T is a set of y integers, where 0 < y < 7. If the average of Set T is : GMAT Problem Solving (PS)
Check GMAT Club App Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 03 Dec 2016, 02:56

### 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

# T is a set of y integers, where 0 < y < 7. If the average of Set T is

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

### Hide Tags

Manager
Joined: 11 Feb 2011
Posts: 134
Followers: 3

Kudos [?]: 176 [0], given: 21

T is a set of y integers, where 0 < y < 7. If the average of Set T is [#permalink]

### Show Tags

18 Mar 2011, 22:15
2
This post was
BOOKMARKED
00:00

Difficulty:

65% (hard)

Question Stats:

60% (03:05) correct 40% (01:27) wrong based on 64 sessions

### HideShow timer Statistics

T is a set of y integers, where 0 < y < 7. If the average of Set T is the positive integer x, which of the following could NOT be the median of Set T?

A. 0
B. x
C. –x
D. (1/3)y
E. (2/7)y

OPEN DISCUSSION OF THIS QUESTION IS HERE: t-is-a-set-of-y-integers-where-0-y-7-if-the-average-of-77475.html
[Reveal] Spoiler: OA

_________________

target:-810 out of 800!

Last edited by Bunuel on 14 Mar 2016, 05:54, edited 1 time in total.
Renamed the topic and edited the question.
Director
Status: Impossible is not a fact. It's an opinion. It's a dare. Impossible is nothing.
Affiliations: University of Chicago Booth School of Business
Joined: 03 Feb 2011
Posts: 920
Followers: 14

Kudos [?]: 331 [0], given: 123

Re: T is a set of y integers, where 0 < y < 7. If the average of Set T is [#permalink]

### Show Tags

18 Mar 2011, 22:26
Think it's E. 2*6/7 is not integer

Posted from my mobile device
SVP
Joined: 16 Nov 2010
Posts: 1672
Location: United States (IN)
Concentration: Strategy, Technology
Followers: 33

Kudos [?]: 504 [0], given: 36

Re: T is a set of y integers, where 0 < y < 7. If the average of Set T is [#permalink]

### Show Tags

18 Mar 2011, 22:45
-2,-1,0,3,10 - A is out

-1,1,3 - B is out

-3,-3,-3 - C is out

1,1,1 - D is out

D - 2y/7 is the only choice, as y < 7, so y can't be divided by 7
_________________

Formula of Life -> Achievement/Potential = k * Happiness (where k is a constant)

GMAT Club Premium Membership - big benefits and savings

Director
Status: Impossible is not a fact. It's an opinion. It's a dare. Impossible is nothing.
Affiliations: University of Chicago Booth School of Business
Joined: 03 Feb 2011
Posts: 920
Followers: 14

Kudos [?]: 331 [0], given: 123

Re: T is a set of y integers, where 0 < y < 7. If the average of Set T is [#permalink]

### Show Tags

18 Mar 2011, 22:49
Median of 5 integers is integer and 2*5/7 is not integer. Hence it is E

Posted from my mobile device
SVP
Joined: 16 Nov 2010
Posts: 1672
Location: United States (IN)
Concentration: Strategy, Technology
Followers: 33

Kudos [?]: 504 [0], given: 36

Re: T is a set of y integers, where 0 < y < 7. If the average of Set T is [#permalink]

### Show Tags

18 Mar 2011, 22:59
To explain further, the answer choices are :

A.0
B.x
C.-x
D.y/3
E.2y/7

-2,-1,0,3,10 - A is out

Because mean = 10/5 = 2 and media n = 0 (y = 5)

-1,1,3 - B is out

Here mean = 1 and median = 1 (y = 3, x = 1)

-3,-3,12 - C is out

Here mean = 2 and median = -3 (y = 3, x = 3, sorry, the extra -3 was a typo)

1,1,1 - D is out

Here mean = 1 and median = 1 = y/3 (x = 3)

D - 2y/7 is the only choice, as y < 7, so y can't be divided by 7
_________________

Formula of Life -> Achievement/Potential = k * Happiness (where k is a constant)

GMAT Club Premium Membership - big benefits and savings

Math Forum Moderator
Joined: 20 Dec 2010
Posts: 2021
Followers: 162

Kudos [?]: 1664 [0], given: 376

Re: T is a set of y integers, where 0 < y < 7. If the average of Set T is [#permalink]

### Show Tags

19 Mar 2011, 00:07
gmat1220 wrote:
Median of 5 integers is integer and 2*5/7 is not integer. Hence it is E

Posted from my mobile device

I know that 2*y/7 is the correct answer. However, I don't understand your logic. Median of 5 integers is not an integer. What about 2 integers, 4 integers and 6 integers.

Median can be a non-integer. 1,1,2,3,4,6. y=6, Mean=3, Median=2.5

If you said, median of 2*y/7 would be a non-terminating decimal for 0<y<6 and median of any set will either be a terminating decimal or an integer, then I would have definitely agreed.

Maybe I didn't understand you fully, here. Care to explain? thanks
_________________
Director
Status: Impossible is not a fact. It's an opinion. It's a dare. Impossible is nothing.
Affiliations: University of Chicago Booth School of Business
Joined: 03 Feb 2011
Posts: 920
Followers: 14

Kudos [?]: 331 [0], given: 123

Re: T is a set of y integers, where 0 < y < 7. If the average of Set T is [#permalink]

### Show Tags

19 Mar 2011, 00:18
Hey fluke
Consider y=1,3,5 the median of odd number of integers is integer. So you have three cases which can be compared with 2 y/7. Since 2y/7 is never integer for odd values of y I am sure this is the answer. "cannot"be true does not mean "never" be true so you still have cases like y=2,4,6 where the median is non integer.

Posted from my mobile device
Director
Status: Impossible is not a fact. It's an opinion. It's a dare. Impossible is nothing.
Affiliations: University of Chicago Booth School of Business
Joined: 03 Feb 2011
Posts: 920
Followers: 14

Kudos [?]: 331 [0], given: 123

Re: T is a set of y integers, where 0 < y < 7. If the average of Set T is [#permalink]

### Show Tags

19 Mar 2011, 00:39
Never be true is the subset of could not be true. Hope that helps.

Posted from my mobile device
Director
Status: No dream is too large, no dreamer is too small
Joined: 14 Jul 2010
Posts: 650
Followers: 42

Kudos [?]: 833 [0], given: 39

Re: T is a set of y integers, where 0 < y < 7. If the average of Set T is [#permalink]

### Show Tags

19 Mar 2011, 01:11
subhashghosh wrote:
To explain further, the answer choices are :

A.0
B.x
C.-x
D.y/3
E.2y/7

-2,-1,0,3,10 - A is out

Because mean = 10/5 = 2 and media n = 0 (y = 5)

-1,1,3 - B is out

Here mean = 1 and median = 1 (y = 3, x = 1)

-3,-3,12 - C is out

Here mean = 2 and median = -3 (y = 3, x = 3, sorry, the extra -3 was a typo)

1,1,1 - D is out

Here mean = 1 and median = 1 = y/3 (x = 3)

D - 2y/7 is the only choice, as y < 7, so y can't be divided by 7

x=3 or 1?

and y is not divided by but how is 2y is not divided by 7.
_________________

Collections:-
PSof OG solved by GC members: http://gmatclub.com/forum/collection-ps-with-solution-from-gmatclub-110005.html
DS of OG solved by GC members: http://gmatclub.com/forum/collection-ds-with-solution-from-gmatclub-110004.html
100 GMAT PREP Quantitative collection http://gmatclub.com/forum/gmat-prep-problem-collections-114358.html
Collections of work/rate problems with solutions http://gmatclub.com/forum/collections-of-work-rate-problem-with-solutions-118919.html
Mixture problems in a file with best solutions: http://gmatclub.com/forum/mixture-problems-with-best-and-easy-solutions-all-together-124644.html

Director
Status: Impossible is not a fact. It's an opinion. It's a dare. Impossible is nothing.
Affiliations: University of Chicago Booth School of Business
Joined: 03 Feb 2011
Posts: 920
Followers: 14

Kudos [?]: 331 [1] , given: 123

Re: T is a set of y integers, where 0 < y < 7. If the average of Set T is [#permalink]

### Show Tags

19 Mar 2011, 06:23
1
KUDOS
fluke,
This what I found from my notes - Which of the following WOTF (could not be true) has to be done necessarily by elimination.

§ WOTF cannot be true? Plug in numbers until we find four answers that could be true. Eliminate 4 answers and odd one is the final answer.

You can easily eliminate A,B,C because they are integers. Now lets consider D vs E.
Evaluate E - Consider y = 3. The median of odd number of integers MUST be integer and expression 2y/7 is not integer for y=3
Evaluate D - Consider y = 3. y/3 is integer. Hence I have to eliminate D. So in the process I eliminated 4 answer choices A through D to get E.

Pls verify the reasoning and let me know if I have missed anything.
fluke wrote:
gmat1220 wrote:
Median of 5 integers is integer and 2*5/7 is not integer. Hence it is E

Posted from my mobile device

I know that 2*y/7 is the correct answer. However, I don't understand your logic. Median of 5 integers is not an integer. What about 2 integers, 4 integers and 6 integers.

Median can be a non-integer. 1,1,2,3,4,6. y=6, Mean=3, Median=2.5

If you said, median of 2*y/7 would be a non-terminating decimal for 0<y<6 and median of any set will either be a terminating decimal or an integer, then I would have definitely agreed.

Maybe I didn't understand you fully, here. Care to explain? thanks
Math Forum Moderator
Joined: 20 Dec 2010
Posts: 2021
Followers: 162

Kudos [?]: 1664 [1] , given: 376

Re: T is a set of y integers, where 0 < y < 7. If the average of Set T is [#permalink]

### Show Tags

19 Mar 2011, 09:43
1
KUDOS
gmat1220 wrote:
fluke,
This what I found from my notes - Which of the following WOTF (could not be true) has to be done necessarily by elimination.

§ WOTF cannot be true? Plug in numbers until we find four answers that could be true. Eliminate 4 answers and odd one is the final answer.

You can easily eliminate A,B,C because they are integers. Now lets consider D vs E.
Evaluate E - Consider y = 3. The median of odd number of integers MUST be integer and expression 2y/7 is not integer for y=3
Evaluate D - Consider y = 3. y/3 is integer. Hence I have to eliminate D. So in the process I eliminated 4 answer choices A through D to get E.

Pls verify the reasoning and let me know if I have missed anything.
fluke wrote:
gmat1220 wrote:
Median of 5 integers is integer and 2*5/7 is not integer. Hence it is E

Posted from my mobile device

I know that 2*y/7 is the correct answer. However, I don't understand your logic. Median of 5 integers is not an integer. What about 2 integers, 4 integers and 6 integers.

Median can be a non-integer. 1,1,2,3,4,6. y=6, Mean=3, Median=2.5

If you said, median of 2*y/7 would be a non-terminating decimal for 0<y<6 and median of any set will either be a terminating decimal or an integer, then I would have definitely agreed.

Maybe I didn't understand you fully, here. Care to explain? thanks

Thanks gmat1220. Yes, I prefer the elimination myself for these type of questions. You have properly eliminated 4 answer choices. Thus, the fifth one got to be the answer.
_________________
Senior Manager
Joined: 08 Nov 2010
Posts: 417
WE 1: Business Development
Followers: 7

Kudos [?]: 100 [1] , given: 161

Re: T is a set of y integers, where 0 < y < 7. If the average of Set T is [#permalink]

### Show Tags

20 Mar 2011, 10:42
1
KUDOS
it can also be proved very easy.

2y/7 will always be not an integer (y<7)
If y is not even - for sure no integer can be = 2y/7 (when y<7)
if y is even - it means the median is the sum of the two middle terms
so (A+B)/2=2y/7
therefore A+B = 4y/7. if y is an integer between 1-6, again 4y/7 is always not an integer.
and we remember that A and B are integers. the sum of two integers is of course integer as well.
Means - A+B can never be equal to 4y/7.
Proved.
_________________
Director
Joined: 01 Feb 2011
Posts: 757
Followers: 14

Kudos [?]: 114 [0], given: 42

Re: T is a set of y integers, where 0 < y < 7. If the average of Set T is [#permalink]

### Show Tags

20 Mar 2011, 16:30
Nice approach there buddy.

144144 wrote:
it can also be proved very easy.

2y/7 will always be not an integer (y<7)
If y is not even - for sure no integer can be = 2y/7 (when y<7)
if y is even - it means the median is the sum of the two middle terms
so (A+B)/2=2y/7
therefore A+B = 4y/7. if y is an integer between 1-6, again 4y/7 is always not an integer.
and we remember that A and B are integers. the sum of two integers is of course integer as well.
Means - A+B can never be equal to 4y/7.
Proved.
Senior Manager
Joined: 08 Nov 2010
Posts: 417
WE 1: Business Development
Followers: 7

Kudos [?]: 100 [0], given: 161

Re: T is a set of y integers, where 0 < y < 7. If the average of Set T is [#permalink]

### Show Tags

20 Mar 2011, 21:34
Kodus?
_________________
VP
Status: There is always something new !!
Affiliations: PMI,QAI Global,eXampleCG
Joined: 08 May 2009
Posts: 1353
Followers: 17

Kudos [?]: 236 [0], given: 10

Re: T is a set of y integers, where 0 < y < 7. If the average of Set T is [#permalink]

### Show Tags

18 May 2011, 22:16
y<7 hence 2y/7 not an integer.

Median has been mentioned as an integer.

Hence E.
_________________

Visit -- http://www.sustainable-sphere.com/
Promote Green Business,Sustainable Living and Green Earth !!

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 12845
Followers: 559

Kudos [?]: 157 [0], given: 0

Re: T is a set of y integers, where 0 < y < 7. If the average of Set T is [#permalink]

### Show Tags

14 Mar 2016, 03:54
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.
_________________
Math Expert
Joined: 02 Sep 2009
Posts: 35840
Followers: 6828

Kudos [?]: 89685 [1] , given: 10381

Re: T is a set of y integers, where 0 < y < 7. If the average of Set T is [#permalink]

### Show Tags

14 Mar 2016, 05:55
1
KUDOS
Expert's post
2
This post was
BOOKMARKED
AnkitK wrote:
T is a set of y integers, where 0 < y < 7. If the average of Set T is the positive integer x, which of the following could NOT be the median of Set T?

A. 0
B. x
C. –x
D. (1/3)y
E. (2/7)y

Phrase "T is a set of y integers, where 0 < y < 7" doesn't mean that T consist of elements from 1 to 6, it means that number of elements in T is from 1 to 6.

T is a set of y integers, where 0 < y < 7. If the average of Set T is the positive integer x, which of the following could NOT be the median of Set T?

A. $$0$$ --> if $$T=\{0, 0, 3\}$$ then $$mean=x=1$$ and $$median=0$$;

B. $$x$$ --> if $$T=\{3\}$$ then $$mean=x=3$$ and $$median=x=3$$;

C. $$-x$$ --> if $$T=\{-1, -1, 5\}$$ then $$mean=x=1$$ and $$median=-x=-1$$;

D. $$\frac{1}{3}y$$ --> if $$T=\{1, 1, 1\}$$ then $$mean=x=1$$, $$# \ of \ elements=y=3$$ and $$median=\frac{1}{3}y=1$$;

E. $$\frac{2}{7}y$$ --> now, as T is a set of integers then the median is either a middle term, so $$integer$$ OR the average of two middle terms so $$\frac{integer}{2}$$, but as $$y$$ is an integer from 1 to 6 then $$\frac{2}{7}y$$ is neither an $$integer$$ nor $$\frac{integer}{2}$$. So $$\frac{2}{7}y$$ could not be the median.

OPEN DISCUSSION OF THIS QUESTION IS HERE: t-is-a-set-of-y-integers-where-0-y-7-if-the-average-of-77475.html
_________________
Re: T is a set of y integers, where 0 < y < 7. If the average of Set T is   [#permalink] 14 Mar 2016, 05:55
Similar topics Replies Last post
Similar
Topics:
4 The integers v,w,x,y and z are such that 0<v<w<x<y<z. The average of t 3 26 Sep 2016, 05:51
8 If x < y < z and y-x > 5, where x is an even integer and y 12 28 Mar 2012, 01:00
5 If x and y are integers such that x<0<y, and z is non 8 24 Jan 2012, 08:49
5 If x < y < z and y-x > 5, where x is an even integer and y a 6 07 Apr 2011, 05:26
31 T is a set of y integers, where 0 < y < 7. If the average of 16 04 Apr 2009, 03:50
Display posts from previous: Sort by

# T is a set of y integers, where 0 < y < 7. If the average of Set T is

 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®.