Common Admission Test (CAT) Questions and Answers with Explanation

Q:

Solve the following equations and find the value of abc?

A) 3	B) 6
C) 9	D) 12

Answer & Explanation Answer: B) 6

Explanation:

From the given equations,

$(a + b + c)^{2} = a^{2} + b^{2} + c^{2} + 2 (ab + bc + ca)$
${(6)}^{2} = 14 + 2 (ab + bc + ca)$
36 - 14 = 2(ab + bc + ca)
22/2 = ab + bc + ca
ab + bc + ca = 11

$a^{3} + b^{3} + c^{3} - 3 abc = (a + b + c) (a^{2} + b^{2} + c^{2} - ab - bc - ca)$
= (6) (14 - 11)
=(6)(3)
=18

Since, $a^{3} + b^{3} + c^{3} - 3 abc = 18$

36 - 3abc = 18

-3abc = 18 - 36

-3abc = -18

abc = 6.

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Filed Under: Math Puzzles
Exam Prep: Bank Exams , CAT

31 9773

Q:

A man pays Rs. 6.40 per litre of milk. He adds water and sells the mixture at Rs. 8 per litre, thereby making 37.5% profit. The proportion of water to milk received by the customers is

A) 1 : 10	B) 10 : 1
C) 9 : 11	D) 11 : 9

Answer & Explanation Answer: A) 1 : 10

Explanation:

Customer ratio of Milk and Water is given by

Milk :: Water

6.4 0

$\frac{8}{1 + \frac{3}{8}} = \frac{64}{11}$

$\frac{64}{11}$ $\frac{64}{10} - \frac{64}{11}$

=> Milk : Water = 110 : 11 = 10 : 1

Therefore, the proportionate of Water to Milk for Customer is 1 : 10

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Filed Under: Alligation or Mixture
Exam Prep: AIEEE , Bank Exams , CAT , GATE
Job Role: Analyst , Bank Clerk , Bank PO

29 9758

Q:

Guess the Missing number in the Number Challenge ?

A) 8	B) 32
C) 44	D) 64

Answer & Explanation Answer: D) 64

Explanation:

The logic in the challenge is

$\sqrt{81} x 6 = 9 x 6 = 54$

$\sqrt{144} x 7 = 84$

Similarly, $\sqrt{64} x 8 = 8 x 8 = 64$ .

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Filed Under: Math Puzzles
Exam Prep: CAT , Bank Exams , AIEEE
Job Role: Bank PO , Bank Clerk

22 9757

Q:

Three maths classes: A, B and C take an algebra test. The average score of class A is 83. The average score of class B is 76. The average score of class C is 85. The average score of class A and B is 79 and average score of class B and C is 81. What is the average score of classes A, B, C ?

A) 81	B) 78
C) 80.5	D) 81.5

Answer & Explanation Answer: D) 81.5

Explanation:

Let the number of students in classes A, B and C be P, Q and R respectively.
Then, total score of A = 83P, total score of B = 76Q, total score of C = 85R.
Also given that,
(83P + 76Q) / (P + Q) = 79
=>4P = 3Q.
(76Q + 85R)/(Q + R) = 81
=>4R = 5Q,
=>Q = 4P/3 and R = 5P/3
Therefore, average score of A, B, C = ( 83P + 76Q + 85R ) / (P + Q + R) = 978/12 = 81.5

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Filed Under: Average
Exam Prep: AIEEE , Bank Exams , CAT , GATE , GRE
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12 9754

Q:

Atmospheric pressure exerted on earth is due to

A) gravitational pull	B) rotation of earth
C) revolution of earth	D) uneven heating of earth

Answer & Explanation Answer: A) gravitational pull

Explanation:

The atmospheric pressure at the surface of the Earth is due to gravitational pull of the earth and is about 14.7 psi.

That means that the weight of a column of air which has a cross section of 1 square inch and which stretches from the surface of the Earth to space is 14.7 pounds.

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Filed Under: Physics
Exam Prep: AIEEE , Bank Exams , CAT , GATE
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7 9749

Q:

egg: fish : : ________ : plant

A) seed	B) stem
C) root	D) leaf

Answer & Explanation Answer: A) seed

Explanation:

Fish is from eggs whereas plant is from seeds.

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Filed Under: Analogy
Exam Prep: AIEEE , Bank Exams , CAT , GATE , GRE , TOEFL
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9 9735

Q:

A cuboid of dimension 24cm x 9cm x 8 cm is melted and smaller cubers are of side 3 cm is formed.find how many such cubes can be formed ?

A) 64	B) 56
C) 48	D) 40

Answer & Explanation Answer: A) 64

Explanation:

Volume of cuboid = (24 x 9 x 8) cm = 1728 cu.cm
Volume of small cube = (3 x 3 x 3) cm = 27 cu.cm

So, No. of small cubes formed = 1728/27 = 64.

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Filed Under: Volume and Surface Area
Exam Prep: CAT , Bank Exams , AIEEE
Job Role: Bank PO , Bank Clerk

5 9732

Q:

Statement :

The 'X' state government has chalked out a plan for the underdeveloped 'Y' district where 80% of the funds will be placed in the hands of a committee of local representatives.

Courses of action :

I. The 'X' state government should decide guidelines and norms for the functioning of the committee.

II. Other state government may follow similar plan if directed by the Central government.

A) If only II follows	B) If only I follows
C) If either I or II follows	D) If neither I nor II follows

Answer & Explanation Answer: B) If only I follows

Explanation:

Once it is decided to place funds in the hands of the committee of local representatives, it is necessary to decide guidelines and norms for the functioning of the committee. Hence I follows. II is not related to the statement.

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Filed Under: Statement and Courses of Action
Exam Prep: AIEEE , Bank Exams , CAT , GATE , GRE , TOEFL
Job Role: Bank Clerk , Bank PO

5 9722

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