In aptitude (decimal percentage simplification), evaluate 39.96% of 649.85 divided by 13.07 and then use the relation 39.96% of 649.85 / 13.07 = 45.14 - ? to find the value of the unknown ?.

Introduction / Context:
This question is a good example of decimal and percentage simplification often seen in aptitude tests. It involves converting a percentage into a decimal, multiplying by a non-integer number, dividing by another decimal, and then linking the result to a simple linear expression to find the unknown value denoted by ?. The focus is on handling decimals carefully and understanding that such questions are designed for approximate but accurate arithmetic, not for complex calculators.

Given Data / Assumptions:
- Expression: 39.96% of 649.85 / 13.07 = 45.14 - ?.
- 39.96% means 39.96 / 100 as a decimal multiplier.
- Division by 13.07 must be done after calculating the percentage of 649.85.
- We solve for the unknown ?, treating all numbers as real decimals.

Concept / Approach:
The main concept is to first compute the left-hand side as accurately as required: value = (39.96 / 100) * 649.85 / 13.07. Once that numerical value is found, the equation becomes value = 45.14 - ?, which can be rearranged to ? = 45.14 - value. Since the answer options are integers (24, 25, 26, 27, 28), we expect the result to be close to one of these values and can round appropriately if the decimal is near a whole number.

Step-by-Step Solution:
Step 1: Convert the percentage to decimal: 39.96% = 0.3996.Step 2: Compute 0.3996 * 649.85. This product is approximately 259.80 (more precisely around 259.8, but the exact intermediate is not crucial as long as we keep enough accuracy).Step 3: Now divide by 13.07: 259.8 / 13.07 is approximately 19.87 (more precisely about 19.8684).Step 4: So the left-hand side value is about 19.87.Step 5: Use the equation 19.87 ≈ 45.14 - ?.Step 6: Rearrange to find ?: ? ≈ 45.14 - 19.87 ≈ 25.27.Step 7: Among the integer options, 25 is the closest to 25.27, so ? is taken as 25.

Verification / Alternative check:
To verify, take ? = 25 and recompute the right-hand side: 45.14 - 25 = 20.14. Our left-hand side estimate was around 19.87, which is reasonably close, considering rounding in intermediate steps. If we use more precise values (for example 259.8684 / 13.07), the left-hand side comes out to around 19.868, and 45.14 - 25.27 exactly matches this, justifying 25 as the nearest integer answer. Exam questions of this style expect the nearest integer rather than an exact non-terminating decimal.

Why Other Options Are Wrong:
- 24: Too low compared to the precise difference of about 25.27, off by more than one unit from the exact decimal answer.
- 26 and 27: These values are too large; they would make 45.14 - ? much smaller than the left-hand side, contradicting the equation.
- 28: Even further from the mathematically justified value; it is inconsistent with the computed decimal.

Common Pitfalls:
Common mistakes include interpreting the expression incorrectly, such as taking 39.96% of (649.85 / 13.07) instead of (39.96% of 649.85) divided by 13.07, or misplacing parentheses mentally. Another source of error is poor handling of decimals, like misplacing the decimal point when converting percentages. Some students also round too early in the computation, leading to large final errors. It is better to keep a few decimal places during intermediate steps and only round to match the answer format at the end.

Final Answer:
The value of the unknown ? that best satisfies the equation is 25.