Common Admission Test (CAT) Questions and Answers with Explanation

Q:

In a party there are 5 couples. Out of them 5 people are chosen at random. Find the probability that there are at the least two couples ?

A) 6/7	B) 19/21
C) 7/31	D) 5/21

Answer & Explanation Answer: D) 5/21

Explanation:

Number of ways of (selecting at least two couples among five people selected) = (⁵C₂ x ⁶C₁)

As remaining person can be any one among three couples left.

Required probability = (⁵C₂ x ⁶C₁)/¹⁰C₅
= (10 x 6)/252 = 5/21

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Filed Under: Probability
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Q:

Refer the below data table and answer the following question.

What is the average bonus in Rs. ?

A) 606154	B) 7880002
C) 253333	D) 224000

Answer & Explanation Answer: A) 606154

Explanation:

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Filed Under: Table Charts
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0 16601

Q:

If the volume of the cube is 729 $c m^{3}$ , then the surface area of the cube will be

A) 486 sq.cm	B) 456 sq.cm
C) 446 sq.cm	D) 476 sq.cm

Answer & Explanation Answer: A) 486 sq.cm

Explanation:

volume = $a^{3}$ = 729;

=> a = 9

surface area= 6 $a^{2}$ = (6 x 9 x 9) = 486 sq.cm

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Filed Under: Volume and Surface Area
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Q:

A man whose speed is 4.5 kmph in still water rows to a certain upstream point and back to the starting point in a river which flows at 1.5 kmph, find his average speed for the total journey ?

A) 5 kmph	B) 7 kmph
C) 3 kmph	D) 4 kmph

Answer & Explanation Answer: D) 4 kmph

Explanation:

Speed of Man = 4.5 kmph
Speed of stream = 1.5 kmph
Speed in DownStream = 6 kmph
Speed in UpStream = 3 kmph
Average Speed = (2 x 6 x 3)/9 = 4 kmph.

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Filed Under: Time and Distance
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Q:

What goes in the water black and comes out red

Answer

A Lobster is one which goes black in water and comes out red.

lobster1585556605.jpg image

Workspace

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45 16562

Q:

Sanjeev ranks seventh from the top and twenty eighth from the bottom in a class. How many students are there in the class?

A) 33	B) 36
C) 35	D) 34

Answer & Explanation Answer: D) 34

Explanation:

Total number of students in the class = 28 + 6 i.e, from top(7-1)

28 + 6 = 34

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Filed Under: Number, Ranking and Time Sequence Test
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64 16556

Q:

Find the LCM of $3^{5}, 3^{11}, 3^{- 11} and 3^{14}$

A) 35	B) 311
C) 3-11	D) 314

Answer & Explanation Answer: D) 314

Explanation:

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Filed Under: HCF and LCM
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Q:

If the rate increases by 2%, the simple interest received on a sum of money increases by Rs. 108. If the time period is increased by 2 years, the simple interest on the same sum increases by Rs.180. The sum is ?

A) Rs. 540	B) Rs. 415
C) Rs. 404	D) Data is not sufficient

Answer & Explanation Answer: D) Data is not sufficient

Explanation:

Let the sum be Rs. p, rate be R% p.a. and time be T years.

Then,

$(\frac{P \times T \times (R + 2)}{100}) - (\frac{P \times T \times R}{100}) = 108 \Rightarrow 2 P T = 10800 . . . . . . (1)$

And,

$(\frac{P \times R \times (T + 2)}{100}) - (\frac{P \times R \times T}{100}) = 180 \Rightarrow 2 P R = 18000 . . . . . . (2)$

Clearly, from (1) and (2), we cannot find the value of p
So, the data is not sufficient.

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Filed Under: Simple Interest
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