Set S includes elements {8, 2, 11, x, 3, y} and has a mean : GMAT Problem Solving (PS)
Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 19 Jan 2017, 01:12

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# Set S includes elements {8, 2, 11, x, 3, y} and has a mean

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Intern
Joined: 03 Apr 2009
Posts: 1
Schools: Wharton
Followers: 0

Kudos [?]: 1 [0], given: 0

Set S includes elements {8, 2, 11, x, 3, y} and has a mean [#permalink]

### Show Tags

28 Apr 2009, 18:47
2
This post was
BOOKMARKED
00:00

Difficulty:

45% (medium)

Question Stats:

67% (02:42) correct 33% (01:39) wrong based on 228 sessions

### HideShow timer Statistics

Set S includes elements {8, 2, 11, x, 3, y} and has a mean of 7 and a median of 5.5. If x < y, then which of the following is the maximum possible value of x?

A. 0
B. 1
C. 2
D. 3
E. 4
[Reveal] Spoiler: OA

Last edited by Bunuel on 13 Jul 2014, 03:26, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
Manager
Joined: 08 Feb 2009
Posts: 146
Schools: Anderson
Followers: 3

Kudos [?]: 49 [1] , given: 3

Re: Set S includes elements {8, 2, 11, x, 3, y} and has a mean [#permalink]

### Show Tags

29 Apr 2009, 07:59
1
KUDOS
First, reach to the point of getting the equation : x + y = 18
It should take about 20 seconds.

Then Substitute the answer choices into the equation.
I don't know what the answer choices in this case are.
But I'm sure, you would be able to eliminate at least 2 or 3 answer choices. (about 10 seconds).

Say you are left with 2 answer choices. (If you are short on time, guess One of the two and you'll have a 50% probability of getting it right.)

The Median (of 6 numbers) = 5.5. See if the AVERAGE of any two numbers among (2,3,8,11) results in the median. In this case, it does for 3 and 8. (15 seconds).
Once you know that the numbers that contribute towards Median are 3 and 8, and not x or y, then given x < y, x 3. (about 10 seconds)

In less than a minute, you have the Correct answer.
GMAT Tutor
Joined: 24 Jun 2008
Posts: 1183
Followers: 420

Kudos [?]: 1505 [1] , given: 4

Re: Set S includes elements {8, 2, 11, x, 3, y} and has a mean [#permalink]

### Show Tags

01 May 2009, 12:33
1
KUDOS
Expert's post
Abdulla wrote:
Set S includes elements {8, 2, 11, x, 3, y} and has a mean of 7 and a median of 5.5. If x < y, then which of the following is the maximum possible value of x?

OA is 3

If any one knows how to solve this problem fast please share it.

Thanks..

Using the fact that the mean is 7, then x+y = 18. Since x and y are different, one must be less than 9, the other greater than 9. Since x is smaller than y, we know that x < 9.

Now we need to use the median, which is the average of the two middle elements. Say x is greater than 3. Then we will have (since y is larger than 9), the elements x and 8 in the middle of our set, and the median will be (8 + x)/2. If x is greater than 3, then this will be larger than 11/2 = 5.5, so x cannot be greater than 3. Can x be exactly equal to 3? Sure. Then y = 15. So the largest possible value for x is 3.
_________________

GMAT Tutor in Toronto

If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 13441
Followers: 575

Kudos [?]: 163 [0], given: 0

Re: Set S includes elements {8, 2, 11, x, 3, y} and has a mean [#permalink]

### Show Tags

12 Jul 2014, 18:33
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Director
Joined: 23 Jan 2013
Posts: 579
Schools: Cambridge'16
Followers: 1

Kudos [?]: 42 [1] , given: 40

Re: Set S includes elements {8, 2, 11, x, 3, y} and has a mean [#permalink]

### Show Tags

11 Sep 2015, 00:55
1
KUDOS
2,3,8,11 and x,y

we are asked maximal x, so can start backsolving from E. If x=4 it will be 3th term and median=4+8/2=6, so out.
If x=3, median=3+8/2=5.5, so right

D
Manager
Joined: 26 Oct 2016
Posts: 117
Location: United States
Concentration: Marketing, International Business
Schools: HBS '19
GPA: 4
WE: Education (Education)
Followers: 5

Kudos [?]: 14 [2] , given: 522

Re: Set S includes elements {8, 2, 11, x, 3, y} and has a mean [#permalink]

### Show Tags

10 Dec 2016, 17:13
2
KUDOS
All solutions mentioned above are confusion below one seems to be very understandble.

You could also say that since the mean is 7, x + y = 18. Since we have an even number of terms in the set, the median must be the average of the two middle numbers. Our possibilities are

(x + y)/2 = 5.5
(3 + 8)/2 = 5.5
(x + 8)/2 = 5.5

The first one doesn't work, as it contradicts our equation above (that x + y = 18).

If x = 3, the other two both work, so x = 3 is a possible solution. x > 3 is not, as we won't have a median of 5.5, so we're set!
_________________

Thanks & Regards,
Anaira Mitch

Re: Set S includes elements {8, 2, 11, x, 3, y} and has a mean   [#permalink] 10 Dec 2016, 17:13
Similar topics Replies Last post
Similar
Topics:
1 Set Y contains elements {2,4,6,8} which of the following sets have sma 1 27 Apr 2016, 18:49
1 Consider a set S = {2, 4, 6, 8, x, y} with distinct elements. If x and 1 30 Jan 2016, 01:55
7 {3, 5, 8, x} For the above mentioned Set, Mean of the set is equal to 3 21 Dec 2015, 10:42
24 A set S = { x, -8, -5, -4, 4, 6, 9, y } with elements arrang 13 02 Jul 2013, 22:30
Set A has 3 elements and set B has 4 elements. The number of 3 30 Sep 2010, 04:11
Display posts from previous: Sort by

# Set S includes elements {8, 2, 11, x, 3, y} and has a mean

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group and phpBB SEO Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.