Common Admission Test (CAT) Questions and Answers with Explanation

Q:

Find the unit digit of 4¹⁹⁸ + 6¹²³⁴⁵ + 348⁶⁶ + 24¹¹ + 1.

A) 3	B) 2
C) 1	D) 0

Answer & Explanation Answer: C) 1

Explanation:

Given that, $4^{198} + 6^{12345} + 348^{66} + 24^{11} + 1$

Now Power Cycle of

4 is 4, 6

6 is 6

8 is 8, 4, 2, 6

1 is 1

$4^{198}$ - 198 is even number , So the unit digit value is 6

$6^{12345}$ - It is always 6

$348^{66}$ - 66/4 the remainder is 2 , So the second value is 4

$24^{11}$ - 11 is odd number, So the unit digit value is 4

1 - It is always 1

Total = 21

Therefore, The unit digit is 1

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26 19881

Q:

What time will it be 18 hours from now in India, if in the USA it is 4:15 AM?

(Hint : IST = US + 9:30 hrs)

A) 1:45 in the afternoon	B) 7:45 in the evening
C) 7:45 in the next morning	D) 1:45 in the next morning

Answer & Explanation Answer: C) 7:45 in the next morning

Explanation:

We know that the time difference between India and USA is 9 hrs 30 min.

India is 9:30 hrs ahead of USA.

Time in India = 4:15 + 9:30 = 13:45 PM.

Required Time after 18 hrs = 13:45 + 18 hrs = 7:45 AM.

Hence it is 7:45 AM on the next morning.

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20 19827

Q:

P and Q can complete a job in 24 days working together. P alone can complete it in 32 days. Both of them worked together for 8 days and then P left. The number of days Q will take to complete the remaining work is ?

A) 56 days	B) 54 days
C) 60 days	D) 64 days

Answer & Explanation Answer: D) 64 days

Explanation:

(P+Q)'s 1 day work = 1/24

P's 1 day work = 1/32

=> Q's 1 day work = 1/24 - 1/32 = 1/96

Work done by (P+Q) in 8 days = 8/24 = 1/3

Remainining work = 1 - 1/3 = 2/3

Time taken by Q to complete the remaining work = 2/3 x 96 = 64 days.

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22 19827

Q:

It takes five minutes to pass a rumour from one person to two other persons. The tree of rumour continues. Find how many minutes does it take spread the rumour to 729 persons ?

A) 45 min	B) 25 min
C) 30 min	D) 36 min

Answer & Explanation Answer: C) 30 min

Explanation:

After 5 mins ..... 3 persons will get rumour
After 10 mins .... 3x2 + 3 = 9 = $3^{2}$ persons will get
after 15 =5x3 min ......9x2 + 9 =27 = $3^{3}$ persons will get news.
.
.
after 5x6 mins ... $3^{6}$ = 729 persons will get news.

Therefore, time taken to spread the rumour to 729 persons is 30 minutes.

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23 19794

Q:

Ram and Raj start a business with investments of Rs. 2500 and Rs. 2250 respectively. After 2 months, Ram takes out Rs.1250 from his capital. After 1 more month, Raj takes out Rs.750 of his capital while Rakesh joins them with a capital of Rs. 3500. At the end of 6 months, they earn a profit of Rs. 2540. Which of the following is the share of each member in the profit ?

A) Ram - Rs. 800, Raj - Rs. 900, Rakesh - Rs. 840	B) Ram - Rs. 900, Raj - Rs. 800, Rakesh - Rs. 840
C) Ram - Rs. 840, Raj - Rs. 920, Rakesh - Rs. 840	D) Ram - Rs. 800, Raj - Rs. 900, Rakesh - Rs. 940

Answer & Explanation Answer: A) Ram - Rs. 800, Raj - Rs. 900, Rakesh - Rs. 840

Explanation:

Initial investment of Ram = Rs.2500.
After 2 months he withdraw Rs.1250 from his capital.
Therefore, we have, Ram invested Rs.2500 for 2 months and Rs.(2500-1250=) 1250 for 4 months.

Raj invested Rs. 2250 for 3 months and Rs.(2250-750=) 1500 for 3 months.

And, Rakesh invested Rs.3500 for 3 months;

Their investing ratio:
Ram:Raj:Rakesh = (2500x2 + 1250x4):(2250x3 + 1500x3):(3500x3)
= (10,000):(11,250):(10,500) = 1000:1125:1050 = 40:45:42

Total profit for 6 months = Rs.2540
Therefore, Ram's share = Rs.(2540 x 40/(40+45+42)) = Rs.(2540 x 40/127) = Rs.800
Raj's share = Rs.(2540 x 45/127) = Rs.900
Rakesh's share = Rs.(2540 x 42/127) = Rs.840

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8 19786

Q:

Two trains are moving in opposite directions at 60 km/hr and 90 km/hr. Their lengths are 1.10 km and 0.9 km respectively. The time taken by the slower train to cross the faster train in seconds is ?

A) 42 sec	B) 44 sec
C) 46 sec	D) 48 sec

Answer & Explanation Answer: D) 48 sec

Explanation:

Relative speed = 60 + 90 = 150 km/hr.

= 150 x 5/18 = 125/3 m/sec.

Distance covered = 1.10 + 0.9 = 2 km = 2000 m.

Required time = 2000 x 3/125 = 48 sec.

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9 19706

Q:

Tally package is developed by

A) Tally Solutions	B) Coral Softwares
C) Vedika Softwares	D) Peutronics

Answer & Explanation Answer: A) Tally Solutions

Explanation:

Tally package is developed by Tally Solutions.

Tally Solutions, then known as Peutronics, was co-founded in 1986 by Shyam Sunder Goenka and his son Bharat Goenka.

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17 19645

Q:

The calendar for the year 1988 is same as which upcoming year ?

A) 2012	B) 2014
C) 2016	D) 2010

Answer & Explanation Answer: C) 2016

Explanation:

We already know that the calendar after a leap year repeats again after 28 years.

Here 1988 is a Leap year, then the same calendar will be in the year = 1988 + 28 = 2016.

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80 19634

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