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CRT_Prep_Aptitude

Total questions: 29

Worksheet time: 32mins

Name
Class
Date
1.
There are two boxes, one containing 32 red balls and the other containing 31 green balls. You are allowed to move the balls between the boxes so that when you choose a box at random and a ball at random from the chosen box, the probability of getting a red ball is maximized. This maximum probability is
a)
25
b)
51
c)
75
d)
50
2.
A man has some socks in his drawer: 14 identical blue, 20 identical red, and 28 identical black. The lights are out and it is totally dark. How many socks must he take out to make sure he has a pair of each colour?
a)
34
b)
50
c)
30
d)
28
3.
A cyclist buys a cycle for 29 pounds paying with a 50 pound cheque. The seller changes the cheque next door and gives the cyclist change. The cheque bounces so the seller paid his neighbor back. The cycle cost the seller 12 pounds. How much did the seller lose?
a)
33 Pounds
b)
40 pounds
c)
51 pounds
d)
28 pounds
4.
The original price of a car was $23600. Because the car owner thought he could get more money for the car, he increased the price of the car to 160% of its original price. After a week, the car had not sold, so the owner then discounted the price by 20%, the car was finally sold. What price was the car sold for?
a)
30208
b)
23908
c)
21890
d)
41890
5.
The chairman of Tata Motors, Ratan Tata, had 300 engineers work for 5 years designing the world's lowest-cost car, convinced that cost-conscious Indian drivers could live without air-conditioning and cup holders. However, after the booking started they found that only 23 percent of initial 253850 orders for the car - the Nano - were for the no frills $2600 model. How much time (in days) would it have taken if there were 500 employees working for double the time?
a)
547.5
b)
129.57
c)
1305.47
d)
210.98
6.
Earl can stuff advertising circulars into envelops at the rate of 36 envelopes per minute and Ellen requires a minute and a half to stuff the same number of envelopes. Working together, how long will it take Earl and Ellen to stuff 360 envelopes?
a)
2min
b)
6min
c)
8min
d)
4min
7.
In 1911, a French physicist Paul Langevin, devised a thought experiment based on Einstien's Special Relativity. In the experiment, a person makes a journey into space at nearly the speed of light and comes back to earth. He finds that he has aged five times less than his twin who stayed back on earth for 40 years. This is popularly known as the Twin Paradox. Now, consider the case of Hansel and Gretel, who are not twins. 9 years ago, Hansel was twice as old as Gretel. If they journey into space, an atomic clock assists in logging the start time of their journey accurately. If they do not journey into space, 9 years hence, Hansel's age will be 4/3 times the age of Greters. Find Hansel's age today in binary numbers.
a)
11000
b)
11011
c)
1010
d)
1011
8.
The number of bacteria in a colony was growing exponentially. At 4 pm yesterday the number of bacteria was 400 and at 6 pm yesterday it was 3600. How many bacteria were there in the colony at 7 pm yesterday?
a)
10800
b)
3600
c)
1200
d)
4800
9.
A multiple choice question has 4 options. Choosing the correct option earns the student 3 marks. However choosing the wrong option incurs negative marks so that if a student chooses an option randomly, his expected score is 0. Suppose a student has successfully eliminated 2 incorrect options. His expected score if he chooses randomly among the remaining options is.
a)
1 mark
b)
1.5 mark
c)
0 mark
d)
3 marks
10.
On the planet Oz, there are 8 days in a week - Sunday to Saturday and another day called Oz day. There are 36 hours in a day and each hour has 90 minutes while each minute has 60 seconds. As on earth, the hour hand covers the dial twice every day. Find the approximate angle between the hands of a clock on Oz when the time is 12:40 am
a)
100 degrees
b)
89 degrees
c)
210 degrees
d)
166 degrees
11.
You're going to get grounded for a week if you don't get at least 80% in your science class. So far you have 237 of the total 300 points. The final test is worth 100 points. What is the minimum score you need to get on the final test? Assume the teacher rounds properly.
a)
67
b)
85
c)
83
d)
90
12.
A water tank is two-fifth full. Pipe A can fill a tank in 10 minutes and pipe B can empty it in 6 minutes. If both the pipes are open, how long will it take to empty or fill the tank completely?
a)
6 min to empty
b)
6 min to fill
c)
9 min to empty
d)
9 min to fill
13.
Two taps A and B can fill a tank in 5 hours and 20 hours respectively. If both the taps are open then due to a leakage, it took 30 minutes more to fill the tank. If the tank is full, how long will it take for the leakage alone to empty the tank?
a)
4.5
b)
9
c)
18
d)
36
14.
Three pipes A, B and C can fill a tank in 6 hours. After working at it together for 2 hours, C is closed and A and B can fill the remaining part in 7 hours. The number of hours taken by C alone to fill the tank is:
a)
10
b)
12
c)
14
d)
16
15.
Bucket P has thrice the capacity as bucket Q. It takes 60 turns for bucket P to fill the empty drum. How many turns it will take for both the buckets P and Q, having each turn together to fill the empty drum?
a)
30
b)
40
c)
45
d)
90
16.
8 men can dig a pit in 20 days. If a man works half as much more as a boy, then 4 men and 9 boys can dig a similar pit in :
a)
10 days
b)
12 days
c)
15 days
d)
16 days
17.
8 children and 12 men complete a certain piece of work in 9 days. If each child takes twice the time taken by a man to finish the work, in how many days will 12 men finish the same work ?
a)
8
b)
15
c)
9
d)
12
18.
Two cyclist A and B cover a distance of 110 km, A reaches to the destination one hour before B. Even if B had given a start of 8 km, he would have reached 12 minutes late. Find the speed of A.
a)
6 k/h
b)
7 k/h
c)
8.5 k/h
d)
11 k/h
19.
In a circular race of 1200m, A and B start from the same point and at the same time with speeds of 27kmph and 45 kmph.  Find when will they meet again for the first time on the trace when they are running in the same direction and Opposite direction?
a)
240, 60 Secs
b)
200, 60 secs  
c)
200, 80 Sec  
d)
None of these
20.
Ten cards numbered 1 to 10 are placed in a box.  And one card is drawn randomly.  If is it is known that the drawn card is more than 3, what is the probability that it is an even number?
a)
( 1/2 )
b)
( 4/7 )
c)
( 3/10 )
d)
( 2/5 )
21.
A boat running upstream takes 8 hours 48 minutes to cover a certain distance, while it takes 4 hours to cover the same distance running downstream. What is the ratio between the speed of the boat and speed of the water current respectively?
a)
(8:3)
b)
(4:3)
c)
(3:4)
d)
(6:2)
22.
A boat takes 90 minutes less to travel 36 miles downstream than to travel the same distance upstream. If the speed of the boat in still water is 10 mph, the speed of the stream is:
a)
2mph
b)
2.5mph
c)
3mph
d)
4mph
23.
A man can row at 5 kmph in still water. If the velocity of current is 1 kmph and it takes him 1 hour to row to a place and come back, how far is the place?
a)
2.4km
b)
2.5km
c)
5km
d)
3.2km
24.
A man can row three-quarters of a kilometre against the stream in (11 + 1/4)Minutes and down the stream in (7 + 1/2) Minutes. The speed (in km/hr) of the man in still water is:
a)
2
b)
3
c)
4
d)
5
25.
33.33% of 16.66% of 14.28% of 126 is?
a)
1
b)
6
c)
16
d)
26
26.
If Sham had 24 shirts by what % his shirts were reduced if he donated 4 of them?
a)
0.166
b)
0.1775
c)
0.18
d)
0.19
27.
In a shop price of Laptop which is marked at $1000 was discounted 20% for Christmas eve and further 30% discounted for New Year eve. What is the price of Laptop now?
a)
500
b)
560
c)
600
d)
970
28.
What is the four digit number in which the first digit is 1/3 of the second, the third is the sum of the first and second, and the last is three times the second?
a)
1349
b)
6578
c)
2345
d)
2134
29.
The difference between a two-digit number and the number obtained by interchanging the digits is 36. What is the difference between the sum and the difference of the digits of the number if the ratio between the digits of the number is 1 : 2 ?
a)
4
b)
5
c)
6
d)
8