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
Modes of a set "help needed"
This topic has expert replies
GMAT/MBA Expert
- Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Joined: Mon Dec 08, 2008 6:26 pm
- Location: Vancouver, BC
- Thanked: 5254 times
- Followed by:1268 members
- GMAT Score:770
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.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
Cheers
Brent
it is 4x-y,y-xBrent@GMATPrepNow wrote: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.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
Cheers
Brent
GMAT/MBA Expert
- Jay@ManhattanReview
- GMAT Instructor
- Posts: 3008
- Joined: Mon Aug 22, 2016 6:19 am
- Location: Grand Central / New York
- Thanked: 470 times
- Followed by:34 members
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
_________________
Manhattan Review GMAT Prep
Locations: New York | Beijing | Auckland | Milan | and many more...
Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.