Olympiad Test: Prime Time - 1 - Class 6 MCQ

A prime number has exactly two factors (1 and itself).

0 → not prime.

1 → has only one factor.

2 → smallest prime (and only even prime).

2, 7, 11 → prime (exactly two factors).

9 → factors are 1, 3, 9 → more than 2 → composite.

Primes between 20 and 30: 23, 29. Wait, let’s check carefully:

21 (not), 22 (not), 23 (prime), 24 (not), 25 (not), 26 (not), 27 (not), 28 (not), 29 (prime).

So only 2 primes.

Correct Answer should be Option B.

Twin primes differ by 2.

(2, 3) differ by 1.

(3, 5) differ by 2, but both are prime → also valid twin primes.

(7, 9) → 9 is not prime.

(11, 13) → differ by 2 and both are prime.

Both (3, 5) and (11, 13) are twin primes, but if only one option is allowed, the best answer = (11, 13).

2 and 3 are prime.

4 = 2 × 2 → first composite number.

1 has only one factor → not prime, not composite.

0 is excluded from both definitions.

2 → prime.

4 → composite.

27 = 3 × 9.

29 = no factors other than 1 and 29 → prime.

33 = 3 × 11.

35 = 5 × 7.

So 29 is prime.

First three primes = 2, 3, 5.

Sum = 2 + 3 + 5 = 10.

6 = 2 × 3 → exactly 2 prime factors.

8 = 2 × 2 × 2 → only one prime factor.

9 = 3 × 3 → only one prime factor.

25 = 5 × 5 → only one prime factor.

So correct = 6.

A prime triplet = three consecutive odd numbers that are prime.

(2, 3, 5) → includes 2 but not all odd.

(3, 5, 7) → all prime, consecutive odd → correct.

(5, 7, 11) → gap more than 2.

(7, 9, 11) → 9 not prime.

So (3, 5, 7) is the only prime triplet.