AMC 8 2019 Problem 8
AMC8 2019 年第 8 题
百分比★★☆☆☆
Gilda has a bag of marbles. She gives 20% of them to her friend Pedro. Then Gilda gives 10% of what is left to another friend, Ebony. Finally, Gilda gives 25% of what is now left in the bag to her brother Jimmy. What percentage of her original bag of marbles does Gilda have left for herself?
Gilda 有一包玻璃球，她把其中 20％给了她的朋友 Pedro，接着她把剩下的 10％给了另一个朋友 Ebony，最后 Gilda 把包里当前剩下的 25％给了她弟弟 Jimmy。问 Gilda 给她自己留了原来玻璃球总数的百分之多少？
- A.20
- B.
- C.38
- D.45
- E.54
正确答案 · Correct Answer
E
解析 · Solution
Solution 1
After Gilda gives 20 % of the marbles to Pedro, she has 80 % of the marbles left. If she then gives 10 % of what's left to Ebony, she has (0.8*0.9) = 72 % of what she had at the beginning. Finally, she gives 25 % of what's left to her brother, so she has (0.75*0.72) = 54% of what she had in the beginning left.
WOLG, suppose that Gilda has 100 marbles. Then, she gives Pedro 20% of 100, which equals 20, leaving her with 80 marbles. Out of 80 marbles, she gives 10% of 80, which is 8 to Ebony. Thus, she remains with 72 marbles. Then, she gives 25% of 72, which equals 18 to Jimmy, finally leaving her with 54. And, =54%= 54. Use this when you have about 10 minutes left and your brain does not function correctly. Since she gave away 20% and 10% of what is left and then another 25% of what is actually left, we can do 20+10+25 or 55%. But it is actually going to be a bit more than 55% because 10% of what is left is not 10% of the total amount. So, the only option that is greater than 100% - 55% is 54.
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