Which of the following numbers will replace the question mark (?) in the given series? 232, 221, 199, ?, 122, 67

Question

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

232, 221, 199, ?, 122, 67

1. A. 155
2. B. 165
3. C. 177
4. D. 166 (Correct answer)

Correct Answer

Option D — 166

Detailed Solution & Explanation

The correct answer is 166.

Key Points

• Take the differences: 232 − 221 = 11, 221 − 199 = 22, then 122 − 67 = 55.
• The differences increase by 11 each time: 11, 22, 33, 44, 55.
• So the missing term = 199 − 33 = 166, and the pattern holds since 166 − 44 = 122.
• The series is 232, 221, 199, 166, 122, 67.

Additional Information

• The differences here are 11, 22, 33, 44, 55 — successive multiples of 11.
• The series is decreasing, so each difference is subtracted rather than added; misreading the direction is the usual error when a difference row itself increases.
• A useful check is to work the row from both ends and meet in the middle, which catches an arithmetic slip immediately.