🇺🇸 AMC 8 ⇄ switch contest
2005 AMC 8

Problem 1

Problem 1 · 2005 AMC 8 Easy
Arithmetic & Operations undo-then-redo

Connie multiplies a number by 2 and gets 60 as her answer. However, she should have divided the number by 2 to get the correct answer. What is the correct answer?

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Answer: B — 15.
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Hint 1 of 2
The 60 isn't the answer — it's a clue about the hidden starting number. What number, doubled, gives 60?
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Hint 2 of 2
Two stages: first undo the wrong operation to recover the original, then do the right one. Don't skip straight to the answer.
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Approach: undo the mistake, then redo correctly
  1. The number 60 is the result of multiplying by 2, so the original number is 60 ÷ 2 = 30. (Undo the wrong step.)
  2. Now do what she should have done to that original: 30 ÷ 2 = 15.
  3. Why this transfers: in any 'someone did the wrong operation' puzzle, run the wrong operation backward to find the true input first — never apply the correct operation to the wrong answer (240 and 120 are the traps for doing exactly that).
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