Number System (Part-5)​​​

31. The largest five-digit number which when divided by 7, 9 and 11, leaves the same remainder as 3 in each case, is: [SSC CGL 05/12/2022 (2nd Shift)]

(a) 95840
(b) 98685
(c) 96720
(d) 99795

Correct Answer: (d) 99795

Solution:L.C.M (7, 9, 11) = 693
Now, largest five digit number is 99999
When we divide 99999 by 693, the reamainder will be 207
Now, the largest number which when divided by 7, 9, and 11 leaves
remainder 3 in each case :- 99792 + 3 = 99795

32. Find the greatest number that will divide 49, 147 and 322 to leave the same remainder in each case. [SSC CGL 06/12/2022 (1st Shift)]

(a) 9
(b) 5
(c) 7
(d) 8

Correct Answer: (c) 7

Solution:

33. If a number K= 42 × 25 × 54 × 135 is divisible by 3ᵃ, then find the maximum value of a. [SSC CGL 07/12/2022 (1st Shift)]

(a) 6
(b) 7
(c) 4
(d) 5

Correct Answer: (b) 7

Solution:

34. 9435 is added to 7593, then 2607 is subtracted from the sum. The result is divisible by: [SSC CGL 07/12/2022 (3rd Shift)]

(a) 4
(b) 10
(c) 3
(d) 5

Correct Answer: (c) 3

Solution:9435 + 7593 - 2607 = 14421
Now, from the option it is only divisible by 3.

35. 7 is added to a certain number and the sum is multiplied by 5. The product is then divided by 3 and 4 is subtracted from the quotient. If the result comes to 16, then what is the original number? [SSC CGL 08/12/2022 (3rd Shift)]

(a) 3
(b) 1
(c) 5
(d) 4

Correct Answer: (c) 5

Solution:

36. If 7-digit number 678p37q is divisible by 75 and p is not a composite, then the values of p and q are: [SSC CGL 08/12/2022 (4th Shift)]

(a) p = 5 q = 5
(b) p = 3 q = 0
(c) p = 3 q = 5
(d) p = 2 q = 5

Correct Answer: (c) p = 3 q = 5

Solution:

37. Any six-digit number that is formed by repeating a three-digit number, is always divisible by: [SSC CGL 12/12/2022 (2nd Shift)]

(a) 111
(b) 1001
(c) 19
(d) 101

Correct Answer: (b) 1001

Solution:

38. Choose the option in which the numbers are in correct ascending order. [SSC CGL 13/12/2022 (2nd Shift)]

(a) 4/5, 2/3, 1/11 and 2/9
(b) 1/11, 2/9, 2/3 and 4/5
(c) 2/9, 1/11, 4/5 and 2/3
(d) 2/3, 4/5, 1/11 and 2/9

Correct Answer: (b) 1/11, 2/9, 2/3 and 4/5

Solution:

39. The sum of two numbers is 680. If the bigger number is decreased by 15% and the smaller number is increased by 15%, then the resultant numbers are equal. Find the smaller number. [SSC CGL 13/12/2022 (2nd Shift)]

(a) 307
(b) 289
(c) 291
(d) 304

Correct Answer: (b) 289

Solution:

40. A four-digit pin, say abcd, of a lock has different non-zero digits. The digits satisfy b = 2a c = 2b d = 2c The pin is divisible by______ . [SSC CGL 13/12/2022 (2nd Shift)]

(a) 2, 3, 5
(b) 2, 3, 7
(c) 2, 3, 13
(d) 2, 3, 11

Correct Answer: (c) 2, 3, 13

Solution:

Number System (Part-5)​​​

31. The largest five-digit number which when divided by 7, 9 and 11, leaves the same remainder as 3 in each case, is: [SSC CGL 05/12/2022 (2nd Shift)]

32. Find the greatest number that will divide 49, 147 and 322 to leave the same remainder in each case. [SSC CGL 06/12/2022 (1st Shift)]

33. If a number K= 42 × 25 × 54 × 135 is divisible by 3ᵃ, then find the maximum value of a. [SSC CGL 07/12/2022 (1st Shift)]

34. 9435 is added to 7593, then 2607 is subtracted from the sum. The result is divisible by: [SSC CGL 07/12/2022 (3rd Shift)]

35. 7 is added to a certain number and the sum is multiplied by 5. The product is then divided by 3 and 4 is subtracted from the quotient. If the result comes to 16, then what is the original number? [SSC CGL 08/12/2022 (3rd Shift)]

36. If 7-digit number 678p37q is divisible by 75 and p is not a composite, then the values of p and q are: [SSC CGL 08/12/2022 (4th Shift)]

37. Any six-digit number that is formed by repeating a three-digit number, is always divisible by: [SSC CGL 12/12/2022 (2nd Shift)]

38. Choose the option in which the numbers are in correct ascending order. [SSC CGL 13/12/2022 (2nd Shift)]

39. The sum of two numbers is 680. If the bigger number is decreased by 15% and the smaller number is increased by 15%, then the resultant numbers are equal. Find the smaller number. [SSC CGL 13/12/2022 (2nd Shift)]

40. A four-digit pin, say abcd, of a lock has different non-zero digits. The digits satisfy b = 2a c = 2b d = 2c The pin is divisible by______ . [SSC CGL 13/12/2022 (2nd Shift)]

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Number System (Part-5)