If x and y are unknown positive integers, is the mean of the : GMAT Data Sufficiency (DS)
Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 23 Jan 2017, 10:06

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

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

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

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

Hide Tags

Intern
Joined: 30 Oct 2011
Posts: 48
Followers: 0

Kudos [?]: 17 [0], given: 13

If x and y are unknown positive integers, is the mean of the [#permalink]

Show Tags

13 Nov 2012, 12:23
4
This post was
BOOKMARKED
00:00

Difficulty:

55% (hard)

Question Stats:

63% (04:24) correct 37% (01:51) wrong based on 194 sessions

HideShow timer Statistics

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

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

OA is
[Reveal] Spoiler:
A
, I am unable to understand why statement 2 is not sufficient. Please help, thanks !
[Reveal] Spoiler: OA

Last edited by Bunuel on 13 Nov 2012, 13:30, edited 1 time in total.
Renamed the topic and edited the question.
Director
Status: Tutor - BrushMyQuant
Joined: 05 Apr 2011
Posts: 583
Location: India
Concentration: Finance, Marketing
Schools: XLRI (A)
GMAT 1: 570 Q49 V19
GMAT 2: 700 Q51 V31
GPA: 3
WE: Information Technology (Computer Software)
Followers: 101

Kudos [?]: 572 [0], given: 55

Re: If x and y are unknown positive integers, is the mean of the [#permalink]

Show Tags

14 Nov 2012, 00:03
If x and y are unknown positive integers, is the mean of the set {6, 7, 1, 5, x, y} greater than the median of the set?

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

STAT1
since x+y = 7 so the mean of the set is fixed
mean = (1 + 5 + 6 + 7 + 7 ) / 6 = 26/6 = 4.33

Since, x and y are both positive integers so only possible values for the pair x,y is (1,6), (2,5) and (3,4). Respective sets will become
{ 1,1,5,6,6,7 } -> median = (5+6)/2 = 5.5
{ 1,2,5,5,6,7 } -> median = (5+5)/2 = 5
{ 1,3,4,5,6,7 } -> median = (4+5)/2 = 4.5

In all the cases median is greater than the mean.
So, A is SUFFICIENT

STAT2
x-y = 3
case1 x=10, y=7
mean = (1+5+6+7+7+10)/6 = 6
set is {1,5,6,7,7,10} -> median = (6+7)/2 = 6.5
median > mean

case2 x=26, y=23
mean = (1+5+6+7+23+26)/6 = 11.3
set is { 1,5,6,7,23,26 } -> median = (6+7)/2 = 6.5
median < mean

So, NOT SUFFICIENT

Hence, Answer is A.
Hope it helps!
_________________

Ankit

Check my Tutoring Site -> Brush My Quant

GMAT Quant Tutor
How to start GMAT preparations?
How to Improve Quant Score?
Gmatclub Topic Tags
Check out my GMAT debrief

How to Solve :
Statistics || Reflection of a line || Remainder Problems || Inequalities

Intern
Joined: 30 Oct 2011
Posts: 48
Followers: 0

Kudos [?]: 17 [0], given: 13

Re: If x and y are unknown positive integers, is the mean of the [#permalink]

Show Tags

14 Nov 2012, 00:09
nktdotgupta wrote:
If x and y are unknown positive integers, is the mean of the set {6, 7, 1, 5, x, y} greater than the median of the set?

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

STAT1
since x+y = 7 so the mean of the set is fixed
mean = (1 + 5 + 6 + 7 + 7 ) / 6 = 26/6 = 4.33

Since, x and y are both positive integers so only possible values for the pair x,y is (1,6), (2,5) and (3,4). Respective sets will become
{ 1,1,5,6,6,7 } -> median = (5+6)/2 = 5.5
{ 1,2,5,5,6,7 } -> median = (5+5)/2 = 5
{ 1,3,4,5,6,7 } -> median = (4+5)/2 = 4.5

In all the cases median is greater than the mean.
So, A is SUFFICIENT

STAT2
x-y = 3
case1 x=10, y=7
mean = (1+5+6+7+7+10)/6 = 6
set is {1,5,6,7,7,10} -> median = (6+7)/2 = 6.5
median > mean

case2 x=26, y=23
mean = (1+5+6+7+23+26)/6 = 11.3
set is { 1,5,6,7,23,26 } -> median = (6+7)/2 = 6.5
median < mean

So, NOT SUFFICIENT

Hence, Answer is A.
Hope it helps!

Thanks for your solution.

In case, X and Y were 'unknown integers' instead of 'unknown positive integers', answer would be E. I am right?
Intern
Status: Fighting to kill GMAT
Joined: 23 Sep 2012
Posts: 33
Location: United States
Concentration: International Business, General Management
Schools: Duke '16
GPA: 3.8
WE: General Management (Other)
Followers: 0

Kudos [?]: 18 [1] , given: 233

Re: If x and y are unknown positive integers, is the mean of the [#permalink]

Show Tags

14 Nov 2012, 00:23
1
This post received
KUDOS
It will take too long time to compute this by using numbers. Is there any shorter way (Bunuel !!!)??
_________________

Kudos is the currency of appreciation.

You can have anything you want if you want it badly enough. You can be anything you want to be and do anything you set out to accomplish, if you hold to that desire with the singleness of purpose. ~William Adams

Many of life's failures are people who did not realize how close to success they were when they gave up. ~Thomas A. Edison

Wir müssen wissen, Wir werden wissen. (We must know, we will know.) ~Hilbert

Director
Status: Tutor - BrushMyQuant
Joined: 05 Apr 2011
Posts: 583
Location: India
Concentration: Finance, Marketing
Schools: XLRI (A)
GMAT 1: 570 Q49 V19
GMAT 2: 700 Q51 V31
GPA: 3
WE: Information Technology (Computer Software)
Followers: 101

Kudos [?]: 572 [0], given: 55

Re: If x and y are unknown positive integers, is the mean of the [#permalink]

Show Tags

14 Nov 2012, 00:24
No, In that case answer will be C as you can find out the exact values of x and y using (1) and (2) so you can tell the mean and median for sure.
_________________

Ankit

Check my Tutoring Site -> Brush My Quant

GMAT Quant Tutor
How to start GMAT preparations?
How to Improve Quant Score?
Gmatclub Topic Tags
Check out my GMAT debrief

How to Solve :
Statistics || Reflection of a line || Remainder Problems || Inequalities

Intern
Joined: 30 Oct 2011
Posts: 48
Followers: 0

Kudos [?]: 17 [0], given: 13

Re: If x and y are unknown positive integers, is the mean of the [#permalink]

Show Tags

14 Nov 2012, 00:56
nktdotgupta wrote:
No, In that case answer will be C as you can find out the exact values of x and y using (1) and (2) so you can tell the mean and median for sure.

Hi Ankit, I tried solving the problem with X and Y as unknown integers but I still think the answer would be A and not C. Can you please help on this. Thanks !
Director
Status: Tutor - BrushMyQuant
Joined: 05 Apr 2011
Posts: 583
Location: India
Concentration: Finance, Marketing
Schools: XLRI (A)
GMAT 1: 570 Q49 V19
GMAT 2: 700 Q51 V31
GPA: 3
WE: Information Technology (Computer Software)
Followers: 101

Kudos [?]: 572 [0], given: 55

Re: If x and y are unknown positive integers, is the mean of the [#permalink]

Show Tags

14 Nov 2012, 01:14
mneeti wrote:
nktdotgupta wrote:
No, In that case answer will be C as you can find out the exact values of x and y using (1) and (2) so you can tell the mean and median for sure.

Hi Ankit, I tried solving the problem with X and Y as unknown integers but I still think the answer would be A and not C. Can you please help on this. Thanks !

Hi,

yes the answer will still be A. I was thinking that taking negative numbers might change the answer but it doesn't look like.
Yes but if x and y can be non integers also then the answer will not be A as in that case both x and y can be equal to 3.5 and the median will be 4.25 in that case.
_________________

Ankit

Check my Tutoring Site -> Brush My Quant

GMAT Quant Tutor
How to start GMAT preparations?
How to Improve Quant Score?
Gmatclub Topic Tags
Check out my GMAT debrief

How to Solve :
Statistics || Reflection of a line || Remainder Problems || Inequalities

Manager
Joined: 28 Jul 2013
Posts: 93
Location: India
Concentration: Marketing, Strategy
GPA: 3.62
WE: Engineering (Manufacturing)
Followers: 1

Kudos [?]: 34 [0], given: 37

Re: If x and y are unknown positive integers, is the mean of the [#permalink]

Show Tags

08 May 2014, 06:25
when we see a summation (x+y) we must understand that this implies a restriction (x & y = positive integer) on x and y. (x,y) can be (1,6), (2,5), (3, 4), (4,3), (5,2) and (6,1). if we consider all these cases we get only one type of answer for this question.

When we see a negative summation between two number the range is not fixed. Eg x-y can be 500000-499997 or x-y can be 7-4
hence choice is not sufficient
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 13517
Followers: 577

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

Re: If x and y are unknown positive integers, is the mean of the [#permalink]

Show Tags

13 Oct 2016, 20:29
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.
_________________
Manager
Joined: 16 Jul 2015
Posts: 57
GMAT 1: 580 Q37 V33
GMAT 2: 580 Q39 V31
GMAT 3: 660 Q44 V36
GMAT 4: 560 Q40 V28
GMAT 5: 580 Q37 V32
GMAT 6: 680 Q45 V37
GMAT 7: 690 Q47 V37
Followers: 0

Kudos [?]: 0 [0], given: 16

Re: If x and y are unknown positive integers, is the mean of the [#permalink]

Show Tags

27 Oct 2016, 07:41
Such questions wherein you need to think of all possible combinations tend to consume a lot of time and at the end of it, there is no guarantee that you have considered all possible number combinations.So is there a definite approach to such questions?
Re: If x and y are unknown positive integers, is the mean of the   [#permalink] 27 Oct 2016, 07:41
Similar topics Replies Last post
Similar
Topics:
1 If x and y are positive integers, is x/y an integer? 3 20 Dec 2015, 04:29
5 If x and y are positive integers, is x y an integer? 4 08 Oct 2015, 07:11
6 If x is a positive integer, is the mean of set S greater tha 5 04 Apr 2014, 18:08
7 If x and y are positive integers, is 4 14 May 2013, 10:21
6 If x and y are positive integers and x is a multiple of y, 13 26 Feb 2011, 16:44
Display posts from previous: Sort by

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

 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®.