Discrete Mathematics Multiple Choice Questions on “Algorithms – Integers and Division”.
1. The quotient when 19 is divided by 6 is?
a) 1
b) 2
c) 3
d) 0
Answer: c
Clarification: 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
Answer: d
Clarification: 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
Answer: b
Clarification: 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.
4. The value of 12 mod 3 is?
a) 0
b) 1
c) 2
d) 3
Answer: a
Clarification: 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
Answer: c
Clarification: 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
Answer: b
Clarification: 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
Answer: c
Clarification: 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
Answer: a
Clarification: 16 divide 102 – 6 = 96.
9. The quotient and remainder when 18 is divided by 5 is?
a) 2 and 3
b) 1 and 2
c) 3 and 2
d) 3 and 3
Answer: d
Clarification: 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
Answer: d
Clarification: By the Division algorithm 15 = 11(1) + 4. Where the remainder is 15 mod 11.