AMC10 2015 B

AMC10 2015 B · Q4

AMC10 2015 B · Q4. It mainly tests Fractions, Arithmetic misc.

Four siblings ordered an extra large pizza. Alex ate $\frac{1}{5}$, Beth $\frac{1}{3}$, and Cyril $\frac{1}{4}$ of the pizza. Dan got the leftovers. What is the sequence of the siblings in decreasing order of the part of the pizza they consumed?

四个兄弟姐妹点了一份超大披萨。Alex 吃了 $\frac{1}{5}$，Beth 吃了 $\frac{1}{3}$，Cyril 吃了 $\frac{1}{4}$。Dan 吃了剩下的部分。他们按吃披萨份额从多到少的顺序是？

(A) Alex, Beth, Cyril, Dan 亚历克斯, 贝丝, 西里尔, 丹

(B) Beth, Cyril, Alex, Dan 贝丝, 西里尔, 亚历克斯, 丹

(D) Beth, Dan, Cyril, Alex 贝丝, 丹, 西里尔, 亚历克斯

(E) Dan, Beth, Cyril, Alex 丹, 贝丝, 西里尔, 亚历克斯

Answer

Correct choice: (C)

正确答案：（C）

Solution

After the first three siblings ate, there was $1-\frac{1}{5} -\frac{1}{3} -\frac{1}{4} = \frac{13}{60}$ of the pizza left for Dan to eat, so Dan ate more than $\frac{1}{5} = \frac{12}{60}$ but less than $\frac{1}{4} = \frac{15}{60}$ of the pizza. Because $\frac{1}{3} > \frac{1}{4} > \frac{13}{60} > \frac{1}{5}$, the order is Beth, Cyril, Dan, Alex.

前三个兄弟姐妹吃完后，剩下 $1-\frac{1}{5} -\frac{1}{3} -\frac{1}{4} = \frac{13}{60}$ 给 Dan，所以 Dan 吃的比 $\frac{1}{5} = \frac{12}{60}$ 多但少于 $\frac{1}{4} = \frac{15}{60}$。因为 $\frac{1}{3} > \frac{1}{4} > \frac{13}{60} > \frac{1}{5}$，顺序是 Beth、Cyril、Dan、Alex。

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