This set of Aptitude Questions and Answers (MCQs) focuses on “Division Algorithm”.

1. On dividing 30879 by a certain number, the quotient is 67 and the remainder is 327. Find the divisor.

a) 476

b) 456

c) 466

d) 444

View Answer

Explanation: Divisor=\(\frac{Dividend-Remainder}{Quotient}=\frac{30879-327}{67}\)=456.

2. In a division sum, the divisor is eleven times the quotient and six times the remainder. If the remainder is 55, determine the dividend.

a) 9955

b) 9855

c) 9985

d) 9965

View Answer

Explanation: Divisor = 6*Remainder = 6*55 = 330.

Quotient = Divisor/11 = 330/11 = 30.

Dividend = Divisor*Quotient + Remainder = 330*30 + 55 = 9955.

3. A number when divided by 91 leaves a remainder 65. If the same number is divided by 13, find the remainder.

a) 12

b) 5

c) 0

d) 7

View Answer

Explanation: On dividing the given number by 91, let k be the quotient and 65 the remainder.

Then, number = 91k + 65 = 13*7k + 13*5 = 13(7k + 5).

The number is completely divisible by 13. Hence the remainder is 0.

4. A number when divided by 9 leaves remainder 6. When square of the same number is divided by 9, find the remainder.

a) 7

b) 5

c) 3

d) 0

View Answer

Explanation: On dividing the given number by 9, let k be the quotient and 6 the remainder.

Then the number is 9k+6.

Square of the number = (9k+6)

^{2}= 81k

^{2}+ 36 + 108k = 9(9k

^{2}+ 4 + 12k)

The square of the number is completely divisible by 9. Hence the remainder is 0.

5. Find the remainder when 7^{18} + 6 is divided by 6.

a) 0

b) 1

c) 3

d) 5

View Answer

Explanation: (x

^{n}– a

^{n}) is divisible by (x – a) for all values of n.

So, 7

^{18}– 1 is divisible by (7 – 1) = 6

7

^{18}+ 6 = (7

^{18}– 1) + 7 = (7

^{18}– 1) + 6 + 1

i.e., when [(7

^{18}– 1) + 7] is divided by 6, the remainder is 1.

6. Find the remainder when 589^{2587} + 9 is divided by 590.

a) 8

b) 1

c) 6

d) 4

View Answer

Explanation: (x

^{n}+ a

^{n}) is divisible by (x + a) for all odd values of n.

So, 589

^{2587}+ 1 is divisible by (589+1) = 590

589

^{2587}+ 9 = (589

^{2587}+ 1) + 8 gives remainder 8 when divided by 590.

7. If 9^{126} is divided by 80, find the remainder.

a) 17

b) 29

c) 79

d) 1

View Answer

Explanation: 9

^{126}= (9

^{2})

^{63}= 81

^{63}.

(x

^{n}– a

^{n}) is divisible by (x – a) for all values of n.

(81

^{63}– 1) is divisible by 80.

(92)

^{63}= 81

^{63}= (81

^{63}– 1) + 1, gives a remainder 1 when divided by 80.

8. Find the remainder when 367^{188} – 333^{188} is divided by 700.

a) 12

b) 0

c) 19

d) 1

View Answer

Explanation: (x

^{n}– a

^{n}) is divisible by (x + a) for all even values of n.

367

^{188}– 333

^{188}is divisible by 367+333=700.

Hence, the remainder is 0.

9. For, what values of n, 3^{2n} – 1 is divisible by 2^{n+2}.

a) 1

b) 3

c) Both 1 and 3

d) Both 1 and 2

View Answer

Explanation: 3

^{2n}– 1 is divisible by 2

^{n+2}for only n = 1 and 2.

When n = 1, 3

^{2}-1 is divisible by 2

^{3}.

When n = 2, 3

^{4}-1 is divisible by 2

^{4}.

10. For any natural number m, m^{3} – m is divisible by which of the following number?

a) 6

b) 12

c) 24

d) 48

View Answer

Explanation: m

^{3}– m = (m – 1)*m*(m + 1)

We know that, any three consecutive natural number is always divisible by 6.

To practice all aptitude questions, please visit “1000+ Quantitative Aptitude Questions”, “1000+ Logical Reasoning Questions”, and “Data Interpretation Questions”.