Find wrong number in series: 34, 7, 37, 14, 36, 28, 43, 56

Concept

Find the wrong number in an alternating series by splitting the series into two sub-series based on position (odd-placed and even-placed terms), then check each sub-series independently for a consistent rule (a fixed addition, a fixed multiplication, etc.). The number that breaks its sub-series' rule is the wrong number.

Application

1. Split the series 34, 7, 37, 14, 36, 28, 43, 56 by position: the odd-placed terms are 34, 37, 36, 43; the even-placed terms are 7, 14, 28, 56.

2. Even-placed terms follow a ×2 rule: 7×2=14, 14×2=28, 28×2=56 — every term fits.

3. Odd-placed terms follow a +3 rule: 34+3=37 (fits), but 37+3=40, not 36 as given; 40+3=43 still fits the next term.

4. So the odd-placed sub-series should read 34, 37, 40, 43, and 36 is the term that breaks the +3 rule.

Cross-check

Replacing 36 with 40 gives the full series 34, 7, 37, 14, 40, 28, 43, 56, where both sub-series now follow a single consistent rule throughout — confirming 36 is the discrepancy.

Result

Result: 36 is the wrong number in the series.