GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

It is currently 18 Feb 2020, 11:04

Close

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
Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

If x and y are unknown positive integers, is the mean of the list {6,

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

Hide Tags

Find Similar Topics 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 61283
If x and y are unknown positive integers, is the mean of the list {6,  [#permalink]

Show Tags

New post 17 Jan 2020, 01:45
00:00
A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

55% (02:47) correct 45% (02:43) wrong based on 58 sessions

HideShow timer Statistics

Director
Director
avatar
P
Joined: 25 Jul 2018
Posts: 547
Re: If x and y are unknown positive integers, is the mean of the list {6,  [#permalink]

Show Tags

New post 17 Jan 2020, 04:48
x , y — unknown positive integers
—> set {6,7,1,5,x,y}
Is the mean of the set greater than the median of the set?

(Statement1): x+ y = 7
There are 3 cases for the values of x and y:

(Case1): 1+6 =7
—> the mean = 26/6 = 4.(3)
--> the median=( 5+6)/2= 5.5
4.(3) < 5.5 (No)

(Case2): 2+5= 7
—> the mean =4.(3).
--> The median = (5+5)/2= 5
4.(3) < 5 (No)

(Case3): 3+4 =7
—> the mean = 4.(3)
--> The median = (4+5)/2= 4.5
4.(3) < 4.5 ( No)
Sufficient

(Statement2): x—y =3
If x =5, y= 2, then
The mean= 4.(3),
the median = (5+5)/2 = 5
4.(3) < 5 (No)

If x= 20, y = 17, then
The mean = 56/6= 9.(3)
the median=( 6+7)/2 = 6.5
—> 9.(3) > 6.5 (Yes)
Insufficient

The answer is A

Posted from my mobile device
GMAT Tutor
avatar
G
Joined: 24 Jun 2008
Posts: 2011
Re: If x and y are unknown positive integers, is the mean of the list {6,  [#permalink]

Show Tags

New post 17 Jan 2020, 05:49
There's a problem with the wording here; in math a "set" does not have repeated elements, but presumably they intend for repetition to be possible (if it's not, Statement 1 is immediately sufficient because x and y need to be 3 and 4).

From Statement 1, we know the exact value of the sum of the six elements, so we can find the mean -- it is 26/6 = 4 + 1/3. Since x and y average to 3.5, one of x or y is less than 3.5, and that's the second-smallest value in the set, and one of them is greater than 3.5, so is at least 4. So to find the median we'll be averaging two numbers, one of which is at least 4 and one of which is at least 5, and the median will be 4.5 or greater, and the median is certainly greater than the mean. So Statement 1 is sufficient.

Using Statement 2, we know x = y + 3. If y is a huge number, the mean will clearly exceed the median. But if y = 1 (assuming repetition of values is allowed), then the mean turns out to be less than the median, so Statement 2 is not sufficient. Even if we disallow repeated values, if y = 8 the mean still turns out to be very slightly less than the median. So the answer is A.
_________________
GMAT Tutor in Montreal

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
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 61283
Re: If x and y are unknown positive integers, is the mean of the list {6,  [#permalink]

Show Tags

New post 17 Jan 2020, 05:54
IanStewart wrote:
There's a problem with the wording here; in math a "set" does not have repeated elements, but presumably they intend for repetition to be possible (if it's not, Statement 1 is immediately sufficient because x and y need to be 3 and 4).

From Statement 1, we know the exact value of the sum of the six elements, so we can find the mean -- it is 26/6 = 4 + 1/3. Since x and y average to 3.5, one of x or y is less than 3.5, and that's the second-smallest value in the set, and one of them is greater than 3.5, so is at least 4. So to find the median we'll be averaging two numbers, one of which is at least 4 and one of which is at least 5, and the median will be 4.5 or greater, and the median is certainly greater than the mean. So Statement 1 is sufficient.

Using Statement 2, we know x = y + 3. If y is a huge number, the mean will clearly exceed the median. But if y = 1 (assuming repetition of values is allowed), then the mean turns out to be less than the median, so Statement 2 is not sufficient. Even if we disallow repeated values, if y = 8 the mean still turns out to be very slightly less than the median. So the answer is A.

_________________________________
Thank you Ian. Replaced "set" with "list".
_________________
GMAT Club Legend
GMAT Club Legend
User avatar
V
Joined: 18 Aug 2017
Posts: 5931
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
GMAT ToolKit User Reviews Badge CAT Tests
Re: If x and y are unknown positive integers, is the mean of the list {6,  [#permalink]

Show Tags

New post 18 Jan 2020, 00:29
given ; 19+x+y/ 6 > middle value avg
#1
x + y = 7 we get pairs ( 7,0 ) ( 6,1) ( 5,2) ( 4,3) ( 5,2)
for all cases we get no as answer
sufficient
#2
x - y = 3
its + difference the value of the mean can be >or < mean of the list
insufficient
IMO A




Bunuel wrote:
If x and y are unknown positive integers, is the mean of the list {6, 7, 1, 5, x, y} greater than the median of the set?

(1) x + y = 7
(2) x - y = 3


Are You Up For the Challenge: 700 Level Questions
VP
VP
avatar
P
Joined: 24 Nov 2016
Posts: 1204
Location: United States
CAT Tests
Re: If x and y are unknown positive integers, is the mean of the list {6,  [#permalink]

Show Tags

New post 22 Jan 2020, 06:00
Bunuel wrote:
If x and y are unknown positive integers, is the mean of the list {6, 7, 1, 5, x, y} greater than the median of the set?

(1) x + y = 7
(2) x - y = 3


{1,5,6,7,x,y}
median is the average of middle terms
mean is (19+x+y)/6
x,y = positive integers ≥ 1

(1) x + y = 7 sufic

(19+x+y)/6=(19+7)/6=26/6=4.333

(x,y)=(1,6): median {1,5,6,7,x,y}={1,1,5,6,6,7}=5.5 > avg
(x,y)=(2,5): median {1,5,6,7,x,y}={1,2,5,5,6,7}=5 > avg
(x,y)=(3,4): median {1,5,6,7,x,y}={1,3,4,5,6,7}=4.5 > avg

(2) x - y = 3 insufic

Ans (A)
GMAT Club Bot
Re: If x and y are unknown positive integers, is the mean of the list {6,   [#permalink] 22 Jan 2020, 06:00
Display posts from previous: Sort by

If x and y are unknown positive integers, is the mean of the list {6,

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





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne