Directions for questions 6-10: In each of the following number series, only…

Concept: In an alternating number series, terms at odd positions form one sub-series and terms at even positions form another, independent sub-series. Each sub-series follows its own simple arithmetic pattern, usually a constant common difference. To locate the wrong term, separate the combined series into its two sub-series and check whether each one keeps a constant, consistent difference throughout.

Applying this to the series:

1. Separate the given series 31, 2, 41, 3, 52, 4, 61, 5, 71, 6 into two sub-series: the terms at odd positions (Series I) and the terms at even positions (Series II).

2. Series I (1st, 3rd, 5th, 7th, 9th terms): 31, 41, 52, 61, 71. Series II (2nd, 4th, 6th, 8th, 10th terms): 2, 3, 4, 5, 6.

3. Series II rises by a constant +1 throughout (2, 3, 4, 5, 6), so it is internally consistent and is not the source of the error.

4. Series I should rise by a constant common difference: 31 to 41 is +10, and 61 to 71 is also +10, so the intended common difference for Series I is +10.

5. Applying +10 to the second term of Series I gives 41 + 10 = 51, not 52. So the term recorded as 52 breaks the pattern and should be replaced by 51.

Cross-check: Substituting 51 in place of 52 gives Series I as 31, 41, 51, 61, 71, where every consecutive pair differs by exactly +10, while Series II remains 2, 3, 4, 5, 6 with every consecutive pair differing by +1. Both sub-series are now fully consistent throughout, confirming 51 is correct.