## 29th SSC CGL Tier II level Question Set, 1st on Number system problems

In this 29th question set of 10 practice problem exercise for SSC CGL Tier II exam and 1st on topic Number System, a few of the problems 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.

### 29th question set - 10 problems for SSC CGL Tier II exam: 1st on Number system problems - time 12 mins

**Problem 1.**

The smallest fraction that should be added to the sum of $2\frac{1}{2}$, $3\frac{1}{3}$, $4\frac{1}{4}$, and $5\frac{1}{5}$, to make the result a whole number is,

- $\frac{43}{60}$
- $\frac{13}{60}$
- $\frac{17}{60}$
- $\frac{1}{4}$

**Problem 2.**

Three electronic devices make a beep after every 48 seconds, 72 seconds and 108 seconds respectively. They beeped together at 10 am. The time when the devices will next make a beep together at the earliest is,

- 10:07:48 hours
- 10:07:12 hours
- 10:07:36 hours
- 10:07:24 hours

**Problem 3.**

Two baskets have 640 oranges. If $\displaystyle\frac{1}{5}$th of the oranges in the first basket be taken to the second basket then number of oranges in both baskets become equal. The number of oranges in the first basket was,

- 300
- 600
- 400
- 800

**Problem 4.**

Which of the following statement(s) is/are true?

- The sum of first 20 odd numbers is 400.
- The total number of positive factors of 72 is 12.
- The largest two digit prime number is 97.

- Only II and III
- Only I and III
- Only I and II
- All are true

**Problem 5.**

N is the largest two digit number which when divided by 3, 4 and 6 leaves the remainders 1, 2 and 4 respectively. What is the remainder when N is divided by 5?

- 4
- 1
- 0
- 2

#### Problem 6.

Twenty one times a positive integer is less than its square by 100. The value of the positive integer is,

- 26
- 42
- 25
- 41

** Problem 7.**

A General of an army wanted to form a square from 36562 armies. After the square formation, he found some armies still left. How many armies were left?

- 81
- 97
- 65
- 36

** Problem 8.**

The sum of two positive integers is 80 and the difference between them is 20. What is the difference between squares of these numbers?

- 2000
- 1600
- 1400
- 1800

** Problem 9.**

Sum of three fractions is $2\frac{11}{24}$. On dividing the largest fraction by the smallest fraction $\displaystyle\frac{7}{6}$ is obtained which is greater than the middle fraction by $\displaystyle\frac{1}{3}$. The smallest fraction is,

- $\displaystyle\frac{5}{8}$
- $\displaystyle\frac{5}{6}$
- $\displaystyle\frac{3}{7}$
- $\displaystyle\frac{3}{4}$

** Problem 10.**

A certain number when successively divided by 8 and 11 leaves remainder 3 and 7 respectively. Find the remainder if the same number is divided by 88.

- 51
- 57
- 59
- 61

### Answers to the questions

**Problem 1. Answer:** Option a: $\displaystyle\frac{43}{60}$.

**Problem 2. Answer:** Option b: 10:07:12 hours.

**Problem 3. Answer:** Option c: 400.

**Problem 4. Answer:** Option d: All are true.

**Problem 5. Answer:** Option a: 4.

**Problem 6. Answer:** Option c: 25.

**Problem 7. Answer:** Option a: 81.

**Problem 8. Answer:** Option b: 1600.

**Problem 9. Answer:** Option d: $\displaystyle\frac{3}{4}$.

**Problem 10. Answer:** Option c: 59.

#### 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 Tier II level Solution Set 29 on Number System 1**

**SSC CGL Tier II level Question Set 29 on Number System 1**

**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**

### Solved Question sets on Number System, HCF and LCM for SSC CHSL

**SSC CHSL level Solved Question set 3 on Number system 1**

**SSC CHSL level Solved Question set 4 on Number system 2**

**SSC CHSL level Solved Question set 5 on HCF and LCM 1**

**SSC CHSL level Solved Question set 6 on HCF and LCM 2**