What comes next: 3, 12, 7, 16, 11, 20, 15, ?
- (a)16
- (b)24
- (c)14
- (d)18
Answer
Why
Correct — B.
Rule: two interleaved strands, each +4 (read term to term, +9 and −5 in turn).
Odd places: 3, 7, 11, 15, each +4.
Even places: 12, 16, 20, each +4.
The missing term is the 8th, an even place.
20 + 4 = 24 → option (b)
Why the others are wrong
- (a)16 — 16 is 15 + 1, and it already sits in fourth place. The step into an even place is +9 throughout (3→12, 7→16, 11→20), so 15 is followed by 24.
- (c)14 — 14 would make the series fall after 15. It falls only when moving into an odd place (12→7, 16→11, 20→15). The 8th place is even, so the step is +9.
- (d)18 — 18 fits neither strand. The even-place terms run 12, 16, 20 in steps of +4, so the next one is 24, not 18.
Concept
When a series rises and falls in turn, split it into alternate terms. Terms 1, 3, 5, 7 form one series and terms 2, 4, 6, 8 form another. Here both are plain +4 runs, one starting at 3 and one at 12.
Read term to term, the same series is +9, −5, +9, −5, and either reading gives 24. The strand view is safer, because it tells you which strand the missing term belongs to.
Key facts
- 3, 7, 11, 15 and 12, 16, 20, 24 are both +4 runs.
- Read term to term, the series alternates +9 and −5.
- The missing term is the 8th, so it belongs to the even-place strand.
Study next
Common traps
- Continuing the odd strand (15 + 4 = 19) when the missing term sits in an even place
- Reading term to term and misjudging whether the next step rises or falls
An interleaved series appears at 18 Sep 2024, 12:30, Reasoning Q.14 (20, 25, 25, 35, 30, 45, ?, 55, 40, keyed 35), where the strands step +5 and +10.
Alternating operations appear at 18 Sep 2024, 16:00, Reasoning Q.16 (3, 6, 9, 18, 21, ?, keyed 42), which runs ×2 and +3 in turn.
Related PYQs
No directly related past PYQ was found.