In this digit based number analogy, 97 is related to 2 by a simple operation on its digits; using the same idea, select the number that completes the pattern: 97 : 2 :: 84 : ?

Introduction / Context:
This is a number analogy that involves working with the digits of two digit numbers. The pair 97 : 2 suggests that a simple operation on the digits 9 and 7 produces the value 2. You must apply the same digit based rule to 84 and choose the correct result from the options. This type of question checks your alertness to basic arithmetic patterns involving digits.

Given Data / Assumptions:

• The first pair is 97 mapped to 2.
• The second pair is 84 mapped to an unknown number.
• The same operation must be applied to both pairs in a consistent way.
• The likely operations are sum, difference or some combination of the digits.

Concept / Approach:
Start by examining common operations on digits. For 97, the sum of digits is 9 plus 7 equals 16, which does not give 2 directly. However, the difference between 9 and 7 equals 2, which matches the given mapping. Therefore, the rule appears to be that the result is the absolute difference between the tens digit and the units digit. We can then apply this difference rule to 84.

Step-by-Step Solution:
Step 1: For the number 97, identify the tens digit as 9 and the units digit as 7.Step 2: Compute the difference between these digits: 9 minus 7 equals 2.Step 3: This matches the given second number in the pair, so the rule is consistent for 97.Step 4: Now apply the same rule to 84. The tens digit is 8 and the units digit is 4.Step 5: Compute the difference between the digits: 8 minus 4 equals 4.Step 6: Among the options, 4 appears as option A, so that is the correct mapping for 84.

Verification / Alternative check:
We can test whether any other simple digit operation might be possible. For 97, the digit sum 9 plus 7 equals 16, which would require further steps like taking the sum of digits again to reach 7 or similar, but 2 cannot be obtained in a straightforward consistent way. The cleanest and simplest rule is the digit difference. Applying that same rule to 84 gives 4, which is clearly present in the options.

Why Other Options Are Wrong:
Option B, 3, would be the digit difference for 63 or 96, not for 84. Option C, 6, could be the digit difference for 42 or 60, but not 84. Option D, 5, similarly does not correspond to 8 minus 4. None of these values arise from the direct digit difference of the number 84, so they do not satisfy the analogy.

Common Pitfalls:
Students sometimes try to overcomplicate the pattern, looking for squares or products of digits when a simple operation would do. Another common mistake is to take the difference in the wrong order or to forget that the absolute difference should be non negative. Here, 8 minus 4 is straightforward, and keeping the rule as simple as possible helps avoid confusion.

Final Answer:
Using the same digit difference rule, 84 corresponds to 4, so option A is correct.