AMC8 2005

AMC8 2005 · Q5

AMC8 2005 · Q5. It mainly tests Casework, GCD & LCM.

Soda is sold in packs of 6, 12 and 24 cans. What is the minimum number of packs needed to buy exactly 90 cans of soda?

苏打水有 6 罐、12 罐和 24 罐的包装。要买正好 90 罐苏打水，需要的最少包装数量是多少？

(A) 4 4

(B) 5 5

(D) 8 8

(E) 15 15

Answer

Correct choice: (B)

正确答案：（B）

Solution

(B) To get the minimum number of packs, purchase as many 24-packs as possible: three 24-packs contain 72 cans, which leaves $90 - 72 = 18$ cans. To get the remaining 18 cans, purchase one 12-pack and one 6-pack. The minimum number of packs is 5.

（B）为了使包装数最少，尽可能多买 24 罐装：三箱 24 罐装共有 72 罐，剩下 $90 - 72 = 18$ 罐。为了凑齐剩余的 18 罐，购买一箱 12 罐装和一箱 6 罐装。最少需要 5 箱。

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