What will come at the place of question mark? 2, 12, 30, 56, 90, ?
- (a)132
- (b)140
- (c)142
- (d)150
Answer
Why
Correct — A.
Rule: n × (n + 1), with n = 1, 3, 5, 7, 9.
2 = 1 × 2, 12 = 3 × 4, 30 = 5 × 6.
56 = 7 × 8, 90 = 9 × 10.
Next n is 11: 11 × 12 = 132.
Check with gaps: 10, 18, 26, 34 grow by 8.
Next gap 42, and 90 + 42 = 132 → option (a).
Why the others are wrong
- (b)140 — 140 would need a gap of 50 after 90, a jump of 16 over the last gap of 34. The gaps grow by 8, so the next one is 42.
- (c)142 — 142 would need a gap of 52 after 90. The gaps run 10, 18, 26, 34 and grow by 8, so the next gap is 42, not 52.
- (d)150 — 150 is 10 × 15, not a product of two consecutive numbers. The pattern's next term is 11 × 12 = 132.
Concept
Two readings solve this series, and they must agree. The first is multiplicative: each term is an odd number times the next whole number, 1 × 2, 3 × 4, 5 × 6 and so on.
The second is differences: 10, 18, 26, 34 climb by 8. Using both catches a slip. 132 fits both readings, and 140, 142 and 150 fit neither.
Products of consecutive numbers, n × (n + 1), are called pronic or oblong numbers. This series takes every second one: 2, 12, 30, 56, 90, 132.
Key facts
- n × (n + 1) for n = 1 to 12: 2, 6, 12, 20, 30, 42, 56, 72, 90, 110, 132, 156.
- Using odd n only (1, 3, 5 …) makes the gaps grow by a constant 8.
- Numbers of the form n × (n + 1) are called pronic or oblong numbers.
Study next
Common traps
- Taking a product such as 10 × 15 = 150 as fitting, without checking that the factors are consecutive
- Adding the last gap again (90 + 34) instead of growing it by 8
12 Sep 2025, 16:00, Reasoning Q.3 starts one term later, 12, 30, 56, 90, 132, ?, and keys 182 = 13 × 14, which confirms 132 as the term after 90.
15 Sep 2025, 16:00, Reasoning Q.18 uses the same product with n rising by 1: 2, 6, 12, 20, 30, keyed 42.
Related PYQs
No directly related past PYQ was found.