Identify the odd one: 2, 3, 5, 7, 11, 13, 17, 20

Correct — C. Rule: the list is the prime numbers in order: 2, 3, 5, 7, 11, 13, 17.

Each of these has no factor other than 1 and itself.

20 = 2 × 2 × 5, so it is composite and breaks the run. The prime after 17 is 19, so 20 does not continue the list either — option (c).

Why the others are wrong

• (a)
  17 — 17 is prime. Neither 2 nor 3 divides it, and 5 × 5 = 25 is already past it, so the test is finished. It is the prime that follows 13.
• (b)
  13 — 13 is prime, divisible only by 1 and 13. It is the prime after 11, exactly where the list places it.
• (d)
  11 — 11 is prime: no number from 2 to 10 divides it. It follows 7 in the list of primes because 8, 9 and 10 are all composite.

A prime has exactly two factors, 1 and itself. The primes below 30 are 2, 3, 5, 7, 11, 13, 17, 19, 23 and 29, and they are worth knowing by sight.

When a list opens 2, 3, 5, 7, test primality before hunting for a difference. The gaps here are 1, 2, 2, 4, 2, 4, 3, which follow no arithmetic rule, but every term except 20 is prime.

Key facts

• The primes below 25 are 2, 3, 5, 7, 11, 13, 17, 19 and 23.
• 20 = 2² × 5, so it is composite.
• To test a number for primality, divide by the primes up to its square root.

Common traps

• Hunting for a constant difference, when the gaps 1, 2, 2, 4, 2, 4 follow no arithmetic rule.
• Assuming every odd number is prime, when 9, 15 and 21 are odd and composite.

No directly related past PYQ was found.