AMC10 2009 A

AMC10 2009 A · Q2

AMC10 2009 A · Q2. It mainly tests Money / coins, Casework.

Four coins are picked out of a piggy bank that contains a collection of pennies, nickels, dimes, and quarters. Which of the following could not be the total value of the four coins, in cents?

从一个装有便士、镍币、角币和25美分硬币的存钱罐中取出4枚硬币。以下哪个不可能是这4枚硬币的总价值（以美分为单位）？

(A) 15 15

(B) 25 25

(D) 45 45

(E) 55 55

Answer

Correct choice: (A)

正确答案：（A）

Solution

The value of any combination of four coins that includes pennies cannot be a multiple of 5 cents, and the value of any combination of four coins that does not include pennies must exceed 15 cents. Therefore the total value cannot be 15 cents. The other four amounts can be made with, respectively, one dime and three nickels; three dimes and one nickel; one quarter, one dime and two nickels; and one quarter and three dimes.

任何包含便士的4枚硬币组合的价值都不是5美分的倍数，而不包含便士的任何4枚硬币组合的价值都必须超过15美分。因此总价值不可能是15美分。其他四个金额分别可以用一枚角币和三枚镍币；三枚角币和一枚镍币；一枚25美分、一枚角币和两枚镍币；一枚25美分和三枚角币来组成。

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