**Number System Questions for SSC CHSL Set-2 PDF**

Download SSC CHSL Number System Questions with answers Set-2 PDF based on previous papers very useful for SSC CHSL Exams. Top-10 Very Important Questions for SSC Exam

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**Question 1: **A number x when divided by 289 leaves 18 as the remainder. The same number when divided by 17 leaves y as a remainder. The value of y is

a) 2

b) 3

c) 1

d) 5

**Question 2: **In the following number series a wrong number is given. Find out that number.

8, 18, 40, 86, 178, 370, 752

a) 178

b) 180

c) 128

d) 156

**Question 3: **Find the unit digit in the product $(4387)^{245} \times (621)^{72}$.

a) 1

b) 2

c) 5

d) 7

**Question 4: **When a number is increased by 24, it becomes 110% of itself. What is the number?

a) 288

b) 360

c) 216

d) 240

**Question 5: **Three consecutive natural numbers are such that the square of the greatest is greater than the product of the other two by 16. The smallest of these numbers is

a) 5

b) 6

c) 7

d) 4

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**Question 6: **How many numbers are there from 300 to 650 which are completely divisible by both 5 and 7?

a) 8

b) 9

c) 10

d) 12

**Question 7: **The sum of a non-zero number and twenty times its reciprocal is 9. What is the number?

a) -5

b) 3

c) -3

d) 5

**Question 8: **If 49 is subtracted from the square of a number, then the result obtained is 576. What is the number?

a) 24

b) 25

c) 23

d) 27

**Question 9: **$\ 3^{11} + 3^{12} + 3^{13} + 3^{14}\ $ is divisible by _____.

a) 7

b) 8

c) 11

d) 14

**Question 10: **If $A = 1 – 10 + 3 – 12 + 5 – 14 + 7 + …$ upto 60 terms, then what is the value of $A$?

a) -360

b) -310

c) -240

d) -270

**Answers & Solutions:**

**1) Answer (C)**

The number is of the form 289n+18.

Which is equal to 17*(17n+1) +1

So, when the number is divided by 17, the reminder is 1

**2) Answer (A)**

In the series : 8, 18, 40, 86, 178, 370, 752

The pattern followed is that we multiply the first number by 2 and add 2 to it, for the second number, we multiply by 2 and add 4, for the third, multiply by 2 and 6 and so on…

8 x 2 + 2 = 18

18 x 2 + 4 = 40

40 x 2 + 6 = 86

86 x 2 + 8 = **180**

180 x 2 + 10 = 370

370 x 2 + 12 = 752

So, the wrong number is 178.

**3) Answer (D)**

we need to find unit digit of $(4387)^{245} \times (621)^{72}$

unit digit of ${4387^{245}}$ = unit digit of ${7^1}$ = 7

unit digit of ${621^{72}}$ = 1

and hence 7 x 1 = 7 is the unit digit for the given expression

**4) Answer (D)**

Let the number be $100x$

According to ques, => $100x + 24 = \frac{110}{100} \times 100x$

=> $100x + 24 = 110x$

=> $110x – 100x = 24$

=> $x = \frac{24}{10} = 2.4$

$\therefore$ Number = $100 \times 2.4 = 240$

=> Ans – (D)

**5) Answer (D)**

Let the three consecutive natural numbers be $(x-1) , (x) , (x+1)$ where $x \geq 2$

Acc. to ques, => $(x + 1)^2 – [x \times (x – 1)] = 16$

=> $(x^2 + 2x + 1) – (x^2 – x) = 16$

=> $3x + 1 = 16$

=> $x = \frac{15}{3} = 5$

$\therefore$ Smallest number = 5 – 1 = 4

**6) Answer (C)**

the numbers which are divisible by both 5 and 7 means those must be divisible by 5X7=35

35th multiple after 300 = 315 = 31*9

35th multiple before 650 = 630 = 31*18

so total numbers which are divisible by 35 in between 300 & 650 are = 18-9+1 = 10.

so the answer is option C.

**7) Answer (D)**

$ x + 20(\frac{1}{x}) = 9$

$\Rightarrow (x^{2}+20) = 9 \times x$

$\Rightarrow x^{2}-9x+20 = 0$

$\Rightarrow(x-4)(x-5)=0$

$\Rightarrow x = 4 or 5$

so the answer is option D.

**8) Answer (B)**

Let the number be $x$

According to ques,

=> $x^2-49=576$

=> $x^2=576+49=625$

=> $x=\sqrt{625}=25$

=> Ans – (B)

**9) Answer (B)**

Expression : $\ 3^{11} + 3^{12} + 3^{13} + 3^{14}\ $

= $3^{11}(1+3+3^2+3^3)$

= $3^{11}\times(1+3+9+27)$

= $3^{11}\times(40)$

$\because$ $40$ is divisible by 8, hence the above expression is also divisible by **8**

=> Ans – (B)

**10) Answer (D)**

$A=1-10+3-12+5-14+7+\dots..upto\ 60\ terms\ .$

or, $A=\left(1+3+5+7+…59\right)-\left(10+12+14+….+68\right)\ .$

or, $A=\frac{\left(1+59\right)\times30}{2}-\frac{\left(10+68\right)\times30}{2}\ .$

or, $A=900-1170\ =-270\ .$

D is correct choice.

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