## Number system hard questions with answers

Solve 10 number system hard questions in SSC CGL Set 30 in 12 minutes. Verify solutions from answers. Learn to solve quick from paired solution set.

Majority of these number system questions are difficult. You need to use basic to advanced number system concepts and techniques to solve these question in time. Best way to learn these is to go through carefully the paired solutions to these questions.

Answers and link to the solution set are at the end.

### 10 Number system hard questions SSC CGL Set 30 - time to solve 12 mins

**Problem 1.**

Thrice the square of a natural number decreased by four times the number is equal to 50 more than the number. The number is,

- 4
- 5
- 6
- 10

**Problem 2.**

The difference between two positive numbers is 3. If sum of their squares is 369, then the sum of the numbers is,

- 25
- 81
- 27
- 33

**Problem 3.**

A number consists of two digits such that the digit in the ten's place is less than the digit in the unit's place by 2. Three times the number added to $\displaystyle\frac{6}{7}$th of the reverse of the number is 108. The sum of the digits of the number is,

- 6
- 8
- 9
- 7

**Problem 4.**

Of three numbers, the second is twice the first and thrice the third. If the average of the numbers is 44, the difference between the first number and the third number is,

- 18
- 12
- 6
- 24

**Problem 5.**

A two digit number is five times the sum of its digits. If 9 is added to the number, the digits interchange their positions. The sum of the digits of the number is,

- 11
- 9
- 6
- 7

#### Problem 6.

In a three digit number, the digit at the hundred's place is two times the digit at the unit's place and sum of the three digits is 18. If the digits are reversed the number is reduced by 396. The difference of hundred's and ten's digits of the number is,

- 5
- 2
- 1
- 3

** Problem 7.**

If the sum of two numbers are multiplied by each number separately, the products so obtained are 247 and 114. The sum of the numbers is,

- 20
- 19
- 21
- 23

** Problem 8.**

A two digit number is three times the sum of its digits. If 45 is added to the number, its digits are interchanged. Sum of the digits of the number is,

- 11
- 7
- 5
- 9

**Problem 9.**

The numbers 2272 and 875 are divided by a three digit number giving same remainders. The sum of the digits of this three digit number is,

- 12
- 13
- 10
- 11

** Problem 10.**

A fraction having denominator 30 and lying between $\frac{5}{8}$ and $\frac{7}{11}$ is,

- $\frac{19}{30}$
- $\frac{18}{30}$
- $\frac{20}{30}$
- $\frac{21}{30}$

Learn to solve the questions quickly in time from the paired solutions to these questions at,

**Number system hard questions: SSC CGL Solution set 30.**

### Answers to the number system hard questions in SSC CGL Set 30

**Problem 1. Answer:** Option b: 5.

**Problem 2. Answer:** Option c : 27.

**Problem 3. Answer:** Option a: 6.

**Problem 4. Answer:** Option b: 12.

**Problem 5. Answer:** Option b: 9.

**Problem 6. Answer:** Option b : 2.

**Problem 7. Answer:** Option b: 19.

**Problem 8. Answer:** Option d: 9.

**Problem 9. Answer:** Option c: 10.

**Problem 10. Answer:** Option a: $\displaystyle\frac{19}{30}$.

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