## 55th SSC CGL level Question Set, 9th on topic Number System

This is the 55th question set of 10 practice problem exercise for SSC CGL exam and 9th on topic Number System. Students must complete this question set in prescribed time first and then only refer to the corresponding solution set for extracting maximum benefits from this resource.

In MCQ test, you need to deduce the answer in shortest possible time and select the right choice.

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.

### 55th question set- 10 problems for SSC CGL exam: 9th on topic Number System - time 15 mins

**Problem 1.**

The smallest number that can be added to 803642 in order to obtain a multiple of 11 is,

- 1
- 7
- 9
- 4

**Problem 2.**

A six digit number is formed by repeating a three digit number twice. For example, two such numbers are, 123123 and 728728. Any number of this form will always be divisible by,

- 7 only
- 13 only
- 1001
- 11 only

**Problem 3.**

The product of two positive numbers is 11520 and the result of their division is $\displaystyle\frac{9}{5}$. The difference between the numbers is,

- 70
- 60
- 64
- 74

**Problem 4.**

If $a$ and $b$ are two odd positive integers, by which of the following positive integers is $(a^4-b^4)$ is always divisible?

- 12
- 3
- 6
- 8

**Problem 5.**

The number 45 is written as a sum of four numbers so that when 2 is added to the first number, 2 is subtracted from the second number, the third number is multiplied by 2 and the fourth divided by 2, the results we get are the same. The four numbers are,

- 8, 12, 10, 15
- 1, 8, 15, 21
- 2, 12, 5, 26
- 8, 12, 5, 20

#### Problem 6.

The fractions $\displaystyle\frac{1}{3}$, $\displaystyle\frac{4}{7}$, and $\displaystyle\frac{2}{5}$ written in ascending order is,

- $\displaystyle\frac{4}{7} \lt \displaystyle\frac{1}{3} \lt \displaystyle\frac{2}{5}$
- $\displaystyle\frac{4}{7} \gt \displaystyle\frac{1}{3} \gt \displaystyle\frac{2}{5}$
- $\displaystyle\frac{2}{5} \lt \displaystyle\frac{4}{7} \lt \displaystyle\frac{1}{3}$
- $\displaystyle\frac{1}{3} \lt \displaystyle\frac{2}{5} \lt \displaystyle\frac{4}{7}$

** Problem 7.**

The numerator of a fraction is 4 less than its denominator. If the numerator is decreased by 2 and the denominator is increased by 1 the denominator becomes eight times the numerator. The fraction is,

- $\displaystyle\frac{5}{9}$
- $\displaystyle\frac{3}{7}$
- $\displaystyle\frac{13}{17}$
- $\displaystyle\frac{4}{8}$

** Problem 8.**

The greatest number among $1.2\times{0.83}$, $1.02-\displaystyle\frac{0.6}{24}$, $0.7+\sqrt{0.16}$, and $\sqrt{1.44}$ is,

- $1.02-\displaystyle\frac{0.6}{24}$
- $1.2\times{0.83}$
- $0.7+\sqrt{0.16}$
- $\sqrt{1.44}$

**Problem 9.**

$(49)^{15} - 1$ is exactly divisible by,

- 50
- 51
- 8
- 29

** Problem 10.**

The greatest fraction among $\displaystyle\frac{2}{3}$, $\displaystyle\frac{5}{6}$, $\displaystyle\frac{11}{15}$, and $\displaystyle\frac{7}{8}$ is,

- $\displaystyle\frac{5}{6}$
- $\displaystyle\frac{7}{8}$
- $\displaystyle\frac{11}{15}$
- $\displaystyle\frac{2}{3}$

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