Problem Solving

Hmna wrote:If the modes of the set {1, 3, 6, 9, 12, 4x y, y x} are 6 and 9, then x + y is
I. 16
II. 19
III. 21
A) I only
B) II only
C) Both I and III
D) Both I and II

Please clarify the values in blue above. It LOOKS like 4xy and yx, but I'm pretty sure that's not what it's supposed to be.

Cheers
Brent

Hmna wrote:If the modes of the set {1, 3, 6, 9, 12, 4x-y, y-x} are 6 and 9, then x + y is
I. 16
II. 19
III. 21
A) I only
B) II only
C) Both I and III
D) Both I and II

Hi Hmna,

You have been posting few questions. I doubt that the source you refer to is a source for the GMAT questions. Moreover, you should write the source of the question and the correct answer in the post.

Anyway, let's switch to this question.

We know that Mode of a set is/are the element(s) that appear the most number of times.

We are given that the Mode of the set {1, 3, 6, 9, 12, 4x-y, y-x} are 6 and 9. Since no element appears twice, and modes are 6 and 9, it implies that between (4x-y) and (y-x), one is 6 and the other is 9.

Say, 4x-y = 6 and y-x = 9 => x=5 and y=14 => x+y=19. The correct answer must be B or D.

Say, 4x-y = 9 and y-x = 6 => x=5 and y=11 => x+y=16. The correct answer is D.

The correct answer: D

Hope this helps!

Relevant book: Manhattan Review GMAT Number Properties Guide

-Jay
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