2005 AMC 8 Problem 1

Attempt Problem 1 of the 2005 AMC 8 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2005 AMC 8 solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

1.

Connie multiplies a number by 22 and gets 6060 as her answer. However, she should have divided the number by 22 to get the correct answer. What is the correct answer?
7.57.5
1515
3030
120120
240240
Answer: B
Concepts:work backwards
Small hint:
Undo Connie’s mistaken multiplication to find the original number.
Big hint:
Then divide that original number by 22.
Solution:
Since Connie multiplied by 2,2, her original number was 60÷2=30.60 \div 2 = 30. To get the correct answer, she must divide by 22 to get 30÷2=15.30 \div 2 = 15.
Thus, B is the correct answer.
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