Common Admission Test (CAT) Questions and Answers with Explanation

Q:

A batsman in his 17th innings makes a score of 85 and their by increasing his average by 3. What is his average after the 17th innings ?

A) 34	B) 36
C) 35	D) 37

Answer & Explanation Answer: D) 37

Explanation:

16x + 85 = 17(x + 3)

x = 34 + 3 = 37

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Q:

Two trains started at the same time, one from A to B and the other from B to A . If they arrived at B and A respectively 4 hours and 9 hours after they passed each other the ratio of the speeds of the two trains was

A) 2:1	B) 3:2
C) 4:3	D) 5:4

Answer & Explanation Answer: B) 3:2

Explanation:

Note : If two trains (or bodies) start at the same time from points A and B towards each other and after crossing they take a and b sec in reaching B and A respectively, then: (A's speed) : (B's speed) = (b : a)

Therefore, Ratio of the speeds of two trains = $\sqrt{9} : \sqrt{4}$ = 3 : 2

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Q:

Study the given bar graph and pie chart to answer the following questions.

The bar graph shows the production (in thousand tonnes) of Wheat, Rice and Maize in different states.

The pie-chart shows the percentage of agricultural land in the given six states.

Productivity = $\frac{Total\: Production}{Area\: of\: agricultural\: land}$

1.The productivity of which state is the maximum ?

1. Bihar 2. Haryana 3. Punjab 4. UP 5. MP

2.The production of which state is the maximum ?

1. Bihar 2. MP 3. Haryana 4. UP 5. Punjab

3.The prodution of wheat in punjab is what per cent more than the production of Maize in odisha ?

1. 350% 2. 250% 3. 300% 4. 200% 5. 400%

4.What is the ratio of the production of Rice in Bihar to the production of Wheat in Haryana ?

1. 2:3 2. 3:2 3. 2:1 4. 1:1 5. 1:2

5.If MP exports 40% of Rice at the rate of Rs.30 per kg and UP exports 30% of Rice at the rate of Rs.32 per kg, then what is the ratio of the income from the exports ?

1. 65:48 2. 31:42 3. 43:54 4. 57:62 5. 1:2

Answer

1. Answer : 2

Explanation : Productivity = Total production/area of Agr.land

Productivity of UP = [ (35000+30000+25000) / (30/100) ] = 300000

Productivity of MP = [ (30000+37500+27500) / (25/100) ] = 380000

Productivity of Bihar = [ (22500+27500+25000) / (20/100) ] = 375000

Productivity of Odisha = [ (22500+15000+10000) / (5/100) ]= 950000

Productivity of Haryana = [ (30000+25000+35000) / (8/100) ] = 1125000

Productivity of Punjab = [ (40000+35000+30000) / (12/100) ] = 875000

The Productivity of Haryana is the maximum.

2. Answer : 5

Explanation : Production of Punjab is maximum = 105000 tonnes

3. Answer : 3

Explanation : Production of Wheat in Punjab = 40000 tones

Production of Maize in Odisha = 10000 tones

Required % = (40000 - 10000)/100 = 300%

4. Answer : 4

Explanation : The ratio of prodution of Rice in Bihar to the production of Wheat in Haryana = 25000 tonnes : 25000 tonnes = 1 : 1

5. Answer : 1

Explanation : Income of MP from export of 40% of Rice at the rate of Rs.30 per kg = Rs.39crore

Income of UP from export of 30% of Rice at the rate of Rs.32 per kg = Rs.28.8 crore

Required ratio = 39 : 28.8 = 390 : 288 = 65 : 48

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Q:

Consider the following statements

P : Suman is brilliant
Q : Suman is rich
R : Suman is honest

The negation of the statement "Suman is brilliant and dishonest if and only if Suman is rich" can be expressed as

1) $(P \land ~ R) \leftrightarrow Q$

2) $~ (P \land R) \leftrightarrow Q$

3) $Q \leftrightarrow (P \land ~ R)$

4) $~ (Q \leftrightarrow (P \land ~ R))$

A) 1	B) 2
C) 3	D) 4

Answer & Explanation Answer: D) 4

Explanation:

Suman is brilliant and dishonest is P $\land$ ~ R
Suman is brilliant and dishonest iff suman is rich is
Q $\leftrightarrow$ (P $\land$ ~ R)

Negative of statement is expressed as
~ (Q $\leftrightarrow$ (P $\land$ ~ R)).

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Q:

Fossil : Extinction :: Puddle : ?

A) Wet	B) Rain
C) Lake	D) Dry

Answer & Explanation Answer: B) Rain

Explanation:

Here the relation between a fossil and extinction is that a fossil remains after an extinction. That is fossils are evidence of an extinction.

Similarly, puddle remains after it is rained. That is puddles are evidence of rain.

Therefore, Fossil is to Extinction as Puddle is to Rain.

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Q:

If the numerator of a fraction is increased by 150% and the denominator of the fraction is increased by 350%, the resultant fraction is 25/51. What is the original fraction ?

A) 31/25	B) 15/17
C) 14/25	D) 11/16

Answer & Explanation Answer: B) 15/17

Explanation:

The original fraction is $\frac{25}{51} \times (\frac{350 + 100}{150 + 100})$ = 15/17.

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Q:

Find the Missing number in the given number series?

5, 9, 15, 23, ?, 45

A) 33	B) 29
C) 31	D) 35

Answer & Explanation Answer: A) 33

Explanation:

The given series follows a pattern that,

+4, +6, +8, +10, +12...

5

5 + 4 = 9

9 + 6 = 15

15 + 8 = 23

23 + 10 = 33

33 + 12 = 45

Hence, the missing number in the series is 33.

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Q:

Find the odd man out of the following number series?

222, 271, 308, 332, 348, 357

A) 271	B) 308
C) 332	D) 348

Answer & Explanation Answer: B) 308

Explanation:

Here the given series 222, 271, 308, 332, 348, 357 follows a pattern that

222

222 + 49 271

271 + 36 = 307 (NOT 308)

307 + 25 = 332

332 + 16 = 348

348 + 9 = 357

Hence, the odd man in the fiven number series is 308.

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