Problem 1 · 2023 AMC 8
Easy
Arithmetic & Operations
order-of-operations
What is the value of (8 × 4 + 2) − (8 + 4 × 2)?
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Answer: D — The answer is 18.
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Hint 1 of 2
The two parentheses use the same three numbers — only the multiply sign moved. So the difference is really a contest between ‘8 × 4’ and ‘4 × 2’.
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Hint 2 of 2
Inside each parentheses, the rule is multiply before you add (order of operations). Evaluate each group, then subtract.
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Approach: order of operations: multiply before you add
- The two parentheses look almost identical — same numbers 8, 4, 2 — but the × sits in a different spot. That's the whole trick: the answer comes from where the multiplication lands, not from the numbers themselves.
- First parentheses: multiply first, so 8 × 4 + 2 = 32 + 2 = 34.
- Second parentheses: 8 + 4 × 2 = 8 + 8 = 16.
- Subtract: 34 − 16 = 18. Sanity check: the first group is much bigger because the big multiply (8 × 4) happens there, so a positive answer feels right.
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