement -3 questions Coding/Decoding based on multiplication Section 3:

Verbal ( 20 Questions)

3 reading comprehension 4 question in each paragraph formation

fill in the blank ( appropriate word) grammar

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