Using the correct BODMAS order of operations, simplify the expression 504 ÷ 42 × 7 − 63 + 28 and determine its final numerical value.

Introduction / Context:
This question evaluates your skill in applying the BODMAS or PEMDAS rule to a numerical expression involving division, multiplication, subtraction, and addition. Correct use of the order of operations is crucial in aptitude tests to avoid simple but costly mistakes.

Given Data / Assumptions:

• The expression to evaluate is 504 ÷ 42 × 7 − 63 + 28.
• We must perform division and multiplication before addition and subtraction.
• All numbers are integers, so the final answer should be an integer.

Concept / Approach:
According to the order of operations, division and multiplication are carried out from left to right before handling subtraction and addition. We simplify step by step, ensuring that each intermediate result is computed correctly before proceeding.

Step-by-Step Solution:
Start with 504 ÷ 42 × 7 − 63 + 28.First, perform the division: 504 ÷ 42 = 12.Next, multiply this result by 7: 12 × 7 = 84.Now we have 84 − 63 + 28.Perform the subtraction: 84 − 63 = 21.Finally, add 28: 21 + 28 = 49.

Verification / Alternative check:
As a check, we can group the last two operations differently but still respect left to right ordering for equal precedence. From 84 − 63 + 28, if we consider the net effect, subtracting 63 and then adding 28 is equivalent to subtracting 35. So 84 − 35 = 49, which matches the earlier result. This confirms that the final answer is consistent across alternative but valid ways of viewing the operations.

Why Other Options Are Wrong:

• 48 and 38 indicate arithmetic mistakes, such as subtracting or adding incorrectly in the last steps.
• 62 might come from adding 63 instead of subtracting it.
• 39 could result from subtracting 63 and then subtracting 28 by mistake instead of adding it.

Common Pitfalls:

• Incorrectly performing the multiplication after handling subtraction or addition, which breaks the BODMAS rule.
• Miscomputing 504 ÷ 42 or the product with 7 due to rushed calculations.
• Sign errors in the final subtraction and addition steps, especially when multiple operations follow each other.

Final Answer:
49