Number System (Part-6)​​​

21. If each of the two numbers 5¹⁶ and 5²⁵ are divided by 6, the remainder are R₁ and R₂, respectively. What is the value of R₁ +R₂/R₂ ? [SSC CGL 19/04/2022 (Morning)]

(a) 1/6
(b) 5/6
(c) 1/5
(d) 6/5

Correct Answer: (d) 6/5

Solution:

22. If the sum of two positive numbers is 65 and the square root of their product is 26, then the sum of their reciprocals is: [SSC CGL Tier II (29/01/2022)]

(a) 3/52
(b) 1/52
(c) 5/52
(d) 7/52

Correct Answer: (c) 5/52

Solution:

23. Let x = (433)²⁴ - (377)³⁸ + (166)⁵⁴. What is the unit digitof x ? [SSC CGL Tier II (29/01/2022)]

(a) 9
(b) 6
(c) 8
(d) 7

Correct Answer: (c) 8

Solution:

24. The sum of the digits of the least number which when divided by 36, 72, 80 and 88 leaves the remainders 16, 52, 60 and 68, respectively, is: [SSC CGL Tier II (03/02/2022)]

(a) 17
(b) 11
(c) 14
(d) 16

Correct Answer: (d) 16

Solution:

25. Let p, q, r and s be positive natural numbers having three exact factors including 1 and the number itself if q> p and both are two-digit numbers, and r> s and both are one-digit numbers, then the value of the expression p - q - 1/r - s is: [SSC CGL Tier II (03/02/2022)]

(a) - s - 1
(b) s -1
(c) 1 - s
(d) s + 1

Correct Answer: (a) - s - 1

Solution:

26. The sum of three fractions A, B and C, A > B > C, is 121/60. When C is divided by B, the resulting fraction is 9/10, which exceeds A by 3/20. What is the difference between B and C ? [SSC CGL Tier II (03/02/2022)]

(a) 1/15
(b) 1/10
(c) 3/10
(d) 7/15

Correct Answer: (a) 1/15

Solution:

27. Let x be the largest 4-digit number which is divisible by each of 16, 21, 24 and 28. The sum of the digits of x is: [SSC MTS 05/10/2021 (Evening)]

(a) 19
(b) 21
(c) 24
(d) 16

Correct Answer: (c) 24

Solution:

28. Let x be the least number which on being divided by 8, 12, 15, 24, 25 and 40 leaves a remainder of 7 in each case. What will be the remainder when x is divided by 29? [SSC MTS 06/10/2021 (Afternoon)]

(a) 18
(b) 27
(c) 19
(d) 20

Correct Answer: (b) 27

Solution:

29. Let x be the least number between 56,000 and 60,000 which when divided by 40, 45, 50 and 55 leaves a remainder of 23 in each case. What is the sum of the digits of x ? [SSC MTS 08/10/2021 (Afternoon)]

(a) 23
(b) 21
(c) 26
(d)19

Correct Answer: (a) 23

Solution:

30. The difference between a positive number and its reciprocal increases by a factor of 175/144 when the number is made to increase by 20%. What is the number ? [SSC MTS 12/10/2021 (Afternoon)]

(a) 7.5
(b) 6
(c) 2.5
(d) 5

Correct Answer: (d) 5

Solution:

Number System (Part-6)​​​

21. If each of the two numbers 5¹⁶ and 5²⁵ are divided by 6, the remainder are R₁ and R₂, respectively. What is the value of R₁ +R₂/R₂ ? [SSC CGL 19/04/2022 (Morning)]

22. If the sum of two positive numbers is 65 and the square root of their product is 26, then the sum of their reciprocals is: [SSC CGL Tier II (29/01/2022)]

23. Let x = (433)²⁴ - (377)³⁸ + (166)⁵⁴. What is the unit digitof x ? [SSC CGL Tier II (29/01/2022)]

24. The sum of the digits of the least number which when divided by 36, 72, 80 and 88 leaves the remainders 16, 52, 60 and 68, respectively, is: [SSC CGL Tier II (03/02/2022)]

25. Let p, q, r and s be positive natural numbers having three exact factors including 1 and the number itself if q> p and both are two-digit numbers, and r> s and both are one-digit numbers, then the value of the expression p - q - 1/r - s is: [SSC CGL Tier II (03/02/2022)]

26. The sum of three fractions A, B and C, A > B > C, is 121/60. When C is divided by B, the resulting fraction is 9/10, which exceeds A by 3/20. What is the difference between B and C ? [SSC CGL Tier II (03/02/2022)]

27. Let x be the largest 4-digit number which is divisible by each of 16, 21, 24 and 28. The sum of the digits of x is: [SSC MTS 05/10/2021 (Evening)]

28. Let x be the least number which on being divided by 8, 12, 15, 24, 25 and 40 leaves a remainder of 7 in each case. What will be the remainder when x is divided by 29? [SSC MTS 06/10/2021 (Afternoon)]

29. Let x be the least number between 56,000 and 60,000 which when divided by 40, 45, 50 and 55 leaves a remainder of 23 in each case. What is the sum of the digits of x ? [SSC MTS 08/10/2021 (Afternoon)]

30. The difference between a positive number and its reciprocal increases by a factor of 175/144 when the number is made to increase by 20%. What is the number ? [SSC MTS 12/10/2021 (Afternoon)]

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Number System (Part-6)