1958 AMC 12 Problem 45
Attempt Problem 45 of the 1958 AMC 12 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 1958 AMC 12 solutions, or check the answer key.
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45.
A check is written for dollars and cents, and both two-digit numbers. In error it is cashed for dollars and cents, the incorrect amount exceeding the correct amount by Then:
cannot exceed
can equal
the amount of the check cannot be a multiple of
the incorrect amount can equal twice the correct amount
the sum of the digits of the correct amount is divisible by
Answer: B
Small Hint:
Write the correct and incorrect amounts in cents
Big Hint:
Their difference simplifies to
Solution:
In cents, the incorrect amount minus the correct amount is Since is cents, so The two-digit values satisfy this relation and have Thus that equality can occur.
Therefore, the correct answer is B.