Mar 20 09:00 PM EDT  10:00 PM EDT Strategies and techniques for approaching featured GMAT topics. Wednesday, March 20th at 9 PM EDT Mar 20 07:00 AM PDT  09:00 AM PDT Join a FREE 1day workshop and learn how to ace the GMAT while keeping your fulltime job. Limited for the first 99 registrants. Mar 23 07:00 AM PDT  09:00 AM PDT Christina scored 760 by having clear (ability) milestones and a trackable plan to achieve the same. Attend this webinar to learn how to build trackable milestones that leverage your strengths to help you get to your target GMAT score. Mar 27 03:00 PM PDT  04:00 PM PDT Join a free live webinar and learn the winning strategy for a 700+ score on GMAT & the perfect application. Save your spot today! Wednesday, March 27th at 3 pm PST
Author 
Message 
TAGS:

Hide Tags

Director
Joined: 03 Sep 2006
Posts: 777

If x is an integer, is the median of the 5 numbers shown gre
[#permalink]
Show Tags
17 Jun 2007, 19:05
Question Stats:
63% (02:20) correct 37% (02:17) wrong based on 389 sessions
HideShow timer Statistics
x,3,1,12,8 If x is an integer, is the median of the 5 numbers shown greater than the average (arithmetic mean ) of the 5 numbers ? (1) x > 6 (2) x is greater than the median of the 5 numbers.
Official Answer and Stats are available only to registered users. Register/ Login.




Math Expert
Joined: 02 Sep 2009
Posts: 53738

If x is an integer, is the median of the 5 numbers shown gre
[#permalink]
Show Tags
02 Nov 2010, 09:09
metallicafan wrote: \(x, 3, 1, 12, 8\)
If x is an integer, is the median of the 5 numbers shown greater than the average (arithmetic mean) of the 5 numbers?
(1) \(x>6\) (2) x is greater than the median of the 5 numbers We have a set: {1, 3, 8, 12, x} Question: is \(median>mean=\frac{x+1+3+8+12}{5}=\frac{x+24}{5}\)? Note that as we have odd (5) # of terms in the set then the median will be the middle term when arranged in ascending (or descending) order. So: if \(x\leq{3}\): {1, x, 3, 8, 12} then \(median=3\); if \(3<x\leq{8}\): {1, 3, x, 8, 12} then \(median=x\); if \(x\geq{8}\): {1, 3, 8, x, 12} then \(median=8\). (1) \(x>6\). If \(x=7\) then the median will be 7 as well: {1, 3, 7, 8, 12} and mean will be \(mean=\frac{7+24}{5}=6.2\), so \(median=7>mean=6.2\) and the answer is YES BUT if \(x\) is very large number then the median will be 8: {1, 3, 8, 12, x=very large number} and mean will be more than median (for example if \(x=26\) then \(mean=\frac{26+24}{5}=10\), so \(median=8<10=mean\)) and the answer will be NO. Not sufficient. (2) x is greater than the median of the 5 numbers > so \(median=8\): now, if \(x=11\) then \(mean=\frac{11+24}{5}=7\), so \(median=8>7=mean\) and the answer is YES. Again it's easy to get answer NO with very large \(x\). Not sufficient. (1)+(2) Again, x=11 and x=very large number give two diffrent answers to the question. Not sufficeint. Answer: E.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics




Senior Manager
Joined: 21 Jun 2006
Posts: 272

Both are sufficient..
put the nos in ascending seq. 1,3,8,12 and x. We don't no where x is positioned.
X > 6 could mean that X is the median or 8 is the median.
if X =7 then mean = 6.2 and X > mean
if x= 11 then mean = 7 and X > mean
X greater than median of 5 nos. Which means that median HAS to be 8.
x> 8
Again satisfies the question for any value of x.
D



Senior Manager
Joined: 03 Jun 2007
Posts: 347

ArvGMAT wrote: Both are sufficient.. put the nos in ascending seq. 1,3,8,12 and x. We don't no where x is positioned.
X > 6 could mean that X is the median or 8 is the median. if X =7 then mean = 6.2 and X > mean if x= 11 then mean = 7 and X > mean
X greater than median of 5 nos. Which means that median HAS to be 8. x> 8 Again satisfies the question for any value of x.
D
what if x is 16 then mean = 8 = median which is not greater so answer is E



VP
Joined: 10 Jun 2007
Posts: 1340

Re: DS Mean, Median
[#permalink]
Show Tags
19 Jun 2007, 15:35
LM wrote: x,3,1,12,8
If x is an integer, is the median of the 5 numbers shown greater than the average (arithmetic mean ) of the 5 numbers ?
(1) X > 6
(2) X is greater than the median of the 5 numbes.
Got E.
(1) plug in x = 7, the lowest avg value is (7+3+1+12+8) / 5 = 31/5 =~ 6
This is lower than the median, which is 7 in this case. However, if x is really large, the avg will shoot through the roof, but the median will remain at 8. INSUFFICIENT.
(2) This tells us that x>8, so plug in x=9. We get (9+3+1+12+8) / 5 = 33/5 =~ 6.6. This still less than 8 ,which is the median. Same reason as above, INSUFFICIENT.
Together, we get x>8, INSUFFICIENT.



Retired Moderator
Status: 2000 posts! I don't know whether I should feel great or sad about it! LOL
Joined: 04 Oct 2009
Posts: 1121
Location: Peru
Schools: Harvard, Stanford, Wharton, MIT & HKS (Government)
WE 1: Economic research
WE 2: Banking
WE 3: Government: Foreign Trade and SMEs

Average question
[#permalink]
Show Tags
02 Nov 2010, 08:41
\(x, 3, 1, 12, 8\) If x is an integer, is the median of the 5 numbers shown greater than the average (arithmetic mean) of the 5 numbers? (1) \(x>6\) (2) x is greater than the median of the 5 numbers
_________________
"Life’s battle doesn’t always go to stronger or faster men; but sooner or later the man who wins is the one who thinks he can."
My Integrated Reasoning Logbook / Diary: http://gmatclub.com/forum/myirlogbookdiary133264.html
GMAT Club Premium Membership  big benefits and savings



Retired Moderator
Status: 2000 posts! I don't know whether I should feel great or sad about it! LOL
Joined: 04 Oct 2009
Posts: 1121
Location: Peru
Schools: Harvard, Stanford, Wharton, MIT & HKS (Government)
WE 1: Economic research
WE 2: Banking
WE 3: Government: Foreign Trade and SMEs

Re: Average question
[#permalink]
Show Tags
02 Nov 2010, 10:33
Thanks Bunuel! Kudos for you
_________________
"Life’s battle doesn’t always go to stronger or faster men; but sooner or later the man who wins is the one who thinks he can."
My Integrated Reasoning Logbook / Diary: http://gmatclub.com/forum/myirlogbookdiary133264.html
GMAT Club Premium Membership  big benefits and savings



Manager
Status: PLAY HARD OR GO HOME
Joined: 25 Feb 2014
Posts: 144
Location: India
Concentration: General Management, Finance
GPA: 3.1

If x is an integer, is the median of the 5 numbers shown gre
[#permalink]
Show Tags
16 Feb 2015, 06:03
That moment when you think ans. is D i.e both statements even alone are sufficient,but it turns out that both of them,even together are insufficient ie ans E.
_________________
ITS NOT OVER , UNTIL I WIN ! I CAN, AND I WILL .PERIOD.



Intern
Joined: 04 Dec 2015
Posts: 47
WE: Operations (Commercial Banking)

If x is an integer, is the median of the 5 numbers shown gre
[#permalink]
Show Tags
18 Dec 2015, 08:37
Bunuel wrote: metallicafan wrote: \(x, 3, 1, 12, 8\)
If x is an integer, is the median of the 5 numbers shown greater than the average (arithmetic mean) of the 5 numbers?
(1) \(x>6\) (2) x is greater than the median of the 5 numbers We have a set: {1, 3, 8, 12, x} Question: is \(median>mean=\frac{x+1+3+8+12}{5}=\frac{x+24}{5}\)? Note that as we have odd (5) # of terms in the set then the median will be the middle term when arranged in ascending (or descending) order. So, if \(x\leq{3}\): {1, x, 3, 8, 12} then \(median=3\), if \(3<x\leq{8}\): {1, 3, x, 8, 12} then \(median=x\) and if \(x\geq{8}\): {1, 3, 8, x, 12} then \(median=8\). (1) \(x>6\). If \(x=7\) then the median will be 7 as well: {1, 3, 7, 8, 12} and mean will be \(mean=\frac{7+24}{5}=6.2\), so \(median=7>mean=6.2\) and the answer is YES BUT if \(x\) is very large number then the median will be 8: {1, 3, 8, 12, x=very large number} and mean will be more than median (for example if \(x=26\) then \(mean=\frac{26+24}{5}=10\), so \(median=8<10=mean\)) and the answer will be NO. Not sufficient. (2) x is greater than the median of the 5 numbers > so \(median=8\): now, if \(x=11\) then \(mean=\frac{11+24}{5}=7\), so \(median=8>7=mean\) and the answer is YES. Again it's easy to get answer NO with very large \(x\). Not sufficient. (1)+(2) Again, x=11 and x=very large number give two diffrent answers to the question. Not sufficeint. Answer: E Just wanted to clarify that I have solved this question using random values. Your approach is pretty precise. Is using random values always a disadvantage on GMAT, given the time constraint? It took me arnd 3 mins to do this question , using random values. Given that it's a 700 level question, taking 3 mins on such questions is justified??? Thanks in advance!!



Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 7097
GPA: 3.82

Re: If x is an integer, is the median of the 5 numbers shown gre
[#permalink]
Show Tags
19 Dec 2015, 05:19
x,3,1,12,8 If x is an integer, is the median of the 5 numbers shown greater than the average (arithmetic mean ) of the 5 numbers ? (1) x > 6 (2) x is greater than the median of the 5 numbers. In the original condition, there is 1 variable(x), which should match with the number of equation. So you need 1 more equation. For 1), 1 equation, for 2) 1 equation, which is likely to make D the answer. In 1) & 2), for 1), when x>0, 1,3,x,8,12/1,3,8,x,12/1,3,8,12,x. mean=(1+3+8+12+x)/5=(24+x)/5 and median=x,8. So, (24+x)/5>x? or (24+x)/5>8? is unknown, which is not sufficient. For 2), in the above, median is 3, x, 8 and from x>3, x>x(impossible), x>8, it is x>8>3. So, although x>8, (24+x)/5>8?, which is x>16?, is not sufficient. Even if 1) & 2), when x>8, you cannot find out (24+x)/5>8?, x>16? from x>8>6>3. Therefore it is not sufficient and the answer is E. > For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.
_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The oneandonly World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only $149 for 3 month Online Course" "Free Resources30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons  try it yourself"



Intern
Joined: 26 Nov 2016
Posts: 6

Re: If x is an integer , is the median of 5 numbers shown greater than
[#permalink]
Show Tags
01 Dec 2016, 19:56
Statement 1: For X>6, Avg<median for X=7,8,9,10,11,12,13,14,15, Avg=median for X= 16 Avg> median for X>16 Statement 2: X>median of 5 number => X> 8 Again u can't decide if Median > Avg Both combined X>8 Can't deduct if median> avg So.. Option E Sent from my C6902 using GMAT Club Forum mobile app



Manager
Joined: 02 Nov 2013
Posts: 81
Location: India

Re: If x is an integer, is the median of the 5 numbers shown gre
[#permalink]
Show Tags
02 Dec 2016, 00:51
Required to put actual values to solve this question. Option 1: considered value of x as 7 and 50. With 7 median > mean. With value of x as 50 median < mean. Not sufficient. Option 2: Same values can be used to eliminate this answer. With 50 median <mean and with value of x as 13, medium > mean. Hence, not sufficient. Considering both the equation also we are not able to solve the question.
My answer is E.



NonHuman User
Joined: 09 Sep 2013
Posts: 10151

Re: If x is an integer, is the median of the 5 numbers shown gre
[#permalink]
Show Tags
14 Feb 2019, 19:32
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.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources




Re: If x is an integer, is the median of the 5 numbers shown gre
[#permalink]
14 Feb 2019, 19:32






