In the following question, one term in the number series is wrong. Find the…

CONCEPT: When a number series does not show one steady pattern from term to term, check whether it is actually two series interleaved together -- one running on the odd positions and another on the even positions. Split the terms accordingly and verify each half independently has its own constant common difference; whichever half breaks its own constant difference contains the wrong term.

1. Write the series with its position number: 3 (1st), 2 (2nd), 8 (3rd), 12 (4th), 13 (5th), 24 (6th), 18 (7th), 32 (8th), 23 (9th), 42 (10th).

2. Take all the odd-position terms together: 3, 8, 13, 18, 23.

3. Take all the even-position terms together: 2, 12, 24, 32, 42.

4. Check the odd-position set: 8-3=5, 13-8=5, 18-13=5, 23-18=5 -- a constant step of +5 throughout, so there is no break here.

5. Check the even-position set: 12-2=10, 24-12=12, 32-24=8, 42-32=10 -- the step size is not constant; it changes right at the 6th term of the original series.

6. The even-position set should also move with a constant step of +10 (matching 2 to 12), so the 6th term of the original series is the one that has gone wrong.

CROSS-CHECK: Restoring a constant +10 step through the even-position set (2, 12, 22, 32, 42) makes every consecutive gap equal to 10, confirming that the 6th term of the original series is the wrong one; the odd-position set was never touched and stays consistent throughout.

ANSWER: 24 is the wrong term in the series.