What would be the next number in the sequence: 52, 56, 48, 64, 32, ?

Introduction / Context:
This number series problem uses alternating addition and subtraction with differences whose magnitudes are doubling. Recognising alternating patterns is essential in reasoning tests because such series often look irregular at first glance. Our task is to determine the next number after 52, 56, 48, 64, 32.

Given Data / Assumptions:
- Sequence: 52, 56, 48, 64, 32, ?- The series alternates between increasing and decreasing values.- A simple numerical pattern involving addition and subtraction is expected.

Concept / Approach:
When a series moves up and down in value, a good strategy is to compute the differences between consecutive terms and see whether these differences themselves follow a pattern. Sometimes the differences may be constant, and at other times they may double or follow another progression. Here, we will calculate these differences and check for a doubling pattern in their magnitudes.

Step-by-Step Solution:
- From 52 to 56: 56 - 52 = +4 (increase of 4).- From 56 to 48: 48 - 56 = -8 (decrease of 8).- From 48 to 64: 64 - 48 = +16 (increase of 16).- From 64 to 32: 32 - 64 = -32 (decrease of 32).- The pattern is: +4, -8, +16, -32. The signs alternate, and the absolute values 4, 8, 16, 32 are doubling each time.- So the next difference should continue the pattern with a positive sign and double the previous magnitude: +64.- Therefore, the missing term is 32 + 64 = 96.

Verification / Alternative check:
- Rebuilding with this rule: 52 (+4) = 56, 56 (-8) = 48, 48 (+16) = 64, 64 (-32) = 32, 32 (+64) = 96.- The pattern of alternating signs with magnitudes 4, 8, 16, 32, 64 is consistent and neatly structured.

Why Other Options Are Wrong:
- 48, 54, 81 and 40 do not correspond to adding 64 to 32, nor do they maintain the doubling pattern of the absolute differences.- Substituting any of these numbers would break the systematic sequence of +4, -8, +16, -32, +64.

Common Pitfalls:
- Some candidates may look only at the differences 4, -8, 16, -32 without recognising that the absolute values are doubling.- Another mistake is to search for a single arithmetic operation instead of realising that the operations alternate between addition and subtraction.- Confusion is also possible if the sign pattern is ignored and attention is only on the sizes of the jumps.

Final Answer:
To continue the alternating doubling pattern, we add 64 to 32, giving 96 as the next number in the sequence.