This set of Discrete Mathematics Multiple Choice Questions & Answers (MCQs) focuses on “The Integers and Division”.

1. The quotient when 19 is divided by 6 is

a) 1

b) 2

c) 3

d )0

View Answer

Explanation: According to the Division Algorithm 19 = 6(3) + 1. Hence, quotient when 19 divided by 6 is 3 = 19 div 6.

2. The remainder when 111 is divided by 12 is

a) 0

b) 1

c) 2

d) 3

View Answer

Explanation: According to the Division Algorithm 111 = 12(9) + 3. Hence, remainder when 111 divided by 12 is 3 = 111 mod 12.

3. The quotient and remainder when -1 is divided by 3 is

a) -1 and -1

b) -1 and 2

c) 1 and 2

d) -1 and -2

View Answer

Explanation: According to the Division Algorithm -1 = 3(-1) + 2. Hence, quotient when -1 divided by 3 is -1 = -1 div 3 and remainder when -1 divided by 3 is 2 = -1 mod 3.

a) 0

b) 1

c) 2

d) 3

View Answer

Explanation: By the Division algorithm 12 = 3(4) + 0. Where remainder is 12 mod 3.

5. The value of 155 mod 9 is

a) 0

b) 1

c) 2

d) 3

View Answer

Explanation: By the Division algorithm 155 = 9(17) + 2. Where remainder is 155 mod 9.

6. Is 17 congruent to 4 modulo 6

a) True

b) False

View Answer

Explanation: 6 does not divide 17 – 4 = 13.

7. If a|b and a|c, then

a) a|bc

b) c|a

c) a|(b+c)

d) b|a

View Answer

Explanation: If a|b and a|c then b = am and c = an for some integer m and n. Hence, b + c = a(m + n). Therefore, a|(b+c).

8. Is 102 congruent to 6 modulo 16

a) True

b) False

View Answer

Explanation: 16 divide 102 – 6 = 96.

a) 2 and 3

b) 1 and 2

c) 3 and 2

d) 3 and 3

View Answer

Explanation: According to the Division Algorithm 18 = 5(3) + 3. Hence, quotient when 18 divided by 5 is 3 = 18 div 5 and remainder when 18 divided by 5 is 3 = 18 mod 5.

10. The value of 15 mod 11 is

a) 1

b) 2

c) 3

d) 4

View Answer

Explanation: By the Division algorithm 15 = 11(1) + 4. Where remainder is 15 mod 11.

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