  # Number System Questions for SSC CGL 2021

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## SSC CGL CHSL CPO MTS Previous Year Maths Questions

Q1. For what value of x is the seven-digit number 46393x8 divisible by 11?

x का कौन सा मान रखने पर सात अंकों की संख्या 46393x8, 11 से विभाजित हो जायेगी ?

SSC CGL 11 June 2019 (Evening)

(a). 5

(b). 3

(c). 2

(d). 7

Q2. What is the value of x so that the seven-digit number 91876x2 is divisible by 72?

X का वह मान ज्ञात करें जिससे सात अंकों की संख्या 91876x2, 72 से विभाजित हो जाए |

SSC CGL 12 June 2019 (Morning)

(a). 2

(b). 7

(c). 5

(d). 3

Q3. What is the value of x such that the seven-digit number 6913x08 is divisible by 88?

x का मान ज्ञात करें जिससे सात अंकों की संख्या 6913x08, 88 से विभाजित हो जाए |

SSC CGL 12 June 2019 (Afternoon)

(a). 4

(b). 2

(c). 8

(d). 6

Q4. What is the value of x so that the seven-digit number 5656x52 is divisible by 72?

x का मान क्या होना चाहिए ताकि सात अंकों की संख्या 5656x52  72 से विभाजित हो जाए ?

SSC CGL 12 June 2019 (Evening)

(a). 5

(b). 4

(c). 7

(d). 8

Q5. What is the value of x so that the seven-digit number 55350x2 is divisible by 72?

x का मान क्या होना चाहिए ताकि सात अंकों की संख्या 55350x2  72 से विभाजित हो जाए ?

SSC CGL 13 June 2019 (Morning)

(a). 1

(b). 8

(c). 7

(d). 3

Q6. What is the value of x so that the seven-digit number 8439x53 is divisible by 99?

x का मान क्या होना चाहिए ताकि सात अंकों की संख्या 8439x53, 99 से विभाजित हो जाए ?

SSC CGL 13 June 2019 (Afternoon)

(a). 9

(b). 4

(c). 3

(d). 6

Q7. If the nine-digit number 8175x45y2 is divisible by 72, then the value of for the largest value of y is:

यदि नौ अंकों की संख्या 8175x45y2   72 से विभाजित है, तो y का सबसे बड़ा मान लेते हुए का मान ज्ञात करें |

SSC CHSL 2 July 2019(Afternoon)

(a). 8

(b). 4

(c). 5

(d). 6

Q8. If an eleven-digit number 5y5888406x6 is divisible by 72, then what is the value of (9x - 2y), for the least value of x?

यदि 11 अंकों की एक संख्या 5y5888406x6  72 से विभाजित है, तो x के सबसे छोटे मान के लिए  (9x - 2y) का मान क्या होगा ?

SSC CHSL 3 July 2019(Morning)

(a). 5

(b). 3

(c). 4

(d). 7

Q9. If a 10-digit number 46789x531y is divisible by 72, then the value of (2x + 5y), for the largest value of x is:

यदि 10 अंकों की एक संख्या 46789x531y   72 से विभाजित है, तो x का सबसे बड़ा मान लेते हुए (2x + 5y) का मान ज्ञात करें |

SSC CHSL 3 July 2019(Evening)

(a). 28

(b). 16

(c). 10

(d). 38

Q10. If a 10-digit number 75y97405x2 is divisible by 72, then the value of (2x-y), for the greatest value of x, is:

यदि 10 अंकों की एक संख्या 75y97405x2, 72 से विभाजित है, तो (2x-y) का मान ज्ञात करें |

SSC CHSL 4 July 2019(Morning)

(a). 24

(b). 21

(c). 12

(d). 18

### Here are the solutions to the above SSC CGL previous year questions of the number system in the short method.

Sol 1.

Ans. (b) 3

number 46393x8 divisible by 11,

For the number to be divisible by 11

(4+3+3+8)-(6+9+x) = 0 or 11

For the difference being 0

x = 3

For the difference being 11

x = 14 which is not possible.

Sol 2.

Ans. (d)

Number 91876x2 is divisible by 72, clearly, it will also be divisible by 9 and 8. For a number to be divisible by 9, the sum of its digits must be divisible by 9.

9+1+8+7+6+x+233+x must be divisible by 9

Cleary x = 3            ……………….(36 is multiple of 9 and next multiple is 45 and for that x =12 which is not possible)

632 are the last three digits of the number which is divisible by 8 so x =3 is the correct answer.

Sol 3.

Ans. (c)

Number 6913x08 is divisible by 88, clearly, it will also be divisible by 11 and 8.

For the number to be divisible by 11

(6+1+x+8)-(9+3+0) = 0 or 11

x= -3 or 8 (but x cannot be negative)

So, x=8

808 are the last three digits of the number which is divisible by 8 so x =8 is the correct answer.

Sol 4.

Ans. (c)

5656x52 is divisible by 72, clearly, it will also be divisible by 9 and 8. For a number to be divisible by 9, the sum of its digits must be divisible by 9.

5+6+5+6+x+5+229+x must be divisible by 9

Cleary x = 7        ……………….(36 is multiple of 9 and next multiple is 45 and for that x =16 which is not possible)

752 are the last three digits of the number which is divisible by 8 so x =7 is the correct answer.

Sol 5.

Ans. (c)

55350x2 is divisible by 72, clearly, it will also be divisible by 9 and 8. For a number to be divisible by 9, the sum of its digits must be divisible by 9.

5+5+3+5+0+x+220+x must be divisible by 9

Cleary x = 7        ……………….(27 is multiple of 9 and next multiple is 36 and for that x =16 which is not possible)

072 are the last three digits of the number which is divisible by 8 so x =7 is the correct answer.

Sol 6.

Ans. (b) 4

8439x53 is divisible by 99, clearly, it will also be divisible by 11 and 9.

For a number to be divisible by 9, the sum of its digits must be divisible by 9.

8+4+3+9+x+5+332+x must be divisible by 9

Cleary x = 4        ……………….(36 is multiple of 9 and next multiple is 45 and for that x =13 which is not possible)

Also, (8+3+4+3)-(4+9+5) = 0, so the number is divisible by 11 also clearly x=4 will be the right answer

Sol 7.

Ans. (c)

8175x45y2 is divisible by 72, clearly, it will also be divisible by 9 and 8. For a number to be divisible by 9, sum of its digits must be divisible by 9.

8+1+7+5+x+4+5+y+2⇒32+x+y must be divisible by 9

So x+y = 4 or 13                ..(as x and y can’t be greater than 9)

For x+y = 4

(x,y) = (0,4), (1,3), (2,2), (3,1), (4,0)

For x+y = 13

(x,y) = (4,9), (5,8), (6,7), (7,6), (8,5), (9,4)

We will check for the largest values of y which is 9.

Last three digits of the number are 592 which is divisible by 8. Clearly x=4 and y=9 are the desired numbers.

Sol 8.

Ans. (b)

5y5888406x6 is divisible by 72, clearly it will also be divisible by 9 and 8. For a number to be divisible by 9, sum of its digits must be divisible by 9.

5+y+5+8+8+8+4+0+6+x+6⇒50+x+y must be divisible by 9

So x+y = 4 or 13                ..(as x and y can’t be greater than 9)

For x+y = 4

(x,y) = (0,4), (1,3), (2,2), (3,1), (4,0)

For x+y = 13

(x,y) = (4,9), (5,8), (6,7), (7,6), (8,5), (9,4)

We will check for the smallest value of x which is 0

Last three digits of the number are 606 which is not divisible by 8.

Now we will check for the second smallest value of x which is 1

Last three digits of the number are 616 which is divisible by 8. Clearly x=1 and y=3 are the desired values.

9x-2y⇒9(1)-2(3) = 3

Sol 9.

Ans. (a) 28

46789x531y is divisible by 72,clearly it will also be divisible by 9 and 8. For a number to be divisible by 9, sum of its digits must be divisible by 9.

4+6+7+8+9+x+5+3+1+y43+x+y must be divisible by 9

So x+y = 11                ..(as x and y can’t be greater than 9)

Possible values of x,y = (2,9), (3,8), (4,7), (5,6), (6,5),(7,4),(8,3) and (9,2)

We will check for the maximum value of x which is 9.

Last three digits of the number is 312 which is divisible by 8 clearly x=9 and y=2 are the desired values.

2x+5y = 2(9)+5(2) = 28

Sol 10.

Ans. (c) 12

75y97405x2 is divisible by 72, clearly it will also be divisible by 9 and 8. For a number to be divisible by 9, sum of its digits must be divisible by 9.

7+5+y+9+7+4+0+5+x+2⇒39+x+y must be divisible by 9

So x+y = 6 or 15                ..(as x and y can’t be greater than 9)

For x+y = 6

Possible values of x and y = (0,6), (1,5), (2,4), (3,3), (4,2), (5,1), (6,0)

For x+y = 15

Possible values of x and y = (6,9), (7,8), (8,7), (9,6)

We will check for the maximum value of x which is 9.

The last three digits of the number are 592 which is divisible by 8 clearly x=9 and y=6 are the desired values.

2x-y = 2(9)-6 = 12

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