Last visit was: 19 Nov 2025, 14:26 It is currently 19 Nov 2025, 14:26
Home
GMAT
Messages
Tests
Schools
Events
Rewards
Chat
My Profile
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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
Back to Forum
Create Topic
 1   2   
User avatar
Zaur
User avatar
Joined: 18 Dec 2006
Last visit: 06 Apr 2009
Posts: 19
Own Kudos:
135
 [130]
Posts: 19
Kudos: 135
 [130]
T is a set of y integers, where 0 < y < 7. If the average of Set T is Updated on: 08 Sep 2023, 08:07
Originally posted by Zaur on 04 Apr 2009, 04:50.
Last edited by Bunuel on 08 Sep 2023, 08:07, edited 5 times in total.
Edited the question and added the OA
10
Kudos
Add Kudos
120
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

75% (hard)

Question Stats:

57% (02:17) correct 43% (01:55) wrong based on 1350 sessions

History

Date
Time
Result
Not Attempted Yet
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
ShowHide Answer
Official Answer
E
Most Helpful Reply
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 19 Nov 2025
Posts: 105,390
Own Kudos:
778,361
 [52]
Given Kudos: 99,977
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 105,390
Kudos: 778,361
 [52]
T is a set of y integers, where 0 < y < 7. If the average of Set T is 25 Sep 2010, 10:28
26
Kudos
Add Kudos
25
Bookmarks
Bookmark this Post
Kronax
How C) -x could be the median?
Set consists of elements from 1 to 6, the average x is positive, the median is negative which is impossible due to the range from 1 to 6.
Show more

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.

Answer: E.

Hope it's clear.
User avatar
GMAT TIGER
User avatar
Joined: 29 Aug 2007
Last visit: 17 Aug 2011
Posts: 1,013
Own Kudos:
1,783
 [7]
Given Kudos: 19
Posts: 1,013
Kudos: 1,783
 [7]
T is a set of y integers, where 0 < y < 7. If the average of Set T is 04 Apr 2009, 22:48
5
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
Zaur
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

thanks in advance
Show more

Its E, which is neither an integer nor a multiple of 0.5. Since the set T's elements are integers, median should be either an integer or a multiple of 0.5.
General Discussion
User avatar
Economist
User avatar
Joined: 01 Apr 2008
Last visit: 24 Dec 2018
Posts: 383
Own Kudos:
4,450
Given Kudos: 18
Name: Ronak Amin
Schools: IIM Lucknow (IPMX) - Class of 2014
Schools: IIM Lucknow (IPMX) - Class of 2014
Posts: 383
Kudos: 4,450
T is a set of y integers, where 0 < y < 7. If the average of Set T is 05 Apr 2009, 00:13
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hi Gmat tiger,
You are right that the median should be either an integer or a multiple of 0.5 ( since the number of integers can be even)
But then, 1/3 is also not an integer and not a multiple of 0.5 !! Couldnt get this :(

GMAT TIGER
Zaur
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

thanks in advance

Its E, which is neither an integer nor a multiple of 0.5. Since the set T's elements are integers, median should be either an integer or a multiple of 0.5.
Show more
User avatar
GMAT TIGER
User avatar
Joined: 29 Aug 2007
Last visit: 17 Aug 2011
Posts: 1,013
Own Kudos:
1,783
 [1]
Given Kudos: 19
Posts: 1,013
Kudos: 1,783
 [1]
T is a set of y integers, where 0 < y < 7. If the average of Set T is 05 Apr 2009, 06:39
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
Economist
Hi Gmat tiger,
You are right that the median should be either an integer or a multiple of 0.5 ( since the number of integers can be even)
But then, 1/3 is also not an integer and not a multiple of 0.5 !! Couldnt get this :(

GMAT TIGER
Zaur
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

thanks in advance

Its E, which is neither an integer nor a multiple of 0.5. Since the set T's elements are integers, median should be either an integer or a multiple of 0.5.
Show more

y could be 2, 3, 4, 5, or 6. If y = either 3 or 6, y/3 is an integer.
User avatar
ksharma12
User avatar
Joined: 03 Feb 2010
Last visit: 29 Apr 2012
Posts: 48
Own Kudos:
735
 [1]
Given Kudos: 4
Posts: 48
Kudos: 735
 [1]
T is a set of y integers, where 0 < y < 7. If the average of Set T is 30 Apr 2010, 12:40
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Can someone break down all the choices as to why they can be median?
User avatar
mmphf
User avatar
Joined: 18 Mar 2010
Last visit: 28 Oct 2012
Posts: 46
Own Kudos:
104
 [2]
Given Kudos: 5
Location: United States
Posts: 46
Kudos: 104
 [2]
T is a set of y integers, where 0 < y < 7. If the average of Set T is 30 Apr 2010, 23:29
1
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
ksharma12
Can someone break down all the choices as to why they can be median?
Show more

Rather than think about whether or not they can be the median, think about whether or not they could be an integer or a multiple of 0.5.

a) 0 integer
b) x could be an integer, all we know is that it's the average
c) –x same as b
d) (1/3)y could be an integer if y=3 or y=6
e) (2/7)y cannot be an integer or multiple of 0.5, as y is 1,2,3,4,5 or 6. Sufficient enough to answer the question
avatar
Kronax
avatar
Joined: 27 Aug 2010
Last visit: 12 Nov 2011
Posts: 13
Own Kudos:
28
Given Kudos: 2
Posts: 13
Kudos: 28
T is a set of y integers, where 0 < y < 7. If the average of Set T is 25 Sep 2010, 09:47
Kudos
Add Kudos
Bookmarks
Bookmark this Post
How C) -x could be the median?
Set consists of elements from 1 to 6, the average x is positive, the median is negative which is impossible due to the range from 1 to 6.
avatar
Ousmane
avatar
Joined: 11 Jul 2012
Last visit: 28 Sep 2018
Posts: 35
Own Kudos:
26
 [1]
Posts: 35
Kudos: 26
 [1]
T is a set of y integers, where 0 < y < 7. If the average of Set T is 17 Oct 2012, 03:04
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
It's not always the case that E holds true.
If T contains only one element, let's say 3. The mean is 3. The median OUGHT to be 3, never -3. So C is right.
Can anyone help me out?
User avatar
EvaJager
User avatar
Joined: 22 Mar 2011
Last visit: 31 Aug 2016
Posts: 514
Own Kudos:
2,326
Given Kudos: 43
WE:Science (Education)
Posts: 514
Kudos: 2,326
T is a set of y integers, where 0 < y < 7. If the average of Set T is 17 Oct 2012, 05:02
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Ousmane
It's not always the case that E holds true.
If T contains only one element, let's say 3. The mean is 3. The median OUGHT to be 3, never -3. So C is right.
Can anyone help me out?
Show more

The question is "which of the following could NOT be the median of Set T?"
It means we have to find the option for which the given number can NEVER be the median of Set T.

So, \(-3\) cannot be the median in your example, but there are many other cases when it can be.
Set T contains integers, so negative numbers are not excluded.

\(2/7y\) can never be an integer when \(0<y<7\), while the median MUST be an integer, doesn't matter what is \(y\) and what are the numbers in the set.
User avatar
BillyZ
User avatar
Current Student
Joined: 14 Nov 2016
Last visit: 03 May 2025
Posts: 1,143
Own Kudos:
22,217
Given Kudos: 926
Location: Malaysia
Concentration: General Management, Strategy
Schools: Sloan '23 (D) Tuck '23 (D) Darden '23 (D) Ross '23 (D) Kellogg '23 (D) Wharton '23 (D) Booth '23 (D) Fuqua '24 (A) Harvard '24 (D) Stanford '24 (D)
GMAT 1: 750 Q51 V40 (Online)
GPA: 3.53
Products:
My Reviews
Schools: Sloan '23 (D) Tuck '23 (D) Darden '23 (D) Ross '23 (D) Kellogg '23 (D) Wharton '23 (D) Booth '23 (D) Fuqua '24 (A) Harvard '24 (D) Stanford '24 (D)
GMAT 1: 750 Q51 V40 (Online)
Posts: 1,143
Kudos: 22,217
T is a set of y integers, where 0 < y < 7. If the average of Set T is 23 Jan 2017, 16:19
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
Kronax
How C) -x could be the median?
Set consists of elements from 1 to 6, the average x is positive, the median is negative which is impossible due to the range from 1 to 6.

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.

Answer: E.

Hope it's clear.
Show more

Dear Bunuel,

Since Set T range from 1 to 6, why the sample of T from part C was T={-1, -1, 5}?
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 19 Nov 2025
Posts: 105,390
Own Kudos:
778,361
 [2]
Given Kudos: 99,977
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 105,390
Kudos: 778,361
 [2]
T is a set of y integers, where 0 < y < 7. If the average of Set T is 24 Jan 2017, 01:16
Kudos
Add Kudos
2
Bookmarks
Bookmark this Post
ziyuenlau
Bunuel
Kronax
How C) -x could be the median?
Set consists of elements from 1 to 6, the average x is positive, the median is negative which is impossible due to the range from 1 to 6.

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.

Answer: E.

Hope it's clear.

Dear Bunuel,

Since Set T range from 1 to 6, why the sample of T from part C was T={-1, -1, 5}?
Show more

You are asking the same question: The phrase "T is a set of y integers, where 0 < y < 7" does NOT mean that T consist of elements from 1 to 6, it means that the number of elements (the number of terms) in T is from 1 to 6, inclusive.
User avatar
EMPOWERgmatRichC
User avatar
Major Poster
Joined: 19 Dec 2014
Last visit: 31 Dec 2023
Posts: 21,784
Own Kudos:
12,807
Given Kudos: 450
Status:GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Expert
Expert reply
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Posts: 21,784
Kudos: 12,807
T is a set of y integers, where 0 < y < 7. If the average of Set T is 16 Jan 2018, 13:11
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hi All,

For this question, you can TEST VALUES to eliminate the 4 answers that COULD be the median of Set T.

We're told that Set T consists of Y integers (where 0 < Y < 7) and that the AVERAGE = X = a POSITIVE INTEGER. We're asked which of the answers could NOT be the median.

Answer A: 0... If Set T is {0,0,3} then the average = 1 and the median = 0. Eliminate A.

Answer B: X... If Set T is {1,1,1} then the average = 1 and the median = 1 = X. Eliminate B.

Answer C: -X... If Set T is {-1,-1,5} then the average = 1 and the median = -1 = -X. Eliminate C.

Answer D: Y/3... If Set T is {1,1,1} then the average = 1 and the median = 1 = Y/3. Eliminate D.

There's only one answer left...

Final Answer:
Show Spoiler
E


GMAT assassins aren't born, they're made,
Rich
User avatar
KarishmaB
User avatar
Joined: 16 Oct 2010
Last visit: 19 Nov 2025
Posts: 16,267
Own Kudos:
77,000
 [4]
Given Kudos: 482
Location: Pune, India
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 16,267
Kudos: 77,000
 [4]
T is a set of y integers, where 0 < y < 7. If the average of Set T is 21 Dec 2018, 22:35
2
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
Zaur
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
Show more


Average of two integers will always be either an integer (if both are odd or both are even) or Integer/2 in lowest form (if one is odd and the other is even). The average can never be integer/7 in lowest terms.

Since y is between 0 and 7 exclusive, y is not divisible by 7 and hence, (2/7)y will be (integer/7) in lowest terms.

Median of a set of odd number of integers will be one of the integers.
Median of a set of even number of integers will be the average of middle two integers.
Hence, median cannot be of the form (2/7)y.

Answer (E)
User avatar
ScottTargetTestPrep
User avatar
Target Test Prep Representative
Joined: 14 Oct 2015
Last visit: 19 Nov 2025
Posts: 21,716
Own Kudos:
26,996
Given Kudos: 300
Status:Founder & CEO
Affiliations: Target Test Prep
Location: United States (CA)
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 21,716
Kudos: 26,996
T is a set of y integers, where 0 < y < 7. If the average of Set T is 02 Mar 2019, 09:19
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Zaur
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
Show more

Let’s analyze each answer choices using actual examples.

A. 0

Let x = 1 and y = 3, then T = {-1, 0, 4} has a median of 0.

B. x

Let x = 1 and y = 3, then T = {-1, 1, 3} has a median of 1, which is x.

C. -x

Let x = 1 and y = 3, then T = {-2, -1, 6} has a median of -1, which is -x.

D. (1/3)y

Let x = 1 and y = 3, then T = {-1, 1, 3} has a median of 1, which is (1/3)y.

Since we are looking for the one that could NOT be the median of Set T, then the correct answer must be E. Indeed, the median of a set of y integers is either an integer (if y is odd) or an integer divided by 2 (if y is even). For no integer value of y between 0 and 7 will the median be in the form (2/7)y.

Answer: E
User avatar
BelalHossain046
User avatar
Joined: 11 Feb 2013
Last visit: 05 Apr 2023
Posts: 198
Own Kudos:
314
Given Kudos: 60
Location: United States (TX)
Concentration: Finance
GMAT 1: 490 Q44 V15
GMAT 2: 690 Q47 V38
GRE 1: Q165 V155
GPA: 3.05
WE:Analyst (Commercial Banking)
GMAT 2: 690 Q47 V38
GRE 1: Q165 V155
Posts: 198
Kudos: 314
T is a set of y integers, where 0 < y < 7. If the average of Set T is 21 Apr 2019, 22:03
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Learnings from this question:
[Assumption: all entities of the dataset are integers]
(1) in case of ONE ENTITY or EVERY ENTITY EQUAL data set, Mean=Median.

(2) Median can an Integer or a fraction in the form of multiple of 0.5.

Median is integer if the dataset has
(a) odd nuodd number of entities
(b) even number of entities with the condition that middle twos are either both odd or both even.

Median is integer if the dataset has
even number of entities with the condition that middle twos are odd and even.


(3) Irrespective of the mean (positive, negative or zero), Median can be anything (positive, negative or zero).
Because mean be affected by extreme values, but Median isn’t affected by extremes. Median is based on POSITION middle value in ascending or descending order).

Posted from my mobile device
User avatar
KarishmaB
User avatar
Joined: 16 Oct 2010
Last visit: 19 Nov 2025
Posts: 16,267
Own Kudos:
77,000
 [1]
Given Kudos: 482
Location: Pune, India
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 16,267
Kudos: 77,000
 [1]
T is a set of y integers, where 0 < y < 7. If the average of Set T is 01 Feb 2021, 03:09
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Zaur
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
Show more

Number of integers in T could be anything from 1 to 6.
Avg of T is x.

We need the median of T. The median of T will be either the middle integer or the avg of two middle integers. So median will always be either an Integer or Integer/2. When an integer is divided by 2, it gives either an integer or something.5.

Can an Integer/2 give you 3.1428? No.
Even Integer/ 2 = Integer
Odd Integer/2 = a.5

Now look at the given options.

(E) (2/7)y
You know that y will be 1/2/3/4/5/6. It cannot be 7 or a multiple of 7. So you will need to divide by 7.
Upon division by 7, you get a non terminating decimal. This cannot be the median.

Answer (E)

It seems that the question is testing statistics, it is actually testing understanding of decimals.
User avatar
adityaganjoo
User avatar
Joined: 10 Jan 2021
Last visit: 04 Oct 2022
Posts: 148
Own Kudos:
32
Given Kudos: 154
Posts: 148
Kudos: 32
T is a set of y integers, where 0 < y < 7. If the average of Set T is 14 Jun 2021, 19:58
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Zaur
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
Show more


(A) 0: {-1,0,2}; y=3; median =0; x>0; Possible
(B) x: {-4x,3x,4x}; y=3; median = x; mean = x; Possible for any x>0; Possible
(C) -x: {-x,-x,-x,7x}; y=4; median = -x, mean = x; possible for x>0; Possible

One quicker way to solve between D & E(It took me 2+ minutes to think about this hack - but that is a learning)

Let us think about (D) and (E)
(E) can never be an integer, since y<7. Although that is fine, since median of a set of integers can be a non integer, we need to think about the origin of '7' in the denominator.
Median of a set of integers with even terms can only have 2 in the denominator; So how did 7 end up there?
Let us analyse (D) first:

(D) (1/3)y has the same problem: The origin of 3 in the denominator
A possible case is: y=3 and median = 1;
So, median = 1 = (1/3)*3 = (1/3)y = (D) Therefore, (D) is possible

Thus, the answer is (E)

But why?
In (E), let try to apply the same logic, that we used in (D)
median = 2; and y = some multiple of 7 = 7k
Thus, median = 2 = (2/7)*7k = (2/7)y.
But, according to the question, 0<y<7; Thus, y<7(1)
So, 7 can never be in denominator.

Thus, the answer is (E)
User avatar
Nikhil30
User avatar
Current Student
Joined: 03 Jan 2019
Last visit: 29 Sep 2021
Posts: 28
Own Kudos:
42
Given Kudos: 13
Schools: Ross '23 (A)
Schools: Ross '23 (A)
Posts: 28
Kudos: 42
T is a set of y integers, where 0 < y < 7. If the average of Set T is 13 Jul 2021, 19:06
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
Kronax
How C) -x could be the median?
Set consists of elements from 1 to 6, the average x is positive, the median is negative which is impossible due to the range from 1 to 6.

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.

Answer: E.

Hope it's clear.
Show more

set T consists of y element , 0<y<7 , why you are considering 0 and -ve number.
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 19 Nov 2025
Posts: 105,390
Own Kudos:
778,361
Given Kudos: 99,977
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 105,390
Kudos: 778,361
T is a set of y integers, where 0 < y < 7. If the average of Set T is 14 Jul 2021, 00:30
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Nikhil30
Bunuel
Kronax
How C) -x could be the median?
Set consists of elements from 1 to 6, the average x is positive, the median is negative which is impossible due to the range from 1 to 6.

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.

Answer: E.

Hope it's clear.

set T consists of y element , 0<y<7 , why you are considering 0 and -ve number.
Show more

I think your doubt is already addressed above.

The phrase "T is a set of y integers, where 0 < y < 7" does NOT mean that T consist of elements from 1 to 6, it means that the number of elements (the number of terms) in T is from 1 to 6, inclusive.
 1   2   
Moderators:
Bunuel
Math Expert
105390 posts
Krunaal
Tuck School Moderator
805 posts