**Number System Questions for SSC CHSL set-3 pdf**

Download SSC CHSL Number System Questions with answers Set-3 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:Â **Sum of four times a fraction and 6 times its reciprocal is 11. What is the fraction?

a)Â 3/4

b)Â 4/3

c)Â 4/7

d)Â 7/4

**Question 2:Â **What is the remainder when 6729 is divided by 35?

a)Â 11

b)Â 7

c)Â 9

d)Â 13

**Question 3:Â **A positive fraction is greater than its reciprocal by 72/77. What is the fraction?

a)Â 7/11

b)Â 11/7

c)Â 4/7

d)Â 7/4

**Question 4:Â **What least number must be added to 4131, so that the sum is completely divisible by 19?

a)Â 10

b)Â 11

c)Â 9

d)Â 12

**Question 5:Â **The sum of a number and 4 times its reciprocal is 5. What is the number?

a)Â 4

b)Â 5

c)Â 6

d)Â 7

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**Question 6:Â **The sum of a fraction and 7 times its reciprocal is 11/2. What is the fraction?

a)Â 7/2

b)Â 2/7

c)Â 3/4

d)Â 4/3

**Question 7:Â **What is the sum of all prime numbers between 60 and 80?

a)Â 272

b)Â 284

c)Â 351

d)Â 414

**Question 8:Â **After deducting 12% from a certain sum and then deducting 25% from the remainder, 2508 is left, then what is the initial sum?

a)Â 3500

b)Â 3450

c)Â 3970

d)Â 3800

**Question 9:Â **For what value of X, 211X will be a perfect square?

a)Â 4

b)Â 5

c)Â 6

d)Â 9

**Question 10:Â **How many numbers are there from 300 to 700 which are divisible by 2, 3 and 7?

a)Â 7

b)Â 8

c)Â 9

d)Â 10

**Answers & Solutions:**

**1)Â AnswerÂ (A)**

Let that fraction be $\frac{1}{x}$

$4 \times \frac{1}{x} + 6x = 11$

$\Rightarrow (4+6x^{2}) = 11 \times x$

$\Rightarrow 6x^{2}-11x+4 = 0$

$\Rightarrow(x-\frac{8}{6})(x-\frac{3}{6})=0$

$\Rightarrow x = 4/3 or 1/2$

$\Rightarrow \text{fraction} = \frac{1}{x} = 3/4 \text(or) 2$

so the answer is option A.

**2)Â AnswerÂ (C)**

35*192 = 6720 is the least nearest multiple of 35.

The remainder when 6729 is divided by 35 = 6729 – 6720 = 9

so the answer is option C.

**3)Â AnswerÂ (B)**

Let the fraction beÂ $x$

According to ques,

=> $x-\frac{1}{x}=\frac{72}{77}$

=> $\frac{x^2-1}{x}=\frac{72}{77}$

=> $77x^2-77=72x$

=> $77x^2-72x-77=0$

=> $77x^2-121x+49x-77=0$

=> $11x(7x-11)+7(7x-11)=0$

=> $(7x-11)(11x+7)=0$

=> $x=\frac{11}{7},\frac{-7}{11}$

$\because x$ is positive, => $x=\frac{11}{7}$

=> Ans – (B)

**4)Â AnswerÂ (B)**

Factorizing 4131 = 19 $\times$ 217 + 8

Thus, on dividing 4131 by 19, the remainder is 8

$\therefore$ The number thatÂ must be added to 4131 so that the sum obtained is completely divisible by 19

= 19 – 8 = 11

=> Ans – (B)

**5)Â AnswerÂ (A)**

Let the fraction beÂ $x$

According to ques,

=> $x+\frac{4}{x}=5$

=> $\frac{x^2+4}{x}=5$

=> $x^2+4=5x$

=> $x^2-5x+4=0$

=> $x^2-x-4x+4=0$

=> $x(x-1)-4(x-1)=0$

=> $(x-1)(x-4)=0$

=> $x=1,4$

=> Ans – (A)

**6)Â AnswerÂ (A)**

Let the fraction beÂ $x$

According to ques,

=> $x+\frac{7}{x}=\frac{11}{2}$

=> $\frac{x^2+7}{x}=\frac{11}{2}$

=> $2x^2+14=11x$

=> $2x^2-11x+14=0$

=> $2x^2-4x-7x+14=0$

=> $2x(x-2)-7(x-2)=0$

=> $(x-2)(2x-7)=0$

=> $x=2,\frac{7}{2}$

=> Ans – (A)

**7)Â AnswerÂ (C)**

Sum of all prime numbers between 60 and 80

= 61 + 67 + 71 + 73 + 79

= 351

=> Ans – (C)

**8)Â AnswerÂ (D)**

Let initial sum = $100x$

After deducting 12%, sum left = $\frac{(100-12)}{100}\times100x=88x$

Similarly, after deducting 25%, sum left = $\frac{75}{100}\times88x=66x$

According to ques,

=> $66x=2508$

=> $x=\frac{2508}{66}=38$

$\therefore$ Initial sum = $100\times38=3800$

=> Ans – (D)

**9)Â AnswerÂ (C)**

We know that $(45)^2=2025$

So, the next number = $(46)^2=2116$

Thus, X is replaced by 6

=> Ans – (C)

**10)Â AnswerÂ (C)**

L.C.M.(2,3,7) = 42

=> Numbers from 300 to 700 which are divisible by 42 are = 336,378,420,…,672

This is an AP with first term = $a=336$ and common difference = $d=42$

Let number of terms = $n$

=> Last term = $a+(n-1)d=672$

=> $336+(n-1)42=672$

=> $(n-1)42=672-336=336$

=> $n-1=\frac{336}{42}=8$

=> $n=8+1=9$

=> Ans – (C)

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