Common Admission Test (CAT) Questions and Answers with Explanation

Q:

What is the smallest number by which 2880 must be divided in order to make it into a perfect square ?

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

Answer & Explanation Answer: D) 5

Explanation:

By trial and error method, we get
2880/3 = 960 is not a perfect square
2880/4 = 720 is not a perfect square
2880/5 = 576 which is perfect square of 24
Hence, 5 is the least number by which 2880 must be divided in order to make it into a perfect square.

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Q:

'P' walked 1 km towards south direction and turned $90^{o}$ ACW and walked 2 km. Then he turned his left and walked 1 km and then he turned his right and walked 2 km. After that he turned $90^{o}$ ACW and walked 3 km. How far is he from the starting point ?

A) 5 km	B) 4 km
C) 2 km	D) 0 km

Answer & Explanation Answer: A) 5 km

Explanation:

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85 17751

Q:

The simple interest on Rs.10 for 4 months at the rate of 3 paise per month is

A) 0.3 Paise	B) 1.2 Paise
C) 30 Paise	D) 3 Paise

Answer & Explanation Answer: B) 1.2 Paise

Explanation:

Given Principal amount P = Rs. 10

Time T = 4 months

Rate of interest R = 3 ps

Interest I = PTR/100 = (10 x 4 x 3)/100 = 12/10 = 1.2 paise.

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Filed Under: Simple Interest
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7 17747

Q:

Thrice the square of a natural number decreased by 4 times the number is equal to 50 more than the number. The number is ?

A) 5	B) 4
C) 7	D) 6

Answer & Explanation Answer: A) 5

Explanation:

Let the number be x. Then,

$3 x^{2}$ - 4x = x + 50

$3 x^{2}$ - 5x - 50 = 0

(3x + 10)(x - 5) = 0

x = 5

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Filed Under: Arithmetical Reasoning
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16 17743

Q:

A man covers half of his journey by train at 60 km/hr, half of the remaining by bus at 30 km/hr and the rest by cycle at 10 km/hr. Find his average speed during the entire journey?

A) 32 kmph	B) 20 kmph
C) 18 kmph	D) 24 kmph

Answer & Explanation Answer: D) 24 kmph

Explanation:

Let the total distance of the journey of a man = d kms

Now, the average speed of the entire journey = $\frac{d}{\frac{d}{120} + \frac{d}{120} + \frac{d}{40}}$ = 24 kmph.

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Filed Under: Time and Distance
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30 17741

Q:

At 6′o clock a clock ticks 6 times. The time between first and last ticks is 30 seconds. How long does it tick at 12′o clock ?

A) 66 sec	B) 55 sec
C) 36 sec	D) 24 sec

Answer & Explanation Answer: A) 66 sec

Explanation:

For ticking 6 times, there are 5 intervals.

Each interval has time duration of 30/5 = 6 secs

At 12 o'clock, there are 11 intervals,
so total time for 11 intervals = 11 x 6 = 66 secs.

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26 17706

Q:

Which atomic power station in India is built completely indigenously?

A) Rawat Bhata	B) Kalpakkam
C) Tarapore	D) Narora

Answer & Explanation Answer: B) Kalpakkam

Explanation:

Madras Atomic Power Station (MAPS) located at Kalpakkam about 80 kilometers (50 mi) south of Chennai, India, is a comprehensive nuclear power production, fuel reprocessing, and waste treatment facility that includes plutonium fuel fabrication for fast breeder reactors (FBRs) is the only atomic power station in India that was built completely indigenously. Which_atomic_power_station_in_India_is_built_completely_indigenously1547792929.jpg image

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47 17652

Q:

If (89)² is added to the square of a number, the answer so obtained is 16202. What is the (1/26) of that number?

A) 5.65	B) 2.7
C) 3.5	D) 6.66

Answer & Explanation Answer: C) 3.5

Explanation:

Let the number is = x

(89)² + x² = 16202

x² = 8281

x = 91

=> (1/26) of 91 = 3.5

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Filed Under: Square Roots and Cube Roots
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