Common Admission Test (CAT) Questions and Answers with Explanation

Q:

A booster pump can be used for filling as well as for emptying a tank. The capacity of the tank is 2400 $m^{3}$ . The emptying capacity of the tank is 10 $m^{3}$ per minute higher than its filling capacity and the pump needs 8 minutes lesser to empty the tank than it needs to fill it. What is the filling capacity of the pump?

A) 50 m^3/min	B) 60 m^3/min
C) 72 m^3/min	D) None of these

Answer & Explanation Answer: A) 50 m^3/min

Explanation:

Let the filling capacity of the pump be x $m^{3}$ /min.

Then, emptying capacity of the pump=(x+10) $m^{3}$ /min.

so, $\frac{2400}{x} - \frac{2400}{x + 10} = 8 \Leftrightarrow x^{2} + 10 x - 3000 = 0$

$\Rightarrow (x - 50) + (x + 60) = 0 \Leftrightarrow x = 50$

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Filed Under: Pipes and Cistern
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38 21272

Q:

Find the quadratic equations whose roots are the reciprocals of the roots of $2 x^{2} + 5 x + 3$ ?

A) $3 x^{2} + 5 x + 2 = 0$

B) $5 x^{2} + 3 x + 2 = 0$

C) $3 x^{2} - 5 x - 2 = 0$

D) None

A) A	B) B
C) C	D) D

Answer & Explanation Answer: A) A

Explanation:

The quadratic equation whose roots are reciprocal of $2 x^{2} + 5 x + 3 = 0$ can be obtained by replacing x by 1/x.

Hence, 2(1/x)(1/x)+ 5(1/x) + 3 = 0

=> $3 x^{2} + 5 x + 2 = 0$

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Filed Under: Mathematical Operations
Exam Prep: GATE , CAT , Bank Exams , AIEEE
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78 21264

Q:

Complete the number series?

11, 12.2, 14.6, 18.2, ?

A) 21.8	B) 23
C) 24.6	D) 25

Answer & Explanation Answer: B) 23

Explanation:

The given number series 11, 12.2, 14.6, 18.2, ?

11

11 + 1.2 = 12.2

12.2 + 2.4 = 14.6

14.6 + 3.6 = 18.2

18.2 + 4.8 = 23

Hence, the next number in the given number series is 23.

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Filed Under: Number Series
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8 21254

Q:

The smallest Union Territory of India is

A) Lakshadweep	B) Pondicherry
C) Daman and Diu	D) Dadar and Nagar Haveli

Answer & Explanation Answer: A) Lakshadweep

Explanation:

Lakshadweep has an area of only about 32 sq km.

The_smallest_Union_Territory_of_India_is1554209119.jpg image

The area of Pondicherry, Daman and Diu and Dadar and Nagar Haveli are about 492 sq km and 491 sq km respectively.

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Filed Under: Indian Geography
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40 21231

Q:

When I was married 10 years ago my wife is the 6th member of the family. Today my father died and a baby born to me.The average age of my family during my marriage is same as today. What is the age of Father when he died ?

A) 50 yrs	B) 60 yrs
C) 70 yrs	D) 65 yrs

Answer & Explanation Answer: B) 60 yrs

Explanation:

Let the Father be x years when he died

Average Age 10 years ago be A

Total Age 10 years ago = 6*A

Total Age after 10 years(Just before father's Death) = 6A + 6*10 = 6A + 60

Father Died and Baby was born => the Total number of people in the family is Same (6)
Baby born today so age of baby = 0

(6A +60 - x)/6 = 6A/6
=> A + 10 -(x/6) = A
=> x/6 = 10
=> x = 60

Therefore we can conclude that the father was 60 years old when he died.

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Filed Under: Problems on Ages
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Q:

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Answer

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161 21220

Q:

Two pipes can fill a tank in 20 and 24 minutes respectively and a waste pipe can empty 3 gallons per minute. All the three pipes working together can fill the tank in 15 minutes. The capacity of the tank is:

A) 60 gallons	B) 100 gallons
C) 120 gallons	D) 180 gallons

Answer & Explanation Answer: C) 120 gallons

Explanation:

Work done by the waste pipe in 1 minute = $\frac{1}{15} - (\frac{1}{20} + \frac{1}{24}) = \frac{1}{15} - \frac{11}{120} = - \frac{1}{40}$ [-ve sign means emptying]

Volume of $\frac{1}{40}$ part = 3 gallons

Volume of whole = (3 x 40) gallons = 120 gallons.

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Filed Under: Pipes and Cistern
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37 21170

Q:

A polygon has 44 diagonals, then the number of its sides are ?

A) 13	B) 9
C) 11	D) 7

Answer & Explanation Answer: C) 11

Explanation:

Let the number of sides be n.

The number of diagonals is given by ⁿC₂ - n

^{Therefore, n}C₂ - n = 44, n>0

ⁿC₂ - n = 44

n²- 3n - 88 = 0

n²-11n + 8n - 88 = 0

n(n - 11) + 8(n - 11) = 0

n = -8 or n = 11.

As n>0, n will not be -8. Therefore, n=11.

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Filed Under: Permutations and Combinations
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25 21118

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