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
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 |
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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