What comes next: 12, 30, 56, 90, 132, ?

Correct — A.
Rule: n × (n + 1), with n = 3, 5, 7, 9, 11.

12 = 3 × 4, 30 = 5 × 6, 56 = 7 × 8.
90 = 9 × 10, 132 = 11 × 12.
Next n is 13: 13 × 14 = 182.

Check with gaps: 18, 26, 34, 42 grow by 8.
Next gap 50, and 132 + 50 = 182 → option (a).

Why the others are wrong

• (b)
  250 — 250 needs a gap of 118 after 132, where the gaps grow by 8 to 50. It is not n × (n + 1) either: 15 × 16 = 240 and 16 × 17 = 272.
• (c)
  190 — 190 needs a gap of 58, a jump of 16 after 42 instead of 8. It falls between 13 × 14 = 182 and 14 × 15 = 210.
• (d)
  293 — 293 is odd. Every term is a number times the next number, and one of any two consecutive numbers is even, so every term here is even.

Two routes solve this series. Products: 12, 30, 56 are 3 × 4, 5 × 6, 7 × 8, an odd number times the next one, and the odd numbers climb by 2.

Gaps: 18, 26, 34, 42 rise by a constant 8, so the next gap is 50. Both routes give 182, and two routes agreeing is a quick check.

Key facts

• 12, 30, 56, 90, 132 are 3 × 4, 5 × 6, 7 × 8, 9 × 10 and 11 × 12.
• A product of two consecutive whole numbers is always even.
• The gaps of this series, 18, 26, 34, 42, 50, grow by 8.

Common traps

• Growing the gap by 16 instead of 8 and picking 190
• Skipping the parity check that rules out 293 at a glance

No directly related past PYQ was found.