In this number analogy, “8 is to 32 as ______ is to 108”. Choose the number that completes the relationship in the same way for both pairs.

Introduction / Context:
This analogy checks recognition of a simple multiplicative pattern. We are given 8 : 32 and asked to find a number that relates to 108 in the same way. Such questions often use basic operations like multiplication or exponentiation and are common in quantitative aptitude tests to assess pattern recognition with small integers.

Given Data / Assumptions:

• First pair: 8 corresponds to 32. • Second pair: ? corresponds to 108. • Options: 22, 24, 27, 29. • We suspect a multiplication relationship, since 32 is a simple multiple or power of 8.

Concept / Approach:
The most obvious relationship is that 32 is 4 times 8, that is, 8 * 4 = 32. If the pattern is “multiply the first number by 4 to get the second”, then in the second pair the unknown number multiplied by 4 must give 108. To find this unknown, we reverse the operation by dividing 108 by 4 and checking which option matches the result.

Step-by-Step Solution:
Step 1: Confirm the pattern in the first pair. 8 * 4 = 32, so the rule could be “multiply by 4”. Step 2: Apply the inverse operation to 108. If x * 4 = 108, then x = 108 / 4. Step 3: Perform the division: 108 / 4 = 27. Step 4: Check whether 27 is among the options. Option 27 is present as option C, so this fits perfectly.

Verification / Alternative check:
We can verify consistency by writing both pairs according to the same formula. First pair: (8, 8 * 4) = (8, 32). Second pair: (27, 27 * 4) = (27, 108). Both pairs now clearly follow the rule (a, 4a). None of the other options, if multiplied by 4, produces 108. For example, 24 * 4 = 96 and 29 * 4 = 116, which are not equal to 108.

Why Other Options Are Wrong:
• 22: 22 * 4 = 88, not 108, so it fails the analogy pattern. • 24: 24 * 4 = 96; again, it does not give 108. • 29: 29 * 4 = 116; this overshoots 108.

Common Pitfalls:
Some candidates may try to use more complex patterns such as squares or cubes when a simple multiplication works perfectly. Others may guess at options near 25 without checking the exact product. The safest approach is always to explicitly compute the operation that links the first pair and then apply it systematically to the second pair, which quickly leads to 27.

Final Answer:
The number that correctly completes the analogy is 27.