## 54th SSC CGL level Question Set, 8th on topic Number System

This is the 54th question set of 10 practice problem exercise for SSC CGL exam and 8th 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.

### 54th question set- 10 problems for SSC CGL exam: 8th on topic Number System - time 15 mins

**Problem 1.**

Sum of squares of two positive integers is 100 and the difference of their squares is 28. The sum of the numbers is,

- 15
- 14
- 13
- 12

**Problem 2.**

A number when divided by 6 leaves a remainder of 3. When the square of the number is divided by 6 the remainder is,

- 0
- 1
- 3
- 2

**Problem 3.**

The average of 5 consecutive positive even numbers is 86. What is the product of the third and the fourth numbers?

- 7704
- 4077
- 4707
- 7568

**Problem 4.**

A four digit number is formed by repeating a 2 digit number like 1212, 3434 etc. Any number of this form is always divisible by,

- 13
- 11
- 7
- Smallest 3 digit prime number

**Problem 5.**

The product of two consecutive odd numbers is 28899. The square root of the smaller number is,

- 13
- 7
- 11
- 3

#### Problem 6.

The largest number that exactly divides any number of the form $p^3-p$, where $p$ is a natural number, is,

- 6
- 12
- 2
- 3

** Problem 7.**

How many numbers less than 1000 are multiples of both 13 and 10?

- 7
- 6
- 8
- 9

** Problem 8.**

A number when divided by 5 leaves a remainder of 3. What will be the remainder when the square of the same number is divided by 5?

- 1
- 4
- 2
- 3

**Problem 9.**

The largest number which when divides 398, 436 and 542 leaves remainders as 7, 11 and 15 respectively, is,

- 7
- 13
- 17
- 23

** Problem 10.**

In a series of odd numbers, the first number is 1, the second 3, the third 5 and so on. What will be the 200th odd number in the series?

- 357
- 421
- 599
- 399

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