Select the number from among the given options that can replace the question mark (?) in the following series. 23, 27, 43, 79, 143, ?

Correct — B.

Rule: the gaps are the squares of consecutive even numbers — 2², 4², 6², 8², 10².

27 − 23 = 4
43 − 27 = 16
79 − 43 = 36
143 − 79 = 64

The next gap is 10² = 100, so 143 + 100 = 243, option (b).

Why the others are wrong

• (a)
  240 — 240 would need a final gap of 97, which is not an even square and does not follow 4, 16, 36, 64 by any reading.
• (c)
  200 — 200 would need a gap of 57. The gaps are already growing — by 12, then 20, then 28 — so the next one has to be larger than 64, not smaller.
• (d)
  250 — 250 would need a gap of 107. The run 2², 4², 6², 8² continues to 10² = 100, and 107 is not a square at all.

Take the first differences before anything else on a number series. Here they are 4, 16, 36, 64 — all perfect squares, and all squares of even numbers.

If the squares do not announce themselves, difference again: 12, 20, 28 rise by a constant 8, which fixes the next gap at 64 + 36 = 100.

Two independent routes reaching 100 is good evidence that the rule has been found rather than guessed.

Key facts

• The differences here are 4, 16, 36, 64 and 100 — the squares of 2, 4, 6, 8 and 10.
• The gaps between those differences — 12, 20, 28, 36 — rise by a constant 8.
• The completed series is 23, 27, 43, 79, 143, 243.

Common traps

• Stopping at the first differences when they do not look like a pattern
• Reading 4, 16, 36, 64 as doubling and expecting 128
• Choosing a round number such as 200 or 250 because it looks like a tidy ending

No directly related past PYQ was found.