Number Problems

Number Problems 

Dear Reader,
Below are four problems based on number system, dealing with some exact divisions.

Question 1

The least number to be added to 3545 so that 65 divides the result exactly is:

a) 50 b) 40 c) 30 d) 20

Answer : c) 30

Solution :

On dividing 3545 by 65, we get remainder 35.
i.e., 3545 = 54x65 + 35.
Therefore, the required number to be added = 65 - 35 = 30.

To check, 3545 + 30 = 3575 = 55 x 65.

Question 2

Which of the following number should be added to 28614 in order to obtain a multiple of 87?

a) 17 b) 12 c) 14 d) 9

Answer : d) 9.

Solution :

On dividing the given number 28614 by 87, we have the remainder = 78.
i.e., 328x87 + 78 = 28614.
Therefore, the required number to be added = 87 - 78 = 9

To check, 28614 + 9 = 28623 = 329x87.

Question 3

What will be the smallest number that must be subtracted from 24305 so that the remainder is exactly divisible by 54?

a) 11 b) 5 c) 7 d) 9

Answer : b) 5

Solution :

On dividing the given number 24305 by 54, we have the remainder = 5.
i.e., 450x54 + 5 = 24305
450x54 = 24305 - 5.
Therefore, the required number to be subtracted = 5

Question 4

What is the least number by which 84 must be multiplied in order to produce a multiple of 128?

a) 32 b) 44 c) 56 d) 68

Answer : a) 32

Solution :

Let the required number be X.
Then, X x 84 is a multiple of 128.
Therefore, X x 84 is a multiple of both 128 and 84.
i.e., LCM of 84 and 128.
LCM of 84 and 128 is 2688.

i.e., the least number which is the multiple of both 84 and 128 is 2688.

Now, X x 84 = 2688
X = 2688/84 = 32.