求问一道prep数学~

378592285 · 发表于 2015-6-19 13:49:08

Henry purchased 3 items during a sale.  He received a 20 percent discount off the regular price of the most expensive item and a 10 percent discount off the regular price of each of the other 2 items.  Was the total amount of the 3 discounts greater than 15 percent of the sum of the regular prices of the 3 items?

(1)  The regular price of the most expensive item was $50, and the regular price of the next most expensive item was $20.

(2)  The regular price of the least expensive item was $15.

搜到以前有人问过的这题解答，但还是不懂啊，数学渣。。。。求大神~~

jptvhe · 发表于 2015-6-19 14:51:21

假设三件商品按照价格降序排列，价格分别为X,Y,Z
那么打折后总价：0.8X+0.9(Y+Z)
需要比较的对象是全部价格打8.5折：0.85(X+Y+Z)
即，是否0.8X+0.9(Y+Z)>0.85(X+Y+Z)？
简化一下这个不等式有：
是否Y+Z>X
只要能够判断价格低的两件商品的总和是否比最贵的商品贵，那么条件就是sufficient
条件1：最贵的商品X50块，第二贵的商品Y20块，说明Z最大也不会超过20。所以Y+Z一定小于X，条件1充分
条件2：最便宜的商品Z15块，不能确定Y+Z是否大于X。如果Z=15,Y=16,X=50则原命题为假，如果Z=15，Y=50，Z=60则原命题为真。所以条件2不充分
答案应该是A

求问一道prep数学~

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