2018阿里巴巴全球数学竞赛预选赛赛题及参考答案VIP专享

The Alibaba Global Mathematics Competition (Hangzhou 2018) consists of 3 problems.Each consists of 3 questions: a, b, and c.This document includes answers for your reference. It is important to note that thereare multiple answers to each question.If you submitted different answers, you maystill get points. We try to write the answers rather thoroughly. It does not mean youranswers need to be as detailed. This document is neither a rubric nor a grading guide.The authors of these answers are not the graders.(correction 11 )Problem 1.a. During the Alibaba 11.11 Shopping Festival, Store A issues “5 RMB off 60 RMB” stackablecoupons. “Stackable” means the multiple coupons can be applied to a single order. For example,an order of 120 RMB at list price, can be reduced to 110 RMB by applying two such coupons.Store A is part of Tmall.com. Tmall.com issues a “60 RMB off 299 RMB” coupon, limited toone per order. This coupon applies to the list price and is stackable with any individual storecoupons. For example, to a product listed at 299 RMB in a Tmall.com store, one pays only 299RMB - (the store discount based on 299 RMB) - 60 RMB. If the total list price is slightly below299RMB, customers often adds filler item(s) (such as socks or tissues) from other Tmall.comstores to reach 299RMB and then apply the coupon.Xiao Ming will buy a 250 RMB pair of headphones and a 600 RMB speaker set from Tmall.comStore A. Xiao Ming has unlimited access to the two types of coupons described. What is theleast amount that he must pay?Answer:709 RMB.To get this answer, we have used filler items from otherstore(s).The answer will be reduced to 705 RMB if there are filler items solelyfrom Store A (but this is...