In this number analogy, 36 is related to 9 by a simple digit operation. Using the same pattern, 49 is related to which of the following numbers?

Introduction / Context:
This question is a basic number analogy involving an operation on the digits of a two digit number. The example 36 : 9 suggests that 9 is derived from 36 by a simple calculation using its digits. You must find which number stands in the same relationship to 49. Problems like this commonly use the sum, difference or product of digits as the key operation, so testing these quickly is usually the best strategy.

Given Data / Assumptions:

The known pair is 36 : 9.
We need to find the number related to 49 in the same way.
The options are 24, 13, 32 and 15.
We are expected to use simple digit operations rather than advanced formulas.
The operation should be unique and consistent between both pairs.

Concept / Approach:
First, split 36 into digits 3 and 6 and inspect how 9 might be obtained. The sum 3 + 6 equals 9, which matches the right hand side perfectly. The difference 6 - 3 equals 3, and the product 3 * 6 equals 18, neither of which matches 9. Therefore, the pattern is that the second number is the sum of the digits of the first number. Applying this to 49, we compute 4 + 9 and see which option matches that result.

Step-by-Step Solution:
Step 1: Break 36 into its digits: 3 and 6. Step 2: Test the sum of digits: 3 + 6 = 9. This exactly matches the paired number. Step 3: Test other possibilities quickly to ensure uniqueness. The difference 6 - 3 = 3 and the product 3 * 6 = 18, which do not match 9. Step 4: Conclude that the rule is “second number = sum of digits of first number”. Step 5: Now apply this rule to 49 by splitting it into 4 and 9. Step 6: Compute 4 + 9 = 13. Step 7: Look at the options and note that 13 appears as one of them, so 49 is related to 13 in the same way that 36 is related to 9.

Verification / Alternative check:
To verify, imagine extending the pattern to other numbers. If 25 were used, the rule would assign it to 2 + 5 = 7, and if 58 were used, it would map to 5 + 8 = 13. This behaviour is simple and consistent. Rechecking 36 confirms that 3 + 6 = 9, and rechecking 49 confirms that 4 + 9 = 13. None of the other answer choices such as 24, 32 or 15 correspond to the sum of the digits of 49 under this rule, reinforcing that 13 is uniquely correct.

Why Other Options Are Wrong:
Twenty four does not arise from adding, subtracting or multiplying 4 and 9 in a way that mirrors the 36 to 9 example. Thirty two is unrelated to the digits 4 and 9 under the simple sum rule. Fifteen is close to 4 * 4 but has no direct connection to 4 and 9 in this context. Because the only clear and consistent operation in the example pair is the sum of digits, any option that does not equal 4 + 9 must be rejected.

Common Pitfalls:
A common error is to assume that the second number must be a square root or a square of some part of the first number, especially since 36 and 49 are both perfect squares. However, the example 36 : 9 is better explained by the sum of its digits than by square roots, because 9 is both the sum and the square root of 81 but not of 36 alone. The decisive test is to see whether the same reasoning extends naturally to 49. Only the sum of digits gives a neat and consistent mapping, so focusing on digit sums rather than square roots leads to the correct answer.

Final Answer:
Since 36 maps to 9 as 3 + 6 and 49 maps to 13 as 4 + 9, the correct completion of the analogy is 13.