## Aptitude questions and answers for number system

1) If one-third of one-fourth of a number is 15, then three-tenths of that number is:

A. 35

B. 36

C. 45

D. 54

Explanation:

Let the number be x.
Then,1/3of 1/4of x = 15
x = 15 x 12 = 180.
So, required number = 3/10 x 180 = 54.

2. Find the number, when 15 is subtracted from 7 times the number, the result is 10 more than twice the number.

A. 5

B. 15

C. 7.5

D. 4

Explanation:

Let the number be x.
7x -15 = 2x + 10 => 5x = 25 => x = 5

3. What is the place value of 7 in the numeral 2734?

A. 70

B. 7

C. 700

D. 7.00

Explanation:

7 × 100 = 700

A number when divided by a divisor leaves a remainder of 24

4. Difference between a two-digit number and the number obtained by interchanging the two digits is 36, what is the difference between two numbers

A. 2

B. 4

C. 8

D. 12

Explanation:

Let the ten digit be x, unit digit is y.
Then (10x + y) - (10y + x) = 36
=> 9x - 9y = 36
=> x - y = 4.

5. The difference between a number and its three- fifth is 50. What is the number?

A. 75

B. 100

C. 125

D. None of these

Explanation:

Let the number be x.
Then, x-3/5x = 50 <=> 2/5x = 50 <=> x = (50*5/2) = 125.

6. Which of the following is an odd prime number?

A. 1

B. 9

C. 3

D. 15

Explanation:

Among the given options, 3 is an odd prime number. Therefore, the answer is option 3.

7. 53904 / 16 / 8 = ?

A. 485

B. 434

C. 456

D. none of these

Solution :

Given expression is 53904 / 16 / 8
Simplifying the above expression, we have:
53904 / 16 / 8 = 53904 x (1/16) x (1/8)
= 13476 x (1/8) x (1/4)
=3369 x 1/8 = 421.13

8. If 3+4=21, 5+2=35, 4+2=24 what is the value of 5+3?

A. 53

B. 48

C. 35

D. 40

Explanation:

3+4=7*3 = 21
5+2=7*5 = 35
4+2=6*4 = 24
5+3=?
5+3=8*5=40

9. A number when divided by 296 leaves 75 as the remainder. When the same number is divided by 37, the remainder will be:

A. 1

B. 3

C. 5

D. 2

Explanation:

Let the Number be Y.
Then Y = 296 q + 75
= (37 x 8)q +( 37 x 2) + 1
= 37 (8q + 2) + 1
Thus, when the number is divided by 37, the remainder is 1

10. What is the difference between the place value and face value of 3 in the numeral 1375?

A. 300

B. 3

C. 297

D. 303

Explanation:

place value of 3 = 3 × 100 = 300
face value of 3 = 3
300 - 3 = 297.

11. What is the minimum number of square marbles required to tile a floor of length 5 meters 78 cm and width 3 meters 74 cm?

A. 176

B. 187

C. 540

D. 748

Explanation:

The marbles used to tile the floor are square marbles.
Therefore, the length of the marble=width of the marble.
As we have to use a whole number of marbles, the side of the square should a factor of both 5 m 78 cm and 3m 74. And it should be the highest factor of 5 m 78 cm and 3m 74.
5 m 78 cm = 578 cm and 3 m 74 cm = 374 cm.
The HCF of 578 and 374 = 34.
Hence, the side of the square is 34.
The number of such square marbles required,
=(578×374)/(34×34)
=17×11= 187 marbles

12. (2400/192) x (2592/72) = ?

A. 450

B. 250

C. 348

D. 429

Explanation:

The given expression is (2400/192) x (2592/72)
Simplifying the above expression, we have:
(2400/192) x (2592/72) = (800/64) x ( 1296/36)
(50/4) x 36
50 x 9 = 450. Hence the answer is option a.

13. Of the three numbers, the second is twice the first and is also thrice the third if the average of the three numbers is 44. Find the largest number?

A. 24

B. 72

C. 65

D. 55

Explanation:

Let the third number be x.
Then the second number = 3x.
First number=3x/2.
Therefore x+3x + (3x/2) = (44*3) or x=24
So largest number = 2nd number = 3x = 72.

14. Three-fourth of a number is 60 more than its one third. The number is :

A. 84

B. 108

C. 144

D. None of these

Explanation:

Let the number be x.
Then, 3/4x-1/3x = 60 <=> 5x/12 = 60 <=> x=(60*12/5) = 144.

15. Find a positive number which when increased by 17 is equal to 60 times the reciprocal of the number?

A. 17

B. 15

C. 8

D. 3

Explanation:

If the number is x,
Then, x + 17 = 60/x
x^2 + 17x - 60 = 0
(x + 20)(x - 3) = 0
x = 3, -20, so x = 3 (as 3 is positive)

16. Ratio between two numbers is 3: 4 and their sum is 420. Find the smaller number?

A. 240

B. 180

C. 160

D. 140

Explanation:

3x + 4x = 420
x = 60 => 3x = 180
A number when divided by a divisor leaves a remainder of 24.

17. When twice the original number is divided by the same divisor, the remainder is 11. What is the value of the divisor?

A. 13

B. 59

C. 35

D. 37

Explanation:

Let the original number be 'a'
Let the divisor be 'd'
Let the quotient of the division of a by d be 'x'
Therefore, we can write the relation as a/d=x and the remainder is 24. i.e., a=dx+24
When twice the original number is divided by d,2a is divided by d.
We know that a=dx+24. Therefore, 2a=2dx+48
The problem states that (2dx+48)/d leaves a remainder of 11.
2dx is perfectly divisible by d and will, therefore, not leave a remainder.
The remainder of 11 was obtained by dividing 48 by d.
When 48 is divided by 37, the remainder that one will obtain is 11.
Hence, the divisor is 37.

18. The sum of all two-digit numbers divisible by 5 is

A. 945

B. 678

C. 439

D. 568

Explanation:

Required numbers are 10,15,20,25,...,95
This is an A.P. in which a=10,d=5 and l=95.
Let the number of terms in it be n.Then t=95
So a+(n-1)d=95.
10+(n-1)*5=95,then n=18.
Required sum=n/2(a+l)=18/2(10+95)=945.

19. There are 20 people at a party. If every person shakes hand with every other person, what is the total number of handshakes?

A. 180

B. 155

C. 145

D. 190

Explanation:

1st person will shake hands with 19 other persons. 2nd person will shake hands with the remaining 18 persons, and so on.
Therefore, total number of handshakes.
= 19 + 18 + 17+ ……………………+ 3 + 2 + 1 = 19 =(19(19+1)/2) =190
So, the correct answer is option 4.

20. The five-digit number 7500A8 is divisible by 4. How many values of A are possible?

A. 0

B. 3

C. 5

D. 4

Explanation:

To find divisibility by 4, we need to consider the last two digits of the number, these should be divisible by 4. Hence, A can take values equal to 0, 2, 4, 6, and 8. Therefore 5 values are possible.
So, the correct answer is option C.

21. The sum of two numbers is 40 and their difference is 4. The ratio of the numbers is :

A. 11: 9

B. 11: 18

C. 21: 19

D. 22: 9

Explanation:

Let the numbers be x and y. Then,
x + y/x - y = 40/4 = 10
(x + y) = 10(x - y)
9x = 11y
x/y = 11/9

22. 64576 is divisible by 3 or not?

A. 64576 is not divisible by 3

B. 64576 is divisible by 3

C. 64576 is not divisible by 3,4

D. None of these

Explanation:

Step 1 - Sum of its digits is 6 + 4 + 5 + 7 + 6 = 28
which is not divisible by 3.
Result - 64576 is not divisible by 3.

23. Find a positive number which when increased by 17 is equal to 60 times the reciprocal of the number?

A. 17

B. 15

C. 8

D. 3

Explanation:

If the number is x,
Then, x + 17 = 60/x
x2 + 17x - 60 = 0
(x + 20)(x - 3) = 0
x = 3, -20, so x = 3 (as 3 is positive)

24. Find the number which when multiplied by 15 is increased by 196

A. 10

B. 12

C. 14

D. 16

Explanation:

Let the number be x.
Then, 15x = x + 196
=› 14 x= 196
=› x = 14.

25. In a meet, persons from five different places have assembled in Bangalore High School. The five places the persons come to represent are 42,60,210,90 and 84. What is the minimum number of rooms that would be required to accommodate so that each room has the same number of occupants and occupants are all from the same places?

A. 44

B. 62

C. 81

D. 96

Explanation:

All the students from each have to be accommodated in a certain number of rooms.
There should be no person leftover (remainder) from any places who can be clubbed together with the person leftover from other places.
To have the minimum number of rooms, the capacity of each room is HCF of all the numbers.
HCF(42,60,210,90,84)=6
Thus Min number of rooms =(42+60+210+90+84)/6=81

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