This Article consist of most important ” Problems on Numbers ” topic that are mostly asked in all competitive exams. We collected these questions from the students who appeared in exams. Now try to solve these questions.

## Problems on Numbers

**Question : 1** A number consists of two digits. If the digits interchange places and the new number is added to the original number, then the resulting number will be divisible by:

A. 3

B. 5

C. 9

D. 11

**Show Answer**

**Correct Answer : ** **D**

**Explanation : **

Let the ten’s digit be x and unit’s digit be y.

Then, number = 10x + y.

Number obtained by interchanging the digits = 10y + x.

(10x + y) + (10y + x) = 11(x + y), which is divisible by 11.

**Question : 2** The sum of the digits of a two-digit number is 15 and the difference between the digits is 3. What is the two-digit number?

A. 69

B. 78

C. 96

D. Cannot be determined

**Show Answer**

**Correct Answer : ** **D**

**Explanation : **

Let the ten’s digit be x and unit’s digit be y.

Then, x + y = 15 and x – y = 3 or y – x = 3.

Solving x + y = 15 and x – y = 3, we get: x = 9, y = 6.

Solving x + y = 15 and y – x = 3, we get: x = 6, y = 9.

So, the number is either 96 or 69.

Hence, the number cannot be determined.

**Question : 3 ** 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. 8

C. 16

D. None of these

**Show Answer**

**Correct Answer : ** **B**

**Explanation : **

Since the number is greater than the number obtained on reversing the digits, so the ten’s digit is greater than the unit’s digit.

Let ten’s and unit’s digits be 2x and x respectively.

Then, (10 x 2x + x) – (10x + 2x) = 36

9x = 36

x = 4.

Required difference = (2x + x) – (2x – x) = 2x = 8.

**Question : 4 ** The difference between a two-digit number and the number obtained by interchanging the positions of its digits is 36. What is the difference between the two digits of that number?

A. 3

B. 4

C. 9

D. None of these

**Show Answer**

**Correct Answer : ** **B**

**Explanation : **

Let the ten’s digit be x and unit’s digit be y.

Then, (10x + y) – (10y + x) = 36

9(x – y) = 36

x – y = 4

**Question : 5 ** Three times the first of three consecutive odd integers is 3 more than twice the third. The third integer is:

A. 9

B. 11

C. 13

D. 15

**Show Answer**

**Correct Answer : ** **D**

**Explanation : **

Let the three integers be x, x + 2 and x + 4.

Then, 3x = 2(x + 4) + 3 x = 11.

Third integer = x + 4 = 15