IMO Number Theory 2 — Questions and Answers
Question 1: What is the value of 2⁵?
- 10
- 16
- 32 (Correct answer)
- 64
Correct answer: 32
2⁵ = 2 × 2 × 2 × 2 × 2 = 32.
Question 2: Which of the following is a perfect square?
- 50
- 64 (Correct answer)
- 72
- 90
Correct answer: 64
64 = 8², so it is a perfect square.
Question 3: What is the remainder when 47 is divided by 5?
- 1
- 2 (Correct answer)
- 3
- 4
Correct answer: 2
47 = 9 × 5 + 2, so the remainder is 2.
Question 4: How many prime numbers are there between 10 and 30?
- 3
- 4
- 5
- 6 (Correct answer)
Correct answer: 6
The primes between 10 and 30 are 11, 13, 17, 19, 23, and 29 — a total of 6.
Question 5: What is the value of √144?
- 11
- 12 (Correct answer)
- 13
- 14
Correct answer: 12
√144 = 12 because 12² = 144.
Question 6: Which of these is NOT a factor of 48?
- 6
- 8
- 9 (Correct answer)
- 12
Correct answer: 9
48 ÷ 9 = 5.33…, which is not a whole number, so 9 is not a factor of 48.
IMO Number Theory 2
What is the value of 2⁵?