# Number System Questions for SSC CGL 2021

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**Number System Questions for SSC CGL 2021**

SSC CGL Tier 2 2019 | SSC CGL Tier 1 2019 | SSC CHSL 2019 | SSC CPO 2020 | SSC MTS 2019 |

SSC CGL Tier 2 2018 | SSC CGL Tier 1 2018 | SSC CHSL 2018 | SSC CPO 2019 | SSC MTS 2017 |

## 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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