Author 
Message 
TAGS:

Hide Tags

Math Expert
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
26 Apr 2019, 03:35
Question Stats:
51% (01:55) correct 49% (01:50) wrong based on 524 sessions
HideShow timer Statistics
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
Official Answer and Stats are available only to registered users. Register/ Login.
_________________




Senior Manager
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
02 May 2019, 15:23
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 longdistance. For more information, please email me at GMATGuruNY@gmail.com.




Math Expert
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
26 Apr 2019, 04:07
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
Joined: 18 Aug 2017
Posts: 5309
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)

Re: If x is a number in the list above, what is the median of the list?
[#permalink]
Show Tags
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
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
27 Apr 2019, 14:47
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
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15498
Location: United States (CA)

Re: If x is a number in the list above, what is the median of the list?
[#permalink]
Show Tags
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.comThe Course Used By GMAT Club Moderators To Earn 750+ souvik101990 Score: 760 Q50 V42 ★★★★★ ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★



Intern
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
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 doublecheck this is possible, the sum = 5.5 x 6 = 33 → x=2. That works, so since two medians are possible, insufficient. Answer A
_________________
SimplyBrilliantPrep.com  Harvard Grad GMAT Instructor with 99th Percentile Scores + Clients Admitted at All Top Business Schools



Intern
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
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
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15498
Location: United States (CA)

Re: If x is a number in the list above, what is the median of the list?
[#permalink]
Show Tags
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.comThe Course Used By GMAT Club Moderators To Earn 750+ souvik101990 Score: 760 Q50 V42 ★★★★★ ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★



Senior Manager
Joined: 22 Feb 2018
Posts: 260
Location: India
Concentration: Entrepreneurship, Healthcare

Re: If x is a number in the list above, what is the median of the list?
[#permalink]
Show Tags
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
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15498
Location: United States (CA)

Re: If x is a number in the list above, what is the median of the list?
[#permalink]
Show Tags
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.comThe Course Used By GMAT Club Moderators To Earn 750+ souvik101990 Score: 760 Q50 V42 ★★★★★ ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★




Re: If x is a number in the list above, what is the median of the list?
[#permalink]
17 Aug 2019, 14:39






