IMO Number Theory 3

Question 1

A number leaves a remainder of 3 when divided by 7. Which could be the number?

Accepted Answer

24

Answer

24 ÷ 7 = 3 remainder 3, so 24 leaves a remainder of 3 when divided by 7.

Question 2

What is the sum of all prime numbers less than 10?

Accepted Answer

17

Answer

Primes less than 10 are 2, 3, 5, 7; their sum = 2 + 3 + 5 + 7 = 17.

Question 3

What is the LCM of 6, 8, and 12?

Accepted Answer

24

Answer

LCM(6, 8, 12) = 24, since 24 is the smallest number divisible by all three.

Question 4

Which statement is true about the number 1?

Accepted Answer

It is neither prime nor composite

Answer

1 is neither prime nor composite by mathematical definition, as prime numbers must have exactly two distinct factors.

Question 5

What is 3⁴?

Accepted Answer

81

Answer

3⁴ = 3 × 3 × 3 × 3 = 81.

IMO - International Mathematics Olympiad Practice Test