AMC10 2014 B

AMC10 2014 B · Q11

AMC10 2014 B · Q11. It mainly tests Fractions, Interest / growth (simple).

For the consumer, a single discount of n% is more advantageous than any of the following discounts: (1) two successive 15% discounts (2) three successive 10% discounts (3) a 25% discount followed by a 5% discount. What is the smallest possible positive integer value of n?

对于消费者来说，单一的 n% 折扣比以下任何折扣更有利：(1) 连续两次 15% 折扣 (2) 连续三次 10% 折扣 (3) 先 25% 折扣后 5% 折扣。n 的最小正整数值是多少？

(A) 27 27

(B) 28 28

(D) 31 31

(E) 33 33

Answer

Correct choice: (C)

正确答案：（C）

Solution

11. Answer (C): If $P$ is the price paid for an item, then the discounted prices with the three given discounts are given by the following calculations: (1) $(0.85)^2P = 0.7225P$ for a discount of 27.75% (2) $(0.9)^3P = 0.729P$ for a discount of 27.1% (3) $(0.75)\cdot(0.95)P = 0.7125P$ for a discount of 28.75% The smallest integer greater than 27.75, 27.1, and 28.75 is 29.

11. 答案（C）：如果 $P$ 是购买某件商品支付的价格，那么在给定的三种折扣下，折后价格由以下计算给出： (1) $(0.85)^2P = 0.7225P$，对应折扣为 27.75% (2) $(0.9)^3P = 0.729P$，对应折扣为 27.1% (3) $(0.75)\cdot(0.95)P = 0.7125P$，对应折扣为 28.75% 大于 27.75、27.1 和 28.75 的最小整数是 29。

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