## 71st SSC CGL level Question Set, 10th on topic Number System

This is the 71st question set of 10 practice problem exercise for SSC CGL exam and 10th on topic Number System. Students must complete this question set prescribed time first and then only refer to the corresponding solution set for extracting maximum benefits from this resource. The link of the solution set is given at the end.

In MCQ test, you need to deduce the answer in shortest possible time and select the right choice. You do not have to write the steps. Writing takes up valuable seconds that you can save by solving problems in mind and writing as little as possible.

Based on our analysis and experience we have seen that, for accurate and quick answering, the student

- must have complete understanding of the basic concepts in the topic area
- is adequately fast in mental math calculation
- should try to solve each problem using the basic and rich concepts in the specific topic area and
- does most of the deductive reasoning and calculation in his or her head rather than on paper.

Actual problem solving is done in the fourth layer. You need to use **your problem solving abilities** to gain an edge in competition.

### 71st question set - 10 problems for SSC CGL exam: 10th on topic Number System - time 15 mins

#### Problem** 1.**

If 1 is added to both the numerator and denominator of a fraction it become $\displaystyle\frac{1}{4}$. If 2 is added to both the numerator and denominator it becomes $\displaystyle\frac{1}{3}$. Sum of the numerator and denominator is,

- 13
- 8
- 27
- 22

#### 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.

If 2 is subtracted from the sum of digits of a two digit number whose unit's digit is twice the ten's digit, the result is one-sixth of the number. The number is,

- 25
- 36
- 24
- 48

#### Problem** 4.**

A number when divided by 361 gives a remainder 47. If the same number is divided by 19 what will be the remainder?

- 1
- 3
- 8
- 9

#### Problem** 5.**

If total head count of cows and hens in a farm is 180 and the total leg count of same cows and hens is 420, the number of cows is,

- 130
- 150
- 30
- 50

#### 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.**

Find the maximum value of $F$ in the following equation, $5E9+2F8+3G7=1114$ where $E$, $F$ and $G$ stands for any integer.

- 5
- 9
- 7
- 8

#### Problem** 9.**

The least number that should be added to 2055 so that the sum is exactly divisible by 27 is,

- 24
- 28
- 27
- 31

** Problem** 10.

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

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

The answers and list of related reading matter on number system are given below.

### Answers to the problems

**Problem 1. Answer:** Option b: 8.

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

**Problem 3. Answer:** Option c: 24.

**Problem 4. Answer:** Option d: 9.

**Problem 5. Answer:** Option c: 30.

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

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

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

**Problem 9. Answer:** Option a: 24.

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

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