  # Number System TCS Questions For SSC CGL 2021 in Hindi and English

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## Number System TCS Questions For SSC CGL 2021 in Hindi and English

Q1. If the 8-digit number 789x531y is divisible by 72, then the value of (5x - 3y) is :

यदि आठ अंकों की संख्या 789x531y 72 से विभाज्य है, तो (5x - 3y) का मान ज्ञात करें |

SSC CGL 4 June 2019 (Afternoon)

(a) 0

(b) -1

(c) 2

(d) 1

Q2. If the 8-digit number 179x091y is divisible by 88. The value of (5x - 8y) is:

यदि 8 अंकों की संख्या 179x091y, 88 से विभाज्य है, तो  (5x - 8y) का मान ज्ञात करें |

SSC CGL 4 June 2019 (Evening)

(a) 4

(b) 7

(c) 9

(d)5

Q3. If the 8-digit number 2074x4y2 is divisible by 88, then the value of (4x+3y) is:

यदि आठ अंकों की संख्या 2074x4y2    88 से विभाज्य है, तो (4x+ 3y) का मान ज्ञात करें |

SSC CGL 6 June 2019 (Morning)

(a) 49

(b) 36

(c)  42

(d)  45

Q4. If a 9-digit number 32x4115y2 is divisible by 88, then the value of (4x - y) from the smallest possible value of x is :

यदि 9  अंकों की संख्या 32x4115y2, 88 से विभाज्य है, x के सबसे छोटे संभव मान से    (4x - y) का मान ज्ञात करें |

SSC CGL 6 June 2019 (Afternoon)

(a) 31

(b) 20

(c) -1

(d) 11

Q5. If a 10 digit number 1330x558y2 is divisible by 88, then the value of (x + y) is :

यदि 10 अंकों की एक संख्या 1330x558y2  88 से विभाजित है, तो (x + y) का मान क्या होगा ?

SSC CGL 7 June 2019 (Morning)

(a) 7

(b) 9

(c) 6

(d) 8

Q6. If a 10-digit number 897359y7x2 is divisible by 72, then what is the value of ( 3x - y ), for the possible greatest value of y?

यदि 10 अंकों की एक संख्या 897359y7x2 72 से विभाजित है, तो y के सबसे बड़े संभव मान को लेते हुए  ( 3x - y ) का मान ज्ञात करें |

SSC CGL 7 June 2019 (Afternoon)

(a) 3

(b) 8

(c) 7

(d) 5

Q7. If a 10 digit number 67127y76x2 is divisible by 88, then the value of (7x - 2y) is :

यदि 10 अंकों की एक संख्या 67127y76x2    88 से विभाजित है, तो (7x - 2y) का मान ज्ञात करें |

SSC CGL 7 June 2019 (Evening)

(a) 10

(b) 7

(c) 3

(d) 5

Q8. If the six digit number 15x1y2 is divisible by 44, then (x + y) is equal to :

यदि छः अंकों की एक संख्या 15x1y2   44 से विभाजित है, तो (x + y) का मान किसके बराबर होगा ?

SSC CGL 10 June 2019 (Afternoon)

(a) 8

(b) 7

(c) 6

(d) 9

Q9. If the six-digit number 6x2904 is divisible by 88, then the value of x is :

यदि छः अंकों की एक संख्या 6x2904 88 से विभाजित है, तो x का मान ज्ञात करें |

SSC CGL 10 June 2019 (Evening)

(a) 5

(b) 6

(c) 7

(d) 8

Q10. If a six-digit number 4x573y is divisible by 72, then the value of (x + y) is:

यदि छः अंकों की एक संख्या 4x573y   72 से विभाजित है, तो (x + y) का मान क्या होगा?

SSC CGL 11 June 2019 (Afternoon)

(a) 9

(b) 4

(c) 8

(d) 6

### Here are the solutions to the above questions of the number system asked in the SSC exams.

Practice Questions Solutions

Sol 1. (b)

For 8-digit number 789x531y to be divisible by 72. It must be divisible by 8 and 9.

For 789x531y to be divisible by 8. Value of y = 2

Again, for 789x5312 to be divisible by 9. Value of x = 1

Therefore, 5x - 3y = -1

Sol 2.

Ans. (a) 4

179x091y is divisible by 88, it must be divisible by 11 and 8.

This number to be divisible by 11⇒  (7+x+9+y) - (1+9+0+1) = 0 or 11

5+x+y = 0 or 11

x+y = -5 or 6

(x+y can’t be negative)

Possible values of x,y for x+y = 6

(0,6), (1,5), (2,4), (3,3), (4,2), (5,1), (6,0)

Last three digits of the number will be divisible by 8 only in case y = 2

Clearly x=4 and y=2 are the desired values

5x-8y = 5(4)-8(2) = 4

Sol 3.

Ans. (d) 45

Since the number is divisible by 88 it must be divisible by 11 and 8.

This number to be divisible by 11 ⇒

2+7+x+y - (0+4+4+2) = 0 or 11

Case 1

For the difference = 0

x+y = 1

Clearly y is either 0 or 1.

The number to be divisible by 8 also last three digits must be divisible by 8.

For y =1

The last three digits are 412 and this is not divisible by 8.

For Y = 0

Last three digits are 402 and this is also not divisible by 8

Case 2:

For the difference = 11

x+y = 12

So, x and y must be (3,9),(4,8),(5,7),(6,6),(7,5),(8,4) and (9,3)

The number to be divisible by 8 also last three digits must be divisible by 8 this is only possible when y = 7 and 3

When y =7, x =5

4x+3y = 4(5)+3(7) = 41

When y=3, x=9

4x+3y = 4(9)+3(3) = 45

Clearly option d is the right answer.

Sol 4.

Ans. (c) -1

Since the number 32x4115y2 is divisible by 88, it must be divisible by 11 and 8.

For the number to be divisible by 11

(3+x+1+5+2)-(2+4+1+y) = 0 or 11

So, 4+x-y = 0 or 11

4+x-y =0 is possible for x=0,1,2,3,4,5 and y=4,5,6,7,8,9

4+x-y = 11 is possible for x = 7,8,9 and y = 0,1,2

Also a number is divisible by 8 if its last three digits are divisible by 8.

We will check for a minimum value of x

For x=0, the last three digits of the number are not divisible by 8.

For x = 1, the last three digits are 552 which is divisible by 8.

So the desired values of x and y are 1 and 5 respectively.

4x-y = 4(1)-5 = -1

Sol 5.

Ans. (b)

Since the number 1330x558y2 is divisible by 88, it must be divisible by 11 and 8.

For the number to be divisible by 11

(1+3+x+5+y)-(3+0+5+8+2) = 0 or 11

x+y-9 = 0 or 11

For

x+y-9 = 0

x+y=9

For

x+y-9 = 11

x+y=20

Sol 6.

Ans. (c) 7

Since the number is divisible by 72 it must be divisible by 9 and 8.

This number to be divisible by 9⇒ (8+9+7+3+5+9+y+7+x+2) must be divisible by 9.

For this x+y = 4 or x+y = 13

Case 1:

For the sum = 4

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

The number to be divisible by 8 also last three digits must be divisible by 8.

For x =4,3,2,0

The last three digits are not divisible by 8.

For x = 1

Last three digits are divisible by 8

Clearly, y = 3

3x-y = 3(1)-3 = 0 (which is not in the given options)

Case 2:

For the sum = 13

So, x and y must be (4,9),(5,8),(6,7),(7,6),(8,5) and (9,4)

The number to be divisible by 8 also last three digits must be divisible by 8 this is only possible when x = 5 and 9

When x =5, y =8

3x-y = 3(5)-8 = 7

When x=9, y = 4

3x-y = 3(9)-4 = 23

Clearly option c is the right answer.

Sol 7.

Ans. (b)

Since the number is divisible by 88 it must be divisible by 11 and 8.

This number to be divisible by 11 (6+1+7+7+x) - (7+2+y+6+2) = 0 or 11

4+x-y = 0 or 11

Case 1:

For 4+x-y = 0

(x,y) is (0,4), (1,5), (2,6), (3,7), (4,8), (5,9)

The number to be divisible by 8 also last three digits must be divisible by 8.

For x =0,1,2,4,5

Last three digits are not divisible by 8.

For x = 3

The last three digits are 632 and this is divisible by 8

Clearly, y = 7    …...(4+x-y)

Case 2 :

For 4+x-y = 11

(x,y) is (9,2), (8,1), (7,0)

For x =9,7 the last three digits of the number are not divisible by 8.

For x=8 last three digits are divisible by 8 and y = 1

For x=8 and y=1

(7x-2y) = 7(8)-2(1) = 54

For x=3 and y=7

(7x-2y) = 7(3)-2(7) = 7

Sol 8.

Ans. (b)

Number 15x1y2 is divisible by 44, clearly, it will also be divisible by 11 and 4.

A number to be divisible by 11

(1+x+y)-(5+1+2) = 0 or 11

For the difference = 0

x+y = 7

For the difference = 11

x+y = 18

But 18 is not given in the options so option b is the right answer.

Sol 9.

Ans. (b) 6

6x2904 is divisible by 88, It will also be divisible by 11 and 8.

For a number to be divisible by 11

(x+9+4)-(6+2+0) = 0 or 11

x = -5 or 6

Sol 10.

Ans. (c) 8

4x573y 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

(4+x+5+7+3+y)⇒19+x+y must be divisible by 9.

Possible values of x+y = 8 or 17    …..(x and y can’t be greater than 9)

17 is not given in the options clearly correct option is c

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