In this number-pair odd-man-out question, four pairs are given: 9 – 81, 8 – 64, 6 – 36 and 7 – 47. In three of these pairs, the second number is the exact square of the first number. In which pair is this square relation not satisfied, making it the odd one out?

Introduction / Context:
This question belongs to the odd-man-out category involving number pairs. The pairs 9 – 81, 8 – 64, 6 – 36 and 7 – 47 are given. In many aptitude tests, relationships such as squares, cubes and simple multiplications are used to connect two numbers in a pair. Here, three pairs follow a straightforward square relation, where the second number is the square of the first. One pair does not follow this rule and has a mismatched second number.

Given Data / Assumptions:
The number pairs are: 9 – 81, 8 – 64, 6 – 36 and 7 – 47.
For most pairs, we suspect that second = first^2 (square of the first number).
Exactly one pair does not satisfy the square relation.
We assume simple integer arithmetic with no additional operations.

Concept / Approach:
The key concept is the square of a number. For any integer n, n^2 is obtained by multiplying the number by itself. If a pair follows the pattern (n, n^2), it means the second number should be exactly equal to n * n. The strategy is to compute the square of the first number in each pair and check whether it equals the second number. The pair that fails this test is the odd one out.

Step-by-Step Solution:
Step 1: Consider the pair 9 – 81. Compute 9^2 = 9 * 9 = 81, which matches the second number. Step 2: Consider the pair 8 – 64. Compute 8^2 = 8 * 8 = 64, which again matches the second number. Step 3: Consider the pair 6 – 36. Compute 6^2 = 6 * 6 = 36, so this pair also follows the square relation. Step 4: Consider the pair 7 – 47. Compute 7^2 = 7 * 7 = 49, but the second number in the pair is 47, not 49. Step 5: Conclude that three pairs have the exact form (n, n^2), while the pair 7 – 47 does not, making it the odd one.
Verification / Alternative check:
As an alternative, you can mentally recall squares of small integers: 6^2 = 36, 7^2 = 49, 8^2 = 64 and 9^2 = 81. Now match these with the second numbers in each pair. The second numbers 81, 64 and 36 clearly appear in the list of squares, but 47 does not. This confirms that the pair 7 – 47 is inconsistent with the square pattern followed by the others.

Why Other Options Are Wrong:
9 – 81 is correct because the second number is 9^2, so this pair fits the pattern and is not the odd one.
8 – 64 is correct because the second number is 8^2, aligning perfectly with the same square relation.
6 – 36 is correct because the second number is 6^2, again matching the intended pattern.
7 – 47 is the only pair where the second number is not equal to 7^2, which should be 49, not 47.

Common Pitfalls:
A common pitfall is to overlook the exact numeric value and wrongly assume 47 is close enough to 49 to be acceptable. In aptitude questions, the relationships are exact, not approximate. Another mistake is to look for more complex patterns when a simple square relation already fits three of the four options perfectly. Always test for straightforward relations like squares or cubes before considering anything more complicated.

Final Answer:
The pair that does not follow the square relation and is therefore the odd one out is 7 – 47.