AMC12 2009 A

AMC12 2009 A · Q4

AMC12 2009 A · Q4. It mainly tests Money / coins.

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、五分镍币、十美分币和二十五美分币的存钱罐中取出四枚硬币。下列哪个不可能是这四枚硬币的总价值（以美分计）？

(A) 15 15

(B) 25 25

(D) 45 45

(E) 55 55

Answer

Correct choice: (A)

正确答案：（A）

Solution

Pre-Note: This solution is kinda just guessing, idk you decide. We can solve this problem by trying out numbers to get the answer choices and use the process of elimination to get the answer. Thinking for a few seconds, you can see that for 15 cents there are no possible ways to get it. Now you may be inclined to chose $\textbf{A}$, but we may have missed some way to get 15 cents, so we try the other answer choices. 25 cents can be made with 3 nickels and 1 dimes, 35 cents can be made with 3 dimes and 1 nickel, 45 cents can be made with 1 quarter, 1 dime, and 2 nickels, and finally, 55 cents can be made with 1 quarter and 3 dimes. Therefore the answer is $\boxed{\textbf{A}}$ MisW (talk) Minor Edits by yanchudeng Post-Note: This is my first time using LaTeX so it may look a little ugly.

预注：这个解法有点像猜测，你自己判断。我们可以通过尝试凑出各个选项并用排除法来解决。想一想就会发现，15 美分没有任何可能的凑法。你可能会倾向于选 $\textbf{A}$，但也许我们漏掉了某种凑出 15 美分的方法，所以再检查其他选项。25 美分可以用 3 枚五分镍币和 1 枚十美分币凑出，35 美分可以用 3 枚十美分币和 1 枚五分镍币凑出，45 美分可以用 1 枚二十五美分币、1 枚十美分币和 2 枚五分镍币凑出，55 美分可以用 1 枚二十五美分币和 3 枚十美分币凑出。因此答案是 $\boxed{\textbf{A}}$ MisW (talk) Minor Edits by yanchudeng 后注：这是我第一次使用 LaTeX，所以可能看起来有点丑。

Topics

AR.014 Money / coins