What should come in place of the question mark '?' in the following number series? 9, 14, 24, 39, 59, ?, 114
- (a)69
- (b)70
- (c)89
- (d)84
Answer
Why
Correct — D.
Rule: differences grow by 5 — +5, +10, +15, +20, +25, +30.
9 + 5 = 14
14 + 10 = 24
24 + 15 = 39
39 + 20 = 59
59 + 25 = 84
Check: 84 + 30 = 114, the printed last term → option (d).
Why the others are wrong
- (a)69 — 69 is 59 + 10, an early gap reused. It also fails the check at the end: 114 − 69 = 45, not the +30 the ladder needs.
- (b)70 — 70 is 59 + 11, leaving a jump of 44 to 114. Neither gap belongs to the +5, +10, +15 … ladder.
- (c)89 — 89 is 59 + 30, which skips the +25 step. The last gap would then be 114 − 89 = 25, so the ladder runs backwards.
Concept
When a series speeds up, write its first differences. Here they are 5, 10, 15, 20, 25 — the multiples of 5 — so each gap is 5 more than the one before.
The last term, 114, is printed after the blank. Use it: the blank must be 59 + 25 and must also leave a gap of 30 to 114. 84 passes both tests.
Key facts
- First differences: 5, 10, 15, 20, 25, 30.
- Second differences are constant at 5.
- A term printed after the blank lets you check the answer from both sides.
Study next
Common traps
- Accepting a value that fits the gap before the blank without testing the gap after it
- Jumping to +30 after 59 and choosing 89
Here the differences are multiples of 5 and the blank sits one place before the end.
25 Sep 2024, 09:00, Reasoning Q.15 uses multiples of 11 the same way, 35, 46, 68, 101, 145, ? with gaps 11, 22, 33, 44, 55, and keys 200.
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