Question

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?

$4$

$5$

$6$

$8$

$15$

Answer: B

Concepts:optimization

Difficulty rating: 730

Solution:

Four packs cannot be enough. Four $24$ -packs would contain $96$ cans, and replacing any $24$ -pack by a smaller pack decreases the total by either $12$ or $18$ cans. There is no way to decrease $96$ by exactly $6$ cans to reach $90$ .

Five packs do work: three $24$ -packs, one $12$ -pack, and one $6$ -pack contain $3\cdot24+12+6=90$ cans. Therefore, the minimum number is $5$ .

Thus, B is the correct answer.

2005 AMC 8 Problem 5

Answer: B

Difficulty rating: 730

Solution:

Problem 5 in Other Years