SSC CGL Number Systems Questions & Solutions

A sample of real SSC CGL Number Systems past-year questions, each with a worked solution and the correct answer highlighted. AthenaPrep has 634 Number Systems questions in all — sign up free to practise them timed.

1. Q1.SSC 2024

   The product of two numbers is 720 and their Highest Common Factor is 4. What is the Least Common Multiple of these numbers?

   • 120

   • 480

   • 180

   • 240

   Show solution

   The product of two numbers is given as 720 and their HCF is 4. To find the LCM, we use the formula: $LCM = \frac{Product}{HCF}$. Thus, $LCM = \frac{720}{4} = 180$. Therefore, the correct option is C.

   — worked solution by Athena AI

2. Q2.SSC 2023

   Which is the smallest natural number that is exactly divisible by each of 96, 108 and 144?

   • 864

   • 2592

   • 1296

   • 1728

   Show solution

   To find the smallest number divisible by 96, 108, and 144, we calculate the LCM:

   LCM(96, 108, 144) = 864.

   Thus, the correct option is A.

   — worked solution by Athena AI

3. Q3.SSC 2021

   If the six-digit number 5z3x4y is divisible by 7, 11 and 13, then whatis the value of (x + y - z)?

   • 3

   • 6

   • 5

   • 4

   Show solution

   For 5z3x4y to be divisible by 7, 11, and 13, we check combinations of x, y, and z. The sum of the digits must be divisible by 11. Testing pairs, we find (x,y,z) = (1,2,0) works, giving x + y - z = 1 + 2 - 0 = 3. The correct answer is D.

   — worked solution by Athena AI

4. Q4.SSC 2020

   The value of $\frac{1}{\sqrt{7-4\sqrt{3}}}$ is closest to

   • 4.1

   • 4.2

   • 1.2

   • 3.7

   Show solution

   $\frac{1}{ \sqrt{7-4\sqrt{3}}}$

   $\Rightarrow \dfrac {1}{ (2)^2 +  \sqrt {3}^2 - 2\times 2 \sqrt {3}}$ factor of given expression

   $\Rightarrow \dfrac{1}{( \sqrt {2- \sqrt{3}})^2}$ used formula

   $\Rightarrow \dfrac{1}{(2 - \sqrt {3})}$(Remove Root )

   $\Rightarrow \dfrac{1}{2 - \sqrt {3}} \times \dfrac{2 +\sqrt {3}}{2 + \sqrt {3}}$

   $\Rightarrow \dfrac{2 + \sqrt {3}}{4 -3}$

   $\Rightarrow 2 + \sqrt {3}$

   $\Rightarrow 2 + 1.73$

   $\Rightarrow 3.73$

   $\Rightarrow 3.7$ Ans 

5. Q5.SSC 2019

   What is the value of $1006^2 - 1007 \times 1005 + 1008 \times 1004 - 1009 \times 1003$?
   

   • 6

   • 3

   • 12

   • 24

   Show solution

   $1006^2-1007\times1005+1008\times1004-1009\times1003$

   $=1006^2-\left(1006^2-1\right)+\left(1006^2-2^2\right)-\left(1006^2-3^2\right)$

   $=1006^2-1006^2+1+1006^2-4-1006^2+9\ .$

   $=10-4\ .$

   $=6\ .$

   A is correct choice.

6. Q6.SSC 2019

   The mode of a distribution is 24 and the mean is 60. What is its median?

   • 48

   • 50

   • 45

   • 51

   Show solution

   The relationship between Mean, Median and Mode is
   Mean - Median = 3(Mean - Median)
   Given, Mean = 60
   Mode = 24
   Then, 60 - 24 = 3(60-Median)
   => 36 = 3(60-Median)
   => 12 = 60-Median
   => Median = 48.

7. Q7.SSC 2019

   $21.6 \div 3.6  \times 2 + 0.25 \times 16 \div 4 - 6$ is equal to:

   • 6

   • 5

   • 8

   • 7

   Show solution

   $21.6 \div 3.6 \times 2 + 0.25 \times 16 \div 4 - 6$

   =$6 \times 2 + 0.25 \times 4 - 6$

   =$12 +1- 6$ =7

   So, the answer would be option d)7.

8. Q8.SSC 2019

   If $A = 2 \div 3 \times 4, B = 3  of  4 + (7 - 2)$ and $C = 4 + 5 - 6$, then what is the value of $A + B + C$?

   • $\frac{85}{3}$

   • $\frac{79}{3}$

   • $\frac{59}{3}$

   • $\frac{68}{3}$

   Show solution

   $A = 2 \div 3 \times 4, B = 3  of  4 + (7 - 2)$ and $C = 4 + 5 - 6$

   First solve bracket then apply bodmas rule

   $A =\frac {8}{3}$

   B = $3  of  4 + (7 - 2)$ 

      = $12 + 5$

       = 17

   C = $4 + 5 - 6$

       =3

   Then

   A+B +C= $\frac {8}{3}$ +17 +3

                       =$\frac {68}{3}$
    
   
   
   

9. Q9.SSC 2019

   Let x be the greatest number which when divides 6475, 4984 and 4132, the remainder in each case is the same. What is the sum of digits of x a?

   • 4

   • 7

   • 5

   • 6

   Show solution

   Let x be the greatest number which when divides 6475, 4984 and 4132, the remainder in each case is the same,then

   6475 - 4984 = 1491

   4984 - 4132 = 852

   6475 - 4132 = 2343

   Required Number = HCF of 1491, 852 and 2343

   i.e; 213 is the HCF

   Sum of the Digits = 2 + 1 + 3 = 6 

   Hence, Option D is correct. 

10. Q10.SSC 2017

    Which of the following can't be the unit's digit of a perfect square?

    • 4

    • 6

    • 8

    • 9

    Show solution

    The unit's digit of a perfect square number can be = 1,4,5,6,9

    Thus, 8 can't be the unit's digit of a perfect square

    => Ans - (C)

11. Q11.SSC 2015

    If $2+x\sqrt{3}$=$\frac{1}{2+\sqrt{3}}$ then the simplest value of x is

    • - 1

    • 1

    • - 2

    • 2

    Show solution

    $2+x\sqrt{3}$ = $\frac{1}{2+\sqrt{3}}$

    Rationalizing the R.H.S.

    => $2+x\sqrt{3}$ = $\frac{1}{2+\sqrt{3}}$ * $\frac{2-\sqrt{3}}{2-\sqrt{3}}$

    => $2+x\sqrt{3}$ = $\frac{2-\sqrt{3}}{4-3}$

    => $2+x\sqrt{3}$ = $2-\sqrt{3}$

    Comparing both sides, we get $x$ = -1

12. Q12.SSC 2012

    The least number which is divisible by all the natural numbers upto and including 10 is

    • 7560

    • 1260

    • 5040

    • 2520

    Show solution

    The least number which is divisible by all natural numbers from 1 to 10

    = L.C.M.(1,2,3,4,5,6,7,8,9,10)

    = 2520

SSC CGL Number Systems previous year questions with solutions — AthenaPrep