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Aptitude Test -Random


Aptitude
Result & Statistics

1.
A and B can complete a work in 15 days and 10 days respectively. They started doing the work together but after 2 days B had to leave and A alone completed the remaining work. The whole work was completed in :



A.
8 days



B.
10 days




C.
12 days



D.
15 days



Answer: Option C
Explanation:
(A + B)'s 1 day's work =

1
+
1

=
1
.



15

10


6


Work done by A and B in 2 days =

1
x 2

=
1
.



6



3


Remaining work =

1 -
1

=
2
.




3


3


Now,
1
work is done by A in 1 day.


15



2
work will be done by a in

15 x
2

= 10 days.


3



3



Hence, the total time taken = (10 + 2) = 12 days.


2.
Mr. Thomas invested an amount of Rs. 13,900 divided in two different schemes A and B at the simple interest rate of 14% p.a. and 11% p.a. respectively. If the total amount of simple interest earned in 2 years be Rs. 3508, what was the amount invested in Scheme B?



A.
Rs. 6400



B.
Rs. 6500




C.
Rs. 7200



D.
Rs. 7500




E.
None of these






Answer: Option A
Explanation:
Let the sum invested in Scheme A be Rs. x and that in Scheme B be Rs. (13900 - x).
Then,

x x 14 x 2

+

(13900 - x) x 11 x 2

= 3508



100



100



28x - 22x = 350800 - (13900 x 22)
6x = 45000
x = 7500.
So, sum invested in Scheme B = Rs. (13900 - 7500) = Rs. 6400.

3.
A batsman scored 110 runs which included 3 boundaries and 8 sixes. What percent of his total score did he make by running between the wickets?



A.
45%



B.
45
5
%


11







C.
54
6
%


11






D.
55%



Answer: Option B
Explanation:
Number of runs made by running = 110 - (3 x 4 + 8 x 6)
= 110 - (60)
= 50.
Required percentage =

50
x 100
% = 45
5
%



110


11



4.
In a certain school, 20% of students are below 8 years of age. The number of students above 8 years of age is of the number of students of 8 years of age which is 48. What is the total number of students in the school?



A.
72



B.
80




C.
120



D.
150




E.
100






Answer: Option E
Explanation:
Let the number of students be x. Then,
Number of students above 8 years of age = (100 - 20)% of x = 80% of x.
80% of x = 48 +
2
of 48


3



80
x = 80


100


x = 100.

5.
A man standing at a point P is watching the top of a tower, which makes an angle of elevation of 30º with the man's eye. The man walks some distance towards the tower to watch its top and the angle of the elevation becomes 60º. What is the distance between the base of the tower and the point P?



A.
43 units



B.
8 units




C.
12 units



D.
Data inadequate




E.
None of these






Answer: Option D
Explanation:
One of AB, AD and CD must have given.

So, the data is inadequate.

6.
4.036 divided by 0.04 gives :



A.
1.009



B.
10.09




C.
100.9



D.
None of these



Answer: Option C
Explanation:
4.036
=
403.6
= 100.9

0.04

4



7.
How many digits will be there to the right of the decimal point in the product of 95.75 and .02554 ?



A.
5



B.
6




C.
7



D.
None of these



Answer: Option B
Explanation:
Sum of decimal places = 7.
Since the last digit to the extreme right will be zero (since 5 x 4 = 20), so there will be 6 significant digits to the right of the decimal point.

8.
0.04 x 0.0162 is equal to:



A.
6.48 x 10-3



B.
6.48 x 10-4




C.
6.48 x 10-5



D.
6.48 x 10-6



Answer: Option B
Explanation:
4 x 162 = 648. Sum of decimal places = 6.
So, 0.04 x 0.0162 = 0.000648 = 6.48 x 10-4

9.
0.002 x 0.5 = ?



A.
0.0001



B.
0.001




C.
0.01



D.
0.1



Answer: Option B
Explanation:
2 x 5 = 10.
Sum of decimal places = 4
0.002 x 0.5 = 0.001

10.
Which of the following fractions is greater than
3
and less than
5
?


4

6






A.
1

2





B.
2

3






C.
4

5





D.
9

10





Answer: Option C
Explanation:
3
= 0.75,   
5
= 0.833,   
1
= 0.5,   
2
= 0.66,   
4
= 0.8,   
9
= 0.9.

4

6

2

3

5

10


Clearly, 0.8 lies between 0.75 and 0.833.

4
lies between
3
and
5
.


5

4

6



11.
If x =
3 + 1
and y =
3 - 1
, then the value of (x2 + y2) is:


3 - 1

3 + 1






A.
10



B.
13




C.
14



D.
15



Answer: Option C
Explanation:
x =
(3 + 1)
x
(3 + 1)
=
(3 + 1)2
=
3 + 1 + 23
= 2 + 3.


(3 - 1)

(3 + 1)

(3 - 1)

2


y =
(3 - 1)
x
(3 - 1)
=
(3 - 1)2
=
3 + 1 - 23
= 2 - 3.


(3 + 1)

(3 - 1)

(3 - 1)

2


x2 + y2 = (2 + 3)2 + (2 - 3)2
   = 2(4 + 3)
   = 14

12.
A man has some hens and cows. If the number of heads be 48 and the number of feet equals 140, then the number of hens will be:



A.
22



B.
23




C.
24



D.
26



Answer: Option D
Explanation:
Let the number of hens be x and the number of cows be y.
Then, x + y = 48 .... (i)
  and 2x + 4y = 140      x + 2y = 70 .... (ii)
Solving (i) and (ii) we get: x = 26, y = 22.
The required answer = 26.

Direction (for Q.No. 13):
Find out the wrong number in the given sequence of numbers.

13.
52, 51, 48, 43, 34, 27, 16



A.
27



B.
34




C.
43



D.
48



Answer: Option B
Explanation:
Subtract 1, 3, 5, 7, 9, 11 from successive numbers.
So, 34 is wrong.

14.
A train 800 metres long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 minute, then the length of the tunnel (in meters) is:



A.
130



B.
360




C.
500



D.
540



Answer: Option C
Explanation:
Speed =

78 x
5

m/sec
=

65

m/sec.




18




3



Time = 1 minute = 60 seconds.
Let the length of the tunnel be x metres.
Then,

800 + x

=
65



60


3

3(800 + x) = 3900
x = 500.

15.
The sum of ages of 5 children born at the intervals of 3 years each is 50 years. What is the age of the youngest child?



A.
4 years



B.
8 years




C.
10 years



D.
None of these



Answer: Option A
Explanation:
Let the ages of children be x, (x + 3), (x + 6), (x + 9) and (x + 12) years.
Then, x + (x + 3) + (x + 6) + (x + 9) + (x + 12) = 50
5x = 20
x = 4.
Age of the youngest child = x = 4 years.

Direction (for Q.No. 16):
Insert the missing number.

16.
11, 13, 17, 19, 23, 29, 31, 37, 41, (....)



A.
43



B.
47




C.
53



D.
51



Answer: Option A
Explanation:
Numbers are all primes. The next prime is 43.

17.
If log10 2 = 0.3010, then log2 10 is equal to:



A.
699

301





B.
1000

301






C.
0.3010



D.
0.6990



Answer: Option B
Explanation:
log2 10 =
1
=
1
=
10000
=
1000
.


log10 2

0.3010

3010

301



18.
By investing in 16% stock at 64, one earns Rs. 1500. The investment made is:



A.
Rs. 5640



B.
Rs. 5760




C.
Rs. 7500



D.
Rs. 9600



Answer: Option B
Explanation:
To earn Rs.
50
, investment = Rs. 64.


3


To earn Rs. 1500, investment = Rs.

64 x
3
x 1500

= Rs. 5760.




50





19.
Speed of a boat in standing water is 9 kmph and the speed of the stream is 1.5 kmph. A man rows to a place at a distance of 105 km and comes back to the starting point. The total time taken by him is:



A.
16 hours



B.
18 hours




C.
20 hours



D.
24 hours



Answer: Option D
Explanation:
Speed upstream = 7.5 kmph.
Speed downstream = 10.5 kmph.
Total time taken =

105
+
105
hours = 24 hours.



7.5

10.5



20.
A boatman goes 2 km against the current of the stream in 1 hour and goes 1 km along the current in 10 minutes. How long will it take to go 5 km in stationary water?



A.
40 minutes



B.
1 hour




C.
1 hr 15 min



D.
1 hr 30 min



Answer: Option C
Explanation:
Rate downstream =

1
x 60
km/hr = 6 km/hr.



10



Rate upstream = 2 km/hr.
Speed in still water =
1
(6 + 2) km/hr = 4 km/hr.


2


Required time =

5
hrs = 1
1
hrs = 1 hr 15 min.



4

4








Aptitude Test 1


Aptitude
Result & Statistics

1.
Find the greatest number that will divide 43, 91 and 183 so as to leave the same remainder in each case.



A.
4



B.
7




C.
9



D.
13



Answer: Option A
Explanation:
Required number = H.C.F. of (91 - 43), (183 - 91) and (183 - 43)
     = H.C.F. of 48, 92 and 140 = 4.

2.
Which of the following fraction is the largest ?



A.
7

8





B.
13

16






C.
31

40





D.
63

80





Answer: Option A
Explanation:
L.C.M. of 8, 16, 40 and 80 = 80.
7
=
70
;  
13
=
65
;  
31
=
62

8

80

16

80

40

80

Since,
70
>
65
>
63
>
62
, so
7
>
13
>
63
>
31


80

80

80

80

8

16

80

40

So,
7
is the largest.


8



3.
.009
= .01

?






A.
.0009



B.
.09




C.
.9



D.
9



Answer: Option C
Explanation:
Let
.009
= .01;     Then x =
.009
=
.9
= .9


x

.01

1



4.
The least perfect square, which is divisible by each of 21, 36 and 66 is:



A.
213444



B.
214344




C.
214434



D.
231444



Answer: Option A
Explanation:
L.C.M. of 21, 36, 66 = 2772.
Now, 2772 = 2 x 2 x 3 x 3 x 7 x 11
To make it a perfect square, it must be multiplied by 7 x 11.
So, required number = 22 x 32 x 72 x 112 = 213444
Learn more problems on : Square Root and Cube Root
Discuss about this problem : Discuss in Forum

5.
If x =
3 + 1
and y =
3 - 1
, then the value of (x2 + y2) is:


3 - 1

3 + 1






A.
10



B.
13




C.
14



D.
15



Answer: Option C
Explanation:
x =
(3 + 1)
x
(3 + 1)
=
(3 + 1)2
=
3 + 1 + 23
= 2 + 3.


(3 - 1)

(3 + 1)

(3 - 1)

2


y =
(3 - 1)
x
(3 - 1)
=
(3 - 1)2
=
3 + 1 - 23
= 2 - 3.


(3 + 1)

(3 - 1)

(3 - 1)

2


x2 + y2 = (2 + 3)2 + (2 - 3)2
   = 2(4 + 3)
   = 14

Direction (for Q.No. 6):
Each of the questions given below consists of a question followed by three statements. You have to study the question and the statements and decide which of the statement(s) is/are necessary to answer the question.

6.
What is Arun's present age?

I. 
Five years ago, Arun's age was double that of his son's age at that time.

II. 
Present ages of Arun and his son are in the ratio of 11 : 6 respectively.

 III. 
Five years hence, the respective ratio of Arun's age and his son's age will become 12 : 7.





A.
Only I and II




B.
Only II and III




C.
Only I and III




D.
Any two of the three




E.
None of these



Answer: Option D
Explanation:
 II. Let the present ages of Arun and his son be 11x and 6x years respectively.
  I. 5 years ago, Arun's age = 2 x His son's age.
III. 5 years hence,
Arun's Age
=
12


Son's age

7

Clearly, any two of the above will give Arun's present age.
Correct answer is (D).

7.
If A = x% of y and B = y% of x, then which of the following is true?



A.
A is smaller than B.



B.
A is greater than B




C.
Relationship between A and B cannot be determined.



D.
If x is smaller than y, then A is greater than B.




E.
None of these






Answer: Option E
Explanation:
x% of y =

x
x y

=

y
x x

= y% of x



100




100




A = B.

8.
If 20% of a = b, then b% of 20 is the same as:



A.
4% of a



B.
5% of a




C.
20% of a



D.
None of these



Answer: Option A
Explanation:
20% of a = b     
20
a = b.


100


b% of 20 =

b
x 20

=

20
a x
1
x 20

=
4
a = 4% of a.



100




100

100



100



9.
3 pumps, working 8 hours a day, can empty a tank in 2 days. How many hours a day must 4 pumps work to empty the tank in 1 day?



A.
9



B.
10




C.
11



D.
12



Answer: Option D
Explanation:
Let the required number of working hours per day be x.
More pumps, Less working hours per day (Indirect Proportion)
Less days, More working hours per day (Indirect Proportion)
Pumps
4
:
3

:: 8 : x

Days
1
:
2



4 x 1 x x = 3 x 2 x 8
x =
(3 x 2 x


(4)

x = 12.

10.
One pipe can fill a tank three times as fast as another pipe. If together the two pipes can fill the tank in 36 minutes, then the slower pipe alone will be able to fill the tank in:



A.
81 min.



B.
108 min.




C.
144 min.



D.
192 min.



Answer: Option C
Explanation:
Let the slower pipe alone fill the tank in x minutes.
Then, faster pipe will fill it in
x
minutes.


3



1
+
3
=
1


x

x

36


4
=
1


x

36

x = 144 min.

11.
A motorboat, whose speed in 15 km/hr in still water goes 30 km downstream and comes back in a total of 4 hours 30 minutes. The speed of the stream (in km/hr) is:



A.
4



B.
5




C.
6



D.
10



Answer: Option B
Explanation:
Let the speed of the stream be x km/hr. Then,
Speed downstream = (15 + x) km/hr,
Speed upstream = (15 - x) km/hr.

30
+
30
= 4
1


(15 + x)

(15 - x)

2


900
=
9


225 - x2

2

9x2 = 225
x2 = 25
x = 5 km/hr.

12.
A man took loan from a bank at the rate of 12% p.a. simple interest. After 3 years he had to pay Rs. 5400 interest only for the period. The principal amount borrowed by him was:



A.
Rs. 2000



B.
Rs. 10,000




C.
Rs. 15,000



D.
Rs. 20,000



Answer: Option C
Explanation:
Principal = Rs.

100 x 5400

= Rs. 15000.



12 x 3




13.
A man walked diagonally across a square lot. Approximately, what was the percent saved by not walking along the edges?



A.
20



B.
24




C.
30



D.
33



Answer: Option C
Explanation:
Let the side of the square(ABCD) be x metres.
Then, AB + BC = 2x metres.
AC = 2x = (1.41x) m.
Saving on 2x metres = (0.59x) m.
Saving % =

0.59x
x 100
%
= 30% (approx.)



2x





14.
By investing in 16% stock at 64, one earns Rs. 1500. The investment made is:



A.
Rs. 5640



B.
Rs. 5760




C.
Rs. 7500



D.
Rs. 9600



Answer: Option B
Explanation:
To earn Rs.
50
, investment = Rs. 64.


3


To earn Rs. 1500, investment = Rs.

64 x
3
x 1500

= Rs. 5760.




50





15.
A man buys a watch for Rs. 1950 in cash and sells it for Rs. 2200 at a credit of 1 year. If the rate of interest is 10% per annum, the man:



A.
gains Rs. 55



B.
gains Rs. 50




C.
loses Rs. 30



D.
gains Rs. 30



Answer: Option B
Explanation:
S.P.
= P.W. of Rs. 2200 due 1 year hence


= Rs.

2200 x 100




100 + (10 x 1)





= Rs. 2000.

Gain = Rs. (2000 - 1950) = Rs. 50.

Direction (for Q.No. 16):
Find the odd man out.

16.
10, 25, 45, 54, 60, 75, 80



A.
10



B.
45




C.
54



D.
75



Answer: Option C
Explanation:
Each of the numbers except 54 is multiple of 5.

Direction (for Q.Nos. 17 - 19):
Find out the wrong number in the given sequence of numbers.

17.
582, 605, 588, 611, 634, 617, 600



A.
634



B.
611




C.
605



D.
600



Answer: Option A
Explanation:
Alternatively 23 is added and 17 is subtracted from the terms. So, 634 is wrong.

18.
36, 54, 18, 27, 9, 18.5, 4.5



A.
4.5



B.
18.5




C.
54



D.
18



Answer: Option B
Explanation:
The terms are alternatively multiplied by 1.5 and divided by 3. However, 18.5 does not satisfy it.

19.
56, 72, 90, 110, 132, 150



A.
72



B.
110




C.
132



D.
150



Answer: Option D
Explanation:
The numbers are 7 x 8, 8 x 9, 9 x 10, 10 x 11, 11 x 12, 12 x 13.
So, 150 is wrong.

Direction (for Q.No. 20):
Insert the missing number.

20.
8, 24, 12, 36, 18, 54, (....)



A.
27



B.
108




C.
68



D.
72



Answer: Option A
Explanation:
Numbers are alternatively multiplied by 3 and divided by 2.
So, the next number = 54 ÷ 2 = 27.

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