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

It is currently 21 Nov 2019, 03:48

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 is a number in the list above, what is the median of the list?

  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: 59229
If x is a number in the list above, what is the median of the list?  [#permalink]

Show Tags

New post 26 Apr 2019, 03:35
18
00:00
A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

51% (01:55) correct 49% (01:50) wrong based on 524 sessions

HideShow timer Statistics

Most Helpful Expert Reply
Senior Manager
Senior Manager
avatar
G
Joined: 04 Aug 2010
Posts: 493
Schools: Dartmouth College
Re: If x is a number in the list above, what is the median of the list?  [#permalink]

Show Tags

New post 02 May 2019, 15:23
4
2
Bunuel wrote:
7, 9, 6, 4, 5, x

If x is a number in the list above, what is the median of the list?

(1) x > 7
(2) The median of the list equals the arithmetic mean of the list.


Given numbers in ascending order:
4, 5, 6, 7, 9

Statement 1:
Smallest 3 numbers are 4, 5, and 6.
Greatest 3 numbers are 7, 9 and x, where x is any number greater than 7.
Thus:
Median = average of the 2 middle numbers \(= \frac{6+7}{2} = 6.5\)
SUFFICIENT.

Rule:
For any set that is SYMMETRICAL ABOUT THE MEDIAN, average = median.

Statement 2:
Case 1: x=2, so that the resulting set -- 2, 4, 5, 6, 7, 9 -- is symmetrical about the median of 5.5
Case 2: x=8, so that the resulting set -- 4, 5, 6, 7, 8, 9 -- is symmetrical about the median of 6.5
Since the median can be different values, INSUFFICIENT.


_________________
GMAT and GRE Tutor
Over 1800 followers
GMATGuruNY@gmail.com
New York, NY
If you find one of my posts helpful, please take a moment to click on the "Kudos" icon.
Available for tutoring in NYC and long-distance.
For more information, please email me at GMATGuruNY@gmail.com.
General Discussion
Math Expert
avatar
V
Joined: 02 Aug 2009
Posts: 8199
Re: If x is a number in the list above, what is the median of the list?  [#permalink]

Show Tags

New post 26 Apr 2019, 04:07
3
2
7, 9, 6, 4, 5, x

If x is a number in the list above, what is the median of the list?

so the list is 4,5,6,7,9 and x can be placed anywhere in between..
Three cases..

(I) \(x\leq{5}\), median is \(\frac{5+6}{2}\).....4,x,5,6,7,9
(II) \(5<x<6\), median is \(\frac{x+6}{2}\)......4,5,x,6,7,9
(III) \(x\geq{6}\), median is \(\frac{7+6}{2}\)....4,5,6,7,x,9

(1) x > 7
x>7 means x>6, so case III, answer is \(\frac{7+6}{2}\)

(2) The median of the list equals the arithmetic mean of the list.
We can have three cases as mentioned above
(I) 4,x,5,6,7,9..... \(x\leq{5}\), median is \(\frac{5+6}{2}=5.5\).....Mean = \(\frac{4+x+5+6+7+9}{6}=5.5....31+x=33...x=2\)
(II) 4,5,x,6,7,9.....\(5<x<6\), median is \(\frac{x+6}{2}\)......Mean = \(\frac{4+x+5+6+7+9}{6}=\frac{x+6}{2}....31+x=3x+18...2x=13...x=6.5\). But out of range from what we had assumed. So, not possible.
(III) 4,5,6,7,x,9.......\(x\geq{6}\), median is \(\frac{7+6}{2}=6.5\)....Mean = \(\frac{4+x+5+6+7+9}{6}=6.5....31+x=39...x=8\)
Thus, two possible values of x, 2 and 8
Insuff

A
_________________
GMAT Club Legend
GMAT Club Legend
User avatar
V
Joined: 18 Aug 2017
Posts: 5309
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
GMAT ToolKit User Premium Member CAT Tests
Re: If x is a number in the list above, what is the median of the list?  [#permalink]

Show Tags

New post 27 Apr 2019, 10:25
Bunuel wrote:
7, 9, 6, 4, 5, x

If x is a number in the list above, what is the median of the list?

(1) x > 7
(2) The median of the list equals the arithmetic mean of the list.


DS89950.01
OG2020 NEW QUESTION


#1
x>7
x=8
so median of set ; 4,5,6,7,8,9; 6+7/2 ; 6.5 for all values of x>7
sufficeint
#2
The median of the list equals the arithmetic mean of the list.

AM = sum of all digits / 6 ; value of x can be <6 , >6 or =6 so AM will vary
insufficient
IMO A
examPAL Representative
User avatar
P
Joined: 07 Dec 2017
Posts: 1155
Re: If x is a number in the list above, what is the median of the list?  [#permalink]

Show Tags

New post 27 Apr 2019, 14:47
2
The Logical approach to this question is to figure out where x is positioned in the list, since the median of 6 numbers is the average of the two numbers in the middle of the list.
Statement (1) tells us that x and 9 are the two largest numbers, so the median is the average of 6 & 7. That's enough information!
Statement (2) tells us that that the median equals the average. This is a rare case in DS questions in which we must switch to the Precise approach in order to check whether there can be more than one option. If x is larger than or equal to 7, the median, as we saw, is the average between 6 and 7, which is 6.5, so:
(7+9+6+4+5+x)/6=6.5
31+x=39
x=8
Now, if x is smaller than or equal to 5, then the median is the average between 5 and 6, which is 5.5, so:
(7+9+6+4+5+x)/6=5.5
31+x=33
x=2
Since we've already found two different options, it means that statement (2) is not enough on its own, and the correct answer is (A).

Posted from my mobile device
_________________
EMPOWERgmat Instructor
User avatar
V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15498
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: If x is a number in the list above, what is the median of the list?  [#permalink]

Show Tags

New post 13 May 2019, 13:12
Hi All,

We're told that X is a number in the list (7, 9, 6, 5, 4, X). We're asked for the MEDIAN of the list. This question can be solved with Stats rules and TESTing VALUES. To start though, since there are six values in the list, the MEDIAN will be the AVERAGE of the two 'middle terms' (once we arrange the list from least to greatest). With a variable, we don't yet know which two values will be the 'middle two' values yet.

(1) X > 7

Fact 1 tells us that X is GREATER than 7, so it will either be the 5th value in the list or the 6th value in the list. For example:
IF....
X = 8, then the list is 4, 5, 6, 7, 8, 9 and the MEDIAN = (6+7)/2 = 13/2 = 6.5
X = 9, then the list is 4, 5, 6, 7, 9, 9 and the MEDIAN = (6+7)/2 = 13/2 = 6.5
X = 10, then the list is 4, 5, 6, 7, 9, 10 and the MEDIAN = (6+7)/2 = 13/2 = 6.5
Etc.
Thus, the answer to the question is ALWAYS 6.5
Fact 1 is SUFFICIENT

(2) The MEDIAN of the list equals the arithmetic MEAN of the list.

The information in Fact 2 requires a bit more work. To start, we can use one of the above TESTs (from Fact 1):
X = 8, then the list is 4, 5, 6, 7, 8, 9 and the MEDIAN = (6+7)/2 = 13/2 = 6.5

However, that's not the only way for the Median to EQUAL the Mean. If the numbers are equally 'spaced out' around the Mean, then the Median will equal the Mean. That can occur with another value of X...
IF... X = 2, then the list is 2, 4, 5, 6, 7, 9 and the MEDIAN = (5+6)/2 = 11/2 = 5.5
Fact 2 is INSUFFICIENT

Final Answer:

GMAT assassins aren't born, they're made,
Rich
_________________
Contact Rich at: Rich.C@empowergmat.com
Image


The Course Used By GMAT Club Moderators To Earn 750+

souvik101990 Score: 760 Q50 V42 ★★★★★
ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★
Intern
Intern
User avatar
Joined: 22 Jun 2012
Posts: 7
Re: If x is a number in the list above, what is the median of the list?  [#permalink]

Show Tags

New post 20 May 2019, 17:19
Bunuel wrote:
7, 9, 6, 4, 5, x

If x is a number in the list above, what is the median of the list?

(1) x > 7
(2) The median of the list equals the arithmetic mean of the list.


DS89950.01
OG2020 NEW QUESTION


First, rewrite the list in order, remembering we don't know where x falls:
4, 5, 6, 7, 9, x

(1) x > 7 → median = (6+7)/2 sufficient

(2) Mean = Median → x could be 8 since making x=8 creates a set of consecutive integers, and for any evenly spaced set, including any set of consecutive integers, the mean = median. So in that case, the median is 6.5, just as it is in statement (1) since x=8 satisfies statement (1).

Now, look for an easy counterexample. Just as statement (1) made it easy to determine the median because we knew what the two middle numbers were, choosing any x≤5 makes the median = (5+6)/2 = 5.5. To double-check this is possible, the sum = 5.5 x 6 = 33 → x=2. That works, so since two medians are possible, insufficient.

Answer A
_________________
Image
SimplyBrilliantPrep.com - Harvard Grad GMAT Instructor with 99th Percentile Scores + Clients Admitted at All Top Business Schools
Intern
Intern
avatar
Joined: 13 Sep 2013
Posts: 10
Re: If x is a number in the list above, what is the median of the list?  [#permalink]

Show Tags

New post 30 May 2019, 09:54
chetan2u wrote:
7, 9, 6, 4, 5, x

If x is a number in the list above, what is the median of the list?

so the list is 4,5,6,7,9 and x can be placed anywhere in between..
Three cases..

(I) \(x\leq{5}\), median is \(\frac{5+6}{2}\).....4,x,5,6,7,9
(II) \(5<x<6\), median is \(\frac{x+6}{2}\)......4,5,x,6,7,9
(III) \(x\geq{6}\), median is \(\frac{7+6}{2}\)....4,5,6,7,x,9

(1) x > 7
x>7 means x>6, so case III, answer is \(\frac{7+6}{2}\)

(2) The median of the list equals the arithmetic mean of the list.
We can have three cases as mentioned above
(I) 4,x,5,6,7,9..... \(x\leq{5}\), median is \(\frac{5+6}{2}=5.5\).....Mean = \(\frac{4+x+5+6+7+9}{6}=5.5....31+x=33...x=2\)
(II) 4,5,x,6,7,9.....\(5<x<6\), median is \(\frac{x+6}{2}\)......Mean = \(\frac{4+x+5+6+7+9}{6}=\frac{x+6}{2}....31+x=3x+18...2x=13...x=6.5\). But out of range from what we had assumed. So, not possible.
(III) 4,5,6,7,x,9.......\(x\geq{6}\), median is \(\frac{7+6}{2}=6.5\)....Mean = \(\frac{4+x+5+6+7+9}{6}=6.5....31+x=39...x=8\)
Thus, two possible values of x, 2 and 8
Insuff

A

this doesnt take into consideration the case where x=6, and then the median will be 6 as well, though the mean will be still out of range. Am i right?
EMPOWERgmat Instructor
User avatar
V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15498
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: If x is a number in the list above, what is the median of the list?  [#permalink]

Show Tags

New post 30 May 2019, 14:01
Hi nakulanand,

In DS questions, you have to pay careful attention to how each of the two Facts 'restricts' the variables involved. With Fact 1, X has to be greater than 7, so X=6 is NOT an option. With Fact 2, you actually have to do a little more work to prove it, but X=6 is NOT an option there either (since Fact 2 tells us that the MEDIAN = MEAN... and X=6 will NOT make that happen).

GMAT assassins aren't born, they're made,
Rich
_________________
Contact Rich at: Rich.C@empowergmat.com
Image


The Course Used By GMAT Club Moderators To Earn 750+

souvik101990 Score: 760 Q50 V42 ★★★★★
ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★
Senior Manager
Senior Manager
avatar
G
Joined: 22 Feb 2018
Posts: 260
Location: India
Concentration: Entrepreneurship, Healthcare
CAT Tests
Re: If x is a number in the list above, what is the median of the list?  [#permalink]

Show Tags

New post 17 Aug 2019, 09:09
Bunuel/chetan2u/veritaskarishma/empowergmatrich

I fall in the trap by choosing option D. Can anyone please verify and correct my logic?

My logic for statement 2, as correct, is that only consecutive numbers have the same mean and median value. So, i saw only digit 8 as x to be consecutive numbers (4,5,6,7,8,9) in the list as other numbers cann't be placed in the list as consecutive numbers. So, i concluded that there will be only median value for the list and i inferred statement 2 to be correct one.

Thanks.

Bunuel wrote:
7, 9, 6, 4, 5, x

If x is a number in the list above, what is the median of the list?

(1) x > 7
(2) The median of the list equals the arithmetic mean of the list.


DS89950.01
OG2020 NEW QUESTION

_________________
Thanks in the forum can be expressed by hitting Kudos!!!
EMPOWERgmat Instructor
User avatar
V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15498
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: If x is a number in the list above, what is the median of the list?  [#permalink]

Show Tags

New post 17 Aug 2019, 14:39
Hi Raxit85,

When dealing with Quant or Verbal concepts, it can often help to think in terms of the simplest examples that you can come up with (since GMAT questions sometimes take concepts that you know and ask you to think about those concepts in ways that you might not have considered).

Here, we're asked to consider how MEAN and MEDIAN might relate to one another. While a group of CONSECUTIVE INTEGERS will have the SAME median and median, that does NOT mean that only consecutive integers fit that pattern.

For example:
1, 2, 3 --> this group of consecutive integers has median = 2 and mean = 2

0, 2, 4 --> this group has the same number of terms as the first group, but they're NOT consecutive; this group ALSO has median = 2 and mean = 2

By thinking about both ideas (all consecutive vs. not all consecutive), you should be able to come up with another group of numbers that fits the information in this prompt. (my explanation - a little higher up in this thread - showcases those ideas).

GMAT assassins aren't born, they're made,
Rich
_________________
Contact Rich at: Rich.C@empowergmat.com
Image


The Course Used By GMAT Club Moderators To Earn 750+

souvik101990 Score: 760 Q50 V42 ★★★★★
ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★
GMAT Club Bot
Re: If x is a number in the list above, what is the median of the list?   [#permalink] 17 Aug 2019, 14:39
Display posts from previous: Sort by

If x is a number in the list above, what is the median of the list?

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





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