Which of the following numbers will replace the question mark (?) in the given series? 11, 36, ?, 121, 185, 266

Question

Which of the following numbers will replace the question mark (?) in the given series?

11, 36, ?, 121, 185, 266

1. A. 68
2. B. 72 (Correct answer)
3. C. 70
4. D. 63

Correct Answer

Option B — 72

Detailed Solution & Explanation

The correct answer is 72.

Key Points

• Examine the differences between consecutive terms: 36 − 11 = 25, 121 − ? and ? − 36 to be found, 185 − 121 = 64, 266 − 185 = 81.
• The differences are perfect squares: 25, 36, 49, 64, 81 — that is 5², 6², 7², 8², 9².
• So the missing term = 36 + 36 = 72, and the next check holds since 72 + 49 = 121.
• The series is therefore 11, 36, 72, 121, 185, 266.

Additional Information

• The differences here are 25, 36, 49, 64, 81 — the squares of 5, 6, 7, 8 and 9 in sequence.
• When the numbers themselves show no obvious pattern, always compute the row of differences; if that row is still unclear, take the differences of the differences.
• It pays to recognise the perfect squares up to at least 20² and the cubes up to 10² on sight, since difference rows in JKSSB series questions are very often built from them.