GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 22 Feb 2019, 06:28

### 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 February
PrevNext
SuMoTuWeThFrSa
272829303112
3456789
10111213141516
17181920212223
242526272812
Open Detailed Calendar
• ### Free GMAT RC Webinar

February 23, 2019

February 23, 2019

07:00 AM PST

09:00 AM PST

Learn reading strategies that can help even non-voracious reader to master GMAT RC. Saturday, February 23rd at 7 AM PT
• ### FREE Quant Workshop by e-GMAT!

February 24, 2019

February 24, 2019

07:00 AM PST

09:00 AM PST

Get personalized insights on how to achieve your Target Quant Score.

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

Author Message
TAGS:

### Hide Tags

Intern
Joined: 03 Apr 2009
Posts: 1
Schools: Wharton
Set S includes elements {8, 2, 11, x, 3, y} and has a mean  [#permalink]

### Show Tags

Updated on: 13 Jul 2014, 03:26
3
00:00

Difficulty:

45% (medium)

Question Stats:

74% (02:35) correct 26% (02:35) wrong based on 294 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

Originally posted by Abdulla on 28 Apr 2009, 18:47.
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: 136
Schools: Anderson
Re: Set S includes elements {8, 2, 11, x, 3, y} and has a mean  [#permalink]

### Show Tags

29 Apr 2009, 07:59
1
2
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: 1350
Re: Set S includes elements {8, 2, 11, x, 3, y} and has a mean  [#permalink]

### Show Tags

01 May 2009, 12:33
1
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

Director
Joined: 23 Jan 2013
Posts: 554
Schools: Cambridge'16
Re: Set S includes elements {8, 2, 11, x, 3, y} and has a mean  [#permalink]

### Show Tags

11 Sep 2015, 00:55
1
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
Director
Joined: 26 Oct 2016
Posts: 636
Location: United States
Schools: HBS '19
GMAT 1: 770 Q51 V44
GPA: 4
WE: Education (Education)
Re: Set S includes elements {8, 2, 11, x, 3, y} and has a mean  [#permalink]

### Show Tags

10 Dec 2016, 17:13
2
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

Director
Joined: 13 Mar 2017
Posts: 703
Location: India
Concentration: General Management, Entrepreneurship
GPA: 3.8
WE: Engineering (Energy and Utilities)
Re: Set S includes elements {8, 2, 11, x, 3, y} and has a mean  [#permalink]

### Show Tags

09 Apr 2018, 20:33
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?

A. 0
B. 1
C. 2
D. 3
E. 4

{8, 2, 11, x, 3, y} ~ {(x,y),2,3,8,11} : Mean = 7
So sum of values = 7*6 = 42
8+2+11+x+3+y = 42
x+y = 42-24 = 18
(x,y) can be (1,17), (2,16), (3,15), ......................, (9,9)

median = 5.5
Since there are even number of items in the set, so the median will be average of mid numbers.
So, average of 3, 8 = 5.5 . hence mid numbers must be 3,8
Also x<y , so x will be on left side of 3 and y will be on right side of 8.

So, x must be less than or equal to 3 and y must be greater than or equal to 8.
Since we need to find the maximum value of x .. x= 3 and y = 15

_________________

CAT 2017 (98.95) & 2018 (98.91) : 99th percentiler
UPSC Aspirants : Get my app UPSC Important News Reader from Play store.

MBA Social Network : WebMaggu

Appreciate by Clicking +1 Kudos ( Lets be more generous friends.)

What I believe is : "Nothing is Impossible, Even Impossible says I'm Possible" : "Stay Hungry, Stay Foolish".

Re: Set S includes elements {8, 2, 11, x, 3, y} and has a mean   [#permalink] 09 Apr 2018, 20:33
Display posts from previous: Sort by