In the following number analogy, 85 becomes 58 by reversing the order of its digits. Using the same pattern, which number should complete the analogy 85 : 58 :: 64 : ?

Introduction / Context:
This is a simple numerical analogy where the relationship between the numbers in the first pair is based on reversing the digits. Once we figure out how 85 changes to 58, we apply exactly the same digit reversal rule to 64. Such questions are designed to test careful observation of digit patterns and positional changes rather than complex arithmetic operations.

Given Data / Assumptions:
First pair: 85 : 58. Second pair: 64 : ?. All numbers are two digit positive integers. Digits are rearranged but not altered individually.

Concept / Approach:
From 85 to 58, we notice that the digits 8 and 5 remain the same but swap their positions. This suggests that the transformation rule is reversing the order of the digits. No addition, subtraction, or multiplication is needed. Therefore, to find the number corresponding to 64, we will reverse its digits in the same manner and then select the matching option.

Step-by-Step Solution:
Step 1: Analyse the first pair. The original number is 85. The first digit is 8 and the second digit is 5. The new number is 58, where the first digit is 5 and the second digit is 8. Thus, the digits have been reversed. Step 2: Apply the same reversal to 64. The original number is 64. The first digit is 6 and the second digit is 4. Reversing the digits gives 46. Step 3: Look for 46 among the options. 46 is present as one of the choices, so it is the correct answer.

Verification / Alternative check:
If we attempted any other pattern such as adding a constant, multiplying, or subtracting digits, the neat symmetry observed in 85 : 58 would not be preserved. For example, 64 plus any constant would not obviously mimic 85 turning into 58. However, the reversal rule works perfectly for the first pair and produces a clean and unambiguous result for the second pair. Therefore, 46 is the only number that satisfies the same transformation.

Why Other Options Are Wrong:
42, 36, and 26 involve different digits or unexplained digit changes and do not result from merely reversing 64. 64 is the original number itself; leaving the digits unchanged would not follow the pattern shown by 85 and 58.

Common Pitfalls:
Sometimes test takers look for unnecessary arithmetic operations when the correct rule is simply positional, such as reversing digits. Another common oversight is to misread the pair and assume it indicates subtraction or some difference rather than reversal. The best strategy is to first check whether a straightforward rearrangement of digits explains the transformation. If it does, then use that same rearrangement rule consistently for the next number.

Final Answer:
Following the same digit reversal pattern, 64 should change to 46.