## 89th SSC CGL level Question Set, 11th on topic Number System

In this 89th question set of 10 practice problem exercise for SSC CGL exam and 11th on topic Number System, a few of the problems especially on fractions should pose a bit of challenge to the student. But with concept and technique based problem solving approach, * explained in the paired solution set*, the student should easily solve most of the problems wholly in mind.

This question set can be used as a * mini-mock test on number system*, even for competitive tests other than SSC CGL.

We should mention that 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. This is what we call **Solving in mind.**

In the solution set, **main focus always is on how to solve in mind in minimum time.**

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.

The * answers to the questions* are given at the end.

### 89th question set - 10 problems for SSC CGL exam: 11th on topic Number System - time 12 mins

#### Problem** 1.**

A fraction is greater than its reciprocal by $\displaystyle\frac{9}{20}$. What is the fraction?

- $\displaystyle\frac{4}{5}$
- $\displaystyle\frac{5}{4}$
- $\displaystyle\frac{4}{3}$
- $\displaystyle\frac{3}{4}$

#### Problem** 2.**

A number is greater than 58 times its reciprocal by $\displaystyle\frac{3}{4}$. What is the number?

- $8$
- $-8$
- $-12$
- $12$

#### Problem 3.

The ten's digit of a two digit number is larger than the unit's digit by 7. If we subtract 63 from the number, the new number obtained is a number formed by interchange of the digits. The new number formed in this way don't have any factor common with the original number. Find the original number.

- 92
- 29
- 70
- 18

#### Problem** 4.**

The reciprocal of the sum of reciprocals of $\displaystyle\frac{2}{9}$ and $\displaystyle\frac{7}{10}$ is,

- $\displaystyle\frac{83}{90}$
- $\displaystyle\frac{14}{83}$
- $\displaystyle\frac{83}{14}$
- $\displaystyle\frac{90}{83}$

#### Problem** 5.**

Which one is the largest among the fractions, $\displaystyle\frac{5}{113}$, $\displaystyle\frac{7}{120}$, $\displaystyle\frac{13}{125}$ and $\displaystyle\frac{17}{160}$

- $\displaystyle\frac{13}{145}$
- $\displaystyle\frac{7}{120}$
- $\displaystyle\frac{5}{113}$
- $\displaystyle\frac{17}{160}$

#### Problem 6.

The sum of three consecutive natural numbers each divisible by 5 is 225. The middle number among them is,

- 75
- 80
- 85
- 70

#### Problem** 7.**

A rational number lying between $\displaystyle\frac{1}{2}$ and $\displaystyle\frac{3}{5}$ is,

- $\displaystyle\frac{3}{5}$
- $\displaystyle\frac{2}{5}$
- $\displaystyle\frac{11}{20}$
- None of these

#### Problem** 8.**

$\left(999\displaystyle\frac{999}{1000}\times{7}\right)$ is equal to,

- $7000\displaystyle\frac{7}{1000}$
- $6683\displaystyle\frac{7}{1000}$
- $6993\displaystyle\frac{7}{1000}$
- $6999\displaystyle\frac{993}{1000}$

#### Problem** 9.**

The number 323 has,

- three prime factors
- two prime factors
- five prime factors
- no prime factor

** Problem** 10.

A, B, C and D purchase a gift worth Rs.60. A pays $\frac{1}{2}$ of what others are paying. B pays $\frac{1}{3}$rd of what others are paying and C pays $\frac{1}{4}$th of what others are paying. What is the amount paid by D?

- Rs.13
- Rs.16
- Rs.15
- Rs.14

The *answers to the questions and list of relevant reading material* are given below.

### Answers to the questions

**Problem 1. Answer:** Option b: $\displaystyle\frac{5}{4}$.

**Problem 2. Answer:** Option a: 8.

**Problem 3. Answer:** Option a: 92.

**Problem 4. Answer:** Option b: $\displaystyle\frac{14}{83}$.

**Problem 5. Answer:** Option d: $\displaystyle\frac{17}{160}$.

**Problem 6. Answer:** Option a: 75.

**Problem 7.** **Answer:** Option c: $\displaystyle\frac{11}{20}$.

**Problem 8. Answer:** Option d: $6999\displaystyle\frac{993}{1000}$.

**Problem 9. Answer:** Option b: two prime factors.

**Problem 10. Answer:** Option a: Rs.13.

#### Valuable guidelines with links to resources on SSC CGL

**7 steps for sure success in SSC CGL tier 1 and tier 2 Competitive tests**

#### Tutorials

**Numbers and Number system and basic mathematical operations**

**Factorization or finding out factors**

**Fractions and decimals basic concepts part 1**

**Basic and Rich Algebra concepts for elegant solutions of SSC CGL problems - **** though on Algebra, it should be useful.**

#### How to solve number system problems quickly in a few steps

**Componendo dividendo applied on number system and ratio proportion problems**

#### Question sets and Solution sets on Number system

**SSC CGL level Solution Set 89 on Number System 11**

**SSC CGL level Question Set 89 on Number System 11**

**SSC CGL level Question Set 71 on Number System 10**

**SSC CGL level Solution Set 71 on Number System 10**

**SSC CGL level Question Set 55 on Number System 9**

**SSC CGL level Solution Set 55 on Number System 9**

**SSC CGL level Question Set 54 on Number System 8**

**SSC CGL level Solution Set 54 on Number System 8**

**SSC CGL level Question Set 46 on Number System 7**

**SSC CGL level Solution Set 46 on Number System 7**

**SSC CGL level Question Set 30 on Number System 6**

**SSC CGL level Solution Set 30 on Number System 6**

**SSC CGL level Question Set 28 on Arithmetic Number System**

**SSC CGL level Solution Set 28 on Arithmetic Number System**

**SSC CGL level Question Set 15 on Arithmetic Number System**

**SSC CGL Level Solution Set 15 on Arithmetic Number System**

**SSC CGL level Question Set 14 on Arithmetic Number System**

**SSC CGL level Solution Set 14 on Arithmetic Number System**

**SSC CGL level Question Set 7 on Arithmetic Number System**

**SSC CGL level Solution Set 7 on Arithmetic Number System**

**SSC CGL level Solution Set 3 on Arithmetic Number System**

**SSC CGL level Question Set 3 on Arithmetic Number System**