Find the odd number pair from the following alternatives based on whether the second number is 7 more or 7 less than the first.

Introduction / Context:
This odd one out question tests your ability to spot a constant difference between numbers in pairs. Simple addition or subtraction patterns are very common in reasoning questions, and identifying the one pair that uses a different pattern is the key.

Given Data / Assumptions:

• Pairs: 28 - 21, 31 - 38, 45 - 52, 64 - 71.
• We examine the relation between the first and second number in each pair.
• We expect a constant difference, usually plus or minus seven.

Concept / Approach:
The natural idea is to subtract the first number from the second number in each pair. If three pairs give the same result and one gives a different result or opposite sign, that pair is the odd one out. Here, we compare 21 - 28, 38 - 31, 52 - 45, and 71 - 64.

Step-by-Step Solution:
For 28 - 21: 21 - 28 = -7, meaning second = first - 7. For 31 - 38: 38 - 31 = 7, so second = first + 7. For 45 - 52: 52 - 45 = 7, so second = first + 7. For 64 - 71: 71 - 64 = 7, again second = first + 7. Three pairs have the pattern first + 7, but one pair has first - 7. Hence 28 - 21 is different.

Verification / Alternative check:
Instead of subtracting second minus first, you can also look at absolute differences. All pairs have a difference of 7, but the sign of the difference is reversed for one pair. The direction of change is important: in three pairs the number increases by 7, while in one pair it decreases by 7. That decreasing pair is the odd one.

Why Other Options Are Wrong:

• 31 - 38: Here the second value is greater than the first by 7, matching the majority rule.
• 45 - 52: Again, the second number is first + 7, so it fits the pattern.
• 64 - 71: Follows the same rule, with the second number 7 more than the first.

Common Pitfalls:
Some students only check absolute differences and conclude that all pairs are similar because every difference is 7. However, the direction of change from first to second number is crucial here. Overlooking the sign of the difference can cause you to miss the unique decreasing pair and choose the wrong answer.

Final Answer:
28 - 21