model 2 divisibility, multiples, add and subtract based number system Practice Questions Answers Test with Solutions & More Shortcuts

Question : 26

When ‘n’ is divisible by 5 the remainder is 2. What is the remainder when $n^2$ is divided by 5 ?

a) 3

b) 2

c) 4

d) 1

Answer: (c)

Required remainder = Remainder obtained by dividing $2^2$ by 5.

Remainder = 4

Question : 27

A number being divided by 52 gives remainder 45. If the number is divided by 13, the remainder will be

a) 6

b) 5

c) 7

d) 12

Answer: (a)

Here, 52 is a multiple of 13. Hence, the required remainder is obtained on dividing 45 by 13. Required remainder = 6.

Question : 28 [SSC CPO S.I.2009]

A number when divided by 192 gives a remainder of 54. What remainder would be obtained on dividing the same number by 16 ?

a) 4

b) 2

c) 8

d) 6

Answer: (d)

Here, the first divisor 192 is a multiple of second divisor 16.

∴ Required remainder

= remainder obtained by dividing 54 by 16 = 6

Question : 29

$9^6$ – 11 when divided by 8 would leave a remainder of :

a) 2

b) 0

c) 6

d) 4

Answer: (c)

If $(x ±1)^n$ is divided by x, the remainder is $(±1)^n$ ,

Now, $9^6$ – 11 == $(8 + 1)^6$ –11

When it is divided by 8,

remainder = + 1 – 11 = – 10

When – 10 is divided by 8,

remainder = – 2 i.e. – 2 + 8 = 6

Question : 30 [SSC CPO 2011]

When a number is divided by 36, the remainder is 19. What will be the remainder when the number is divided by 12 ?

a) 5

b) 7

c) 0

d) 3

Answer: (b)

Here, the first divisor (36) is exactly divisible by the second divisor (12).

∴ Required remainder = Remainder obtained after 19 is divided by 12 = 7

IMPORTANT quantitative aptitude EXERCISES

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