Find the wrong number in the following series: 37, 47, 52, 67, 87, 112, 142.

Introduction / Context:
This series is constructed from a simple arithmetic progression applied to a hidden version of the sequence. One term has been altered, and you must identify which value does not fit the intended pattern of regularly increasing differences. Such questions are standard in banking and aptitude exams.

Given Data / Assumptions:

• Series: 37, 47, 52, 67, 87, 112, 142.
• Exactly one number is wrong.
• The intended pattern is likely an arithmetic progression with increasing step size.

Concept / Approach:
We examine the differences between consecutive terms and check whether these differences can be part of a simple sequence, such as adding 5, then 10, then 15, and so on. If one number is incorrect, it will cause the corresponding differences to break this pattern, pointing to the wrong entry.

Step-by-Step Solution:
Step 1: Compute the differences as given. 47 - 37 = 10. 52 - 47 = 5. 67 - 52 = 15. 87 - 67 = 20. 112 - 87 = 25. 142 - 112 = 30. Step 2: Differences: 10, 5, 15, 20, 25, 30. Step 3: Notice that except for the first two, the sequence 5, 15, 20, 25, 30 suggests a pattern of differences which should have started from 5 and then increased by 5 each time: 5, 10, 15, 20, 25, 30. Step 4: If we replace the second term 47 by 42, the sequence becomes 37, 42, 52, 67, 87, 112, 142. Step 5: Now recompute differences: 42 - 37 = 5, 52 - 42 = 10, 67 - 52 = 15, 87 - 67 = 20, 112 - 87 = 25, 142 - 112 = 30. Step 6: These differences form a perfect arithmetic sequence with common difference 5.

Verification / Alternative check:
With the corrected series 37, 42, 52, 67, 87, 112, 142, every step adds 5 more than the previous step. The hidden structure is now an arithmetic progression in the differences. Since only one term needed adjustment and this adjustment falls neatly on the second term, the original given value 47 must have been the error in the series.

Why Other Options Are Wrong:
If we assume that 52, 67, 87, or 112 is wrong and try to fix the series by changing one of those terms, we do not obtain a simple linear progression in the differences. Either we end up with inconsistent step sizes or we have to alter more than one number. Because the question specifies only one wrong term, 47 is the only candidate whose replacement restores a perfectly regular pattern.

Common Pitfalls:
Students sometimes stop after seeing the first difference of 10 and assume the series is random. Another mistake is to search for multiplicative or factorial patterns when the problem is a straightforward linear one. Always systematically compute all differences and look for hidden arithmetic progressions among them before exploring more complicated rules.

Final Answer:
The number that breaks the intended pattern and is therefore wrong is 47.