## Third SSC CGL level Question Set, topic Arithmetic Number system

This is the third question set of 10 practice problem exercise for SSC CGL exam on topic Arithmetic Number System. Students must complete this question set in prescribed time first and then only refer to the corresponding solution set.

It is emphasized here that answering in MCQ test is not at all the same as answering in a school test where you need to derive the solution in perfectly elaborated steps.

In MCQ test instead, you need basically to deduce the answer in shortest possible time and select the right choice. None will ask you about what steps you followed.

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

Actual problem solving happens in items 3 and 4 above. But how to do that?

You need to use **your problem solving abilities** only. There is no other recourse.

### Third question set- 10 problems for SSC CGL exam: topic Arithmetic Number System - time 20 mins

**Q1.** If $3^{4x}\times{9^{6x}} = 81^8$, $x=?$,

- 2
- 3
- 4
- 8

**Q2.** Which one of the following is a perfect square as well as a cube?

- 81
- 125
- 343
- 64

**Q3.** If the digits of a two digit number are interchanged in position, the absolute value of the difference of the two numbers would be always divisible by,

- 5
- 7
- 9
- 11

**Q4.** If two bells chime at intervals of 4 mins and 15 mins, after how long would they chime together first if they had chimed together in the beginning?

- 26 mins
- 52 mins
- 1 hour 18 minutes
- 1 hour

**Q5.** How many numbers from 20 to 50 have no number from 2 to 10 as factors?

- 0
- 14
- 7
- 4

**Q6.** $\displaystyle\frac{256\times{256} - 144\times{144}}{112}$ is,

- 420
- 400
- 360
- 360

** Q7.** If the digits in the unit's and ten's places of a three digit number are interchanged, the new number formed is found to be larger than the original by 63. All possible values that the unit's digit of the original number can take are,

- 7, 8, 9
- 2, 7, 9
- 0, 1, 2
- 1, 2, 8

** Q8.** The sum of all the three digit numbers, each of which on division by 5 leaves a remainder 3 is,

- 180
- 1550
- 6995
- 99090

**Q9.** Unit's digit in $264^{102} + 264^{103}$ is,

- 0
- 4
- 6
- 8

** Q10.** Unit's digit of $2137^{754}$ is,

- 1
- 3
- 7
- 9

### Other resources on Number system and related topic

You may refer to our other useful resources on number system and other related topics especially algebra.

The first should of course be the solution to this question. Carefully go through the solution absorbing the ideas explained in the process of reaching the solutions. You won't be able to retain this knowledge unless you apply this analytical deductive thinking on other problems repeatedly.

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

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

#### Solution to this question set

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

#### Tutorials

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

**Factorization or finding out factors**

**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 Question Set 71 on Number System 10**

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

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

**SSC CGL level Question Set 55, 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 Sysem**

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

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

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

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