In aptitude (nested bracket simplification), evaluate the expression 27 - [38 - {46 - (15 - 13 - 2)}] using the correct order of operations and bracket handling to obtain a single integer value.

Introduction / Context:
This question checks the ability to handle nested brackets and apply the correct order of operations in arithmetic expressions. Aptitude exams frequently include such problems to assess attention to detail and comfort with basic arithmetic under time pressure. The expression uses different bracket types: parentheses, curly braces, and square brackets, but the rule is the same: always simplify the innermost bracket first and then work outward step by step.

Given Data / Assumptions:
- Expression: 27 - [38 - {46 - (15 - 13 - 2)}].
- Standard order of operations is followed: first brackets (from innermost to outermost), then multiplication and division, then addition and subtraction from left to right.
- All numbers are integers and operations are basic addition and subtraction.

Concept / Approach:
The key concept is to simplify one layer of brackets at a time. Start from the innermost parentheses, compute that result, substitute it back into the next level of brackets, and continue outward. Carefully track signs, especially when subtracting entire bracketed expressions, because sign mistakes are the most common source of errors in these problems.

Step-by-Step Solution:
Step 1: Identify the innermost bracket: (15 - 13 - 2).Step 2: Compute inside the parentheses from left to right: 15 - 13 = 2, then 2 - 2 = 0. So (15 - 13 - 2) = 0.Step 3: Substitute back into the curly braces: {46 - (15 - 13 - 2)} becomes {46 - 0} = 46.Step 4: Substitute this into the square brackets: [38 - {46 - (15 - 13 - 2)}] becomes [38 - 46].Step 5: Compute 38 - 46 = -8.Step 6: Now the full expression is 27 - [38 - {46 - (15 - 13 - 2)}] = 27 - (-8).Step 7: Subtracting a negative is the same as adding: 27 - (-8) = 27 + 8 = 35.

Verification / Alternative check:
We can quickly verify by recomputing the inner part: (15 - 13 - 2) = 0, so {46 - 0} = 46, then [38 - 46] = -8, then 27 - (-8) = 35. Repeating the calculation confirms that there are no sign errors and that the sequence of operations has been followed correctly from inner to outer brackets.

Why Other Options Are Wrong:
- 31 or 33: These likely arise from mistakes such as miscomputing 38 - 46 as -6 or misinterpreting 27 - (-8) as 27 - 8 instead of 27 + 8.
- 30 or 29: These values suggest that either the inner parentheses were not evaluated correctly or that the negative sign in front of the square bracket was mishandled, yielding an incorrect intermediate value.

Common Pitfalls:
Typical errors involve miscalculating the innermost bracket or forgetting that subtracting a negative yields addition. Some students perform operations in the wrong order, for example, starting from the left without respecting bracket hierarchy, which leads to completely different results. Always remember to go from inside to outside and to rewrite the expression clearly after each simplification step to avoid confusion.

Final Answer:
The simplified value of the expression is 35.