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Modes of a set "help needed"

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by Hmna » Fri Apr 28, 2017 5:15 am
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
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Last edited by Hmna on Fri Apr 28, 2017 6:28 am, edited 2 times in total.
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by Brent@GMATPrepNow » Fri Apr 28, 2017 5:52 am
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
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by Hmna » Fri Apr 28, 2017 6:31 am
Brent@GMATPrepNow wrote:
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
it is 4x-y,y-x
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by Jay@ManhattanReview » Sat Apr 29, 2017 3:05 am
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
Image
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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