Select the number from among the given options that can replace the question mark (?) in the following series. 176,167,156,147,136, ?

Correct — C. Take the differences before looking for anything cleverer.

176 − 167 = 9
167 − 156 = 11
156 − 147 = 9
147 − 136 = 11

Rule: the subtractions alternate −9, −11, −9, −11.

The fifth step is a −9, so 136 − 9 = 127 → option (c).

Why the others are wrong

• (a)
  126 — 126 is 136 − 10. Ten is the average of the two step sizes, not one of them — the series alternates 9 and 11 and never uses 10.
• (b)
  119 — 119 is 136 − 17, a step size that appears nowhere in the series. It looks plausible only if you assume the gaps keep growing.
• (d)
  124 — 124 is 136 − 12, again a step size the series never uses. The gaps here alternate between two fixed values; they do not climb.

A number series that resists a single common difference is usually running two interleaved patterns, and taking the differences exposes it at once.

Here the differences are 9, 11, 9, 11. Read that either as two step sizes taking turns, or as two sub-series: the odd-position terms 176, 156, 136 fall by 20, and the even-position terms 167, 147 also fall by 20.

Both readings land on 127 — as 136 − 9 on the alternating view, and as 147 − 20 on the sub-series view.

Key facts

• The series 176, 167, 156, 147, 136 has differences of 9, 11, 9, 11.
• Its odd-position terms 176, 156, 136 fall by 20 each time.
• Its even-position terms 167 and 147 also fall by 20, which makes 127 the next even-position term.

Common traps

• Averaging the two gaps to 10 and answering 126
• Assuming the gaps grow steadily and answering 124
• Testing only the first difference and treating the whole series as a constant −9

No directly related past PYQ was found.