Problem 1 · 2017 AMC 8
Easy
Arithmetic & Operations
order-of-operations
Which of the following values is the largest?
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Answer: A — 10 (option A).
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Hint 1 of 2
Every option uses the same four digits 2, 0, 1, 7 — the only difference is whether a + or a × sits between them. Adding keeps the digits; multiplying by 0 or 1 throws value away.
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Hint 2 of 2
Order of operations (PEMDAS): all multiplications happen before any addition. The biggest result comes from the option that multiplies least — here, the all-plus option.
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Approach: compare without full computation
- The insight: all-addition (A) keeps every digit working for you; any × either zeroes out a term (anything × 0) or wastes one (anything × 1). So (A) should win — no arithmetic needed to see it leads.
- Confirm: (A) 2 + 0 + 1 + 7 = 10; (B) 0 + 1 + 7 = 8; (C) 2 + 0 + 7 = 9; (D) 2 + 0 + 7 = 9; (E) 0.
- Largest is (A) = 10. You'll see this again: when options differ only by an operation, ask which operation grows the value rather than computing all five.
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