Track / Stage 4 / 270 of 340 #530 of 1964

Problem 530

AMC 12 late, AIME early

Number theory Difficulty 4.9 Find the answer

10. The product of three different positive integers is 24 . What is the largest possible sum of these integers?
A 9
B 11
C 12
D 15
E 16

Your answer

Multiple choice: answer with the letter of the option you want.

Official solution

Solution
D

The possible sets of three different positive integers with a product of 24 are $1,2,12 ; 1,3,8$ ; $1,4,6$ and $2,3,4$ with corresponding sums $15,12,11$ and 9 . Therefore the largest possible sum of these integers is 15 .

Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic, difficulty and ordering added by this site.