Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 10 Sep 2012
Posts: 139

What is the median of the numbers 4, 5, 6, 7, 9, and x? [#permalink]
Show Tags
Updated on: 01 Nov 2012, 15:47
Question Stats:
54% (01:19) correct 46% (01:03) wrong based on 277 sessions
HideShow timer Statistics
What is the median of the numbers 4, 5, 6, 7, 9, and x? (1) x > 7 (2) The mean of the six numbers is equal to their median. The solution states that the answer is A but in my opinion the answer is D.
The mean of a sequence is equal to the median of that sequence. Which means that x can only be 8 according to Stat(2) (in order to make the mean of that set the same as the median). The numbers that the solution cites, to me, seems invalid. For example, the solution states x<5. Let's take 4 then. If x=4, the mean becomes 5.83, but the median is 5.5, which doesn't satisfy Stat(2). Could someone clarify this?
Here is the official solution: This is a "what is the value of..." DS question. In this type of question, a statement will be sufficient only if it leads to a single value of the variable (or expression) that you're asked about.
Remember:
The median is the middle number in a set of numbers, arranged in ascending or descending order. To find the median consider the number of elements: If the number of elements is odd, the median is the middle number. If the number of elements is even the median is the average of the middle two elements. Together with x, there are 6 numbers; therefore, the median will be calculated as the average of the two middle numbers. Therefore, the real issue of the question is the values of the two middle numbers.
According to Stat. (2),
The average of 4,5,6,7,9, and x is equal to the median. The median, which is also the average, will vary according to the value of x:
If x<5, the median is equal to the average of the two middle numbers > 5 and 6 = 5.5. But,
If x>7, the median is equal to the average of the two middle numbers > 6 and 7 = 6.5. No single value can be determined for the median of the set, so Stat.(2)>IS.
Official Answer and Stats are available only to registered users. Register/ Login.
Originally posted by anon1 on 01 Nov 2012, 15:43.
Last edited by Bunuel on 01 Nov 2012, 15:47, edited 1 time in total.
Renamed the topic and edited the question.



Math Expert
Joined: 02 Sep 2009
Posts: 46207

Re: What is the median of the numbers 4, 5, 6, 7, 9, and x? [#permalink]
Show Tags
01 Nov 2012, 16:10
What is the median of the numbers 4, 5, 6, 7, 9, and x?The median of a set with even number of terms is the average of two middle terms when arranged in ascending/descending order. (1) x > 7 > two middle terms are 6 and 7, thus median=(6+7)/2=6.5. Sufficient. (2) The mean of the six numbers is equal to their median. If \(x\leq{5}\), then two middle terms are 5 and 6, thus median=(5+6)/2=5.5. In this case mean=(4+5+6+7+9+x)/6=5.5 > x=2. Possible scenario. If \(x\geq{7}\), then two middle terms are 6 and 7, thus median=(6+7)/2=6.5. In this case mean=(4+5+6+7+9+x)/6=6.5 > x=8. Possible scenario. Not sufficient. Answer: A. P.S. For (2): if \(5<x<7\), then two middle terms are x and 6, thus median=(x+6)/2. In this case mean=median=(4+5+6+7+9+x)/6=(x+6)/2 > x=6.5. Also, possible scenario.
_________________
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



Math Expert
Joined: 02 Sep 2009
Posts: 46207

Re: What is the median of the numbers 4, 5, 6, 7, 9, and x? [#permalink]
Show Tags
01 Nov 2012, 16:13
anon1 wrote: What is the median of the numbers 4, 5, 6, 7, 9, and x? (1) x > 7 (2) The mean of the six numbers is equal to their median. The solution states that the answer is A but in my opinion the answer is D.
The mean of a sequence is equal to the median of that sequence. Which means that x can only be 8 according to Stat(2) (in order to make the mean of that set the same as the median). The numbers that the solution cites, to me, seems invalid. For example, the solution states x<5. Let's take 4 then. If x=4, the mean becomes 5.83, but the median is 5.5, which doesn't satisfy Stat(2). Could someone clarify this?
Here is the official solution: This is a "what is the value of..." DS question. In this type of question, a statement will be sufficient only if it leads to a single value of the variable (or expression) that you're asked about.
Remember:
The median is the middle number in a set of numbers, arranged in ascending or descending order. To find the median consider the number of elements: If the number of elements is odd, the median is the middle number. If the number of elements is even the median is the average of the middle two elements. Together with x, there are 6 numbers; therefore, the median will be calculated as the average of the two middle numbers. Therefore, the real issue of the question is the values of the two middle numbers.
According to Stat. (2),
The average of 4,5,6,7,9, and x is equal to the median. The median, which is also the average, will vary according to the value of x:
If x<5, the median is equal to the average of the two middle numbers > 5 and 6 = 5.5. But,
If x>7, the median is equal to the average of the two middle numbers > 6 and 7 = 6.5. No single value can be determined for the median of the set, so Stat.(2)>IS. Similar questions to practice: ifsetsconsistsofthenumbers1528andnis132570.htmlwhatisthevalueofninthelistabove137225.htmliftherangeofthesetcontainingthenumbersxyandz127089.htmlthesumoftheintegersinlistsisthesameasthesumof127755.htmlgiventheascendingsetofpositiveintegersabcde115675.htmlHope it helps.
_________________
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



Manager
Joined: 10 Sep 2012
Posts: 139

Re: What is the median of the numbers 4, 5, 6, 7, 9, and x? [#permalink]
Show Tags
01 Nov 2012, 16:33
Bunuel wrote: Thank you so much!!!



Intern
Joined: 04 Mar 2012
Posts: 6

Re: What is the median of the numbers 4, 5, 6, 7, 9, and x? [#permalink]
Show Tags
24 Oct 2013, 07:21
Bunuel wrote: What is the median of the numbers 4, 5, 6, 7, 9, and x?
The median of a set with even number of terms is the average of two middle terms when arranged in ascending/descending order.
(1) x > 7 > two middle terms are 6 and 7, thus median=(6+7)/2=6.5. Sufficient.
(2) The mean of the six numbers is equal to their median.
If \(x\leq{5}\), then two middle terms are 5 and 6, thus median=(5+6)/2=5.5. In this case mean=(4+5+6+7+9+x)/6=5.5 > x=2. Possible scenario. If \(x\geq{7}\), then two middle terms are 6 and 7, thus median=(6+7)/2=6.5. In this case mean=(4+5+6+7+9+x)/6=6.5 > x=8. Possible scenario. Not sufficient.
Answer: A.
P.S. For (2): if \(5<x<7\), then two middle terms are x and 6, thus median=(x+6)/2. In this case mean=median=(4+5+6+7+9+x)/6=(x+6)/2 > x=6.5. Also, possible scenario. why have you taken mean =median i.e 5.5 and 6.5 . Mean =Median is only in evenly spaced sets. Please explain?



Math Expert
Joined: 02 Sep 2009
Posts: 46207

Re: What is the median of the numbers 4, 5, 6, 7, 9, and x? [#permalink]
Show Tags
24 Oct 2013, 07:35
kop wrote: Bunuel wrote: What is the median of the numbers 4, 5, 6, 7, 9, and x?
The median of a set with even number of terms is the average of two middle terms when arranged in ascending/descending order.
(1) x > 7 > two middle terms are 6 and 7, thus median=(6+7)/2=6.5. Sufficient.
(2) The mean of the six numbers is equal to their median.
If \(x\leq{5}\), then two middle terms are 5 and 6, thus median=(5+6)/2=5.5. In this case mean=(4+5+6+7+9+x)/6=5.5 > x=2. Possible scenario. If \(x\geq{7}\), then two middle terms are 6 and 7, thus median=(6+7)/2=6.5. In this case mean=(4+5+6+7+9+x)/6=6.5 > x=8. Possible scenario. Not sufficient.
Answer: A.
P.S. For (2): if \(5<x<7\), then two middle terms are x and 6, thus median=(x+6)/2. In this case mean=median=(4+5+6+7+9+x)/6=(x+6)/2 > x=6.5. Also, possible scenario. why have you taken mean =median i.e 5.5 and 6.5 . Mean =Median is only in evenly spaced sets.Please explain? That's not true. Consider: {0, 1, 1, 2} > mean=1=median. So, if a set is evenly spaced, then mean=median, but if mean=median, then it's not necessary the set to be evenly spaced. Does this make sense?
_________________
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



Intern
Joined: 04 Mar 2012
Posts: 6

Re: What is the median of the numbers 4, 5, 6, 7, 9, and x? [#permalink]
Show Tags
24 Oct 2013, 10:36
Bunuel wrote: kop wrote: Bunuel wrote: What is the median of the numbers 4, 5, 6, 7, 9, and x?
The median of a set with even number of terms is the average of two middle terms when arranged in ascending/descending order.
(1) x > 7 > two middle terms are 6 and 7, thus median=(6+7)/2=6.5. Sufficient.
(2) The mean of the six numbers is equal to their median.
If \(x\leq{5}\), then two middle terms are 5 and 6, thus median=(5+6)/2=5.5. In this case mean=(4+5+6+7+9+x)/6=5.5 > x=2. Possible scenario. If \(x\geq{7}\), then two middle terms are 6 and 7, thus median=(6+7)/2=6.5. In this case mean=(4+5+6+7+9+x)/6=6.5 > x=8. Possible scenario. Not sufficient.
Answer: A.
P.S. For (2): if \(5<x<7\), then two middle terms are x and 6, thus median=(x+6)/2. In this case mean=median=(4+5+6+7+9+x)/6=(x+6)/2 > x=6.5. Also, possible scenario. why have you taken mean =median i.e 5.5 and 6.5 . Mean =Median is only in evenly spaced sets.Please explain? That's not true. Consider: {0, 1, 1, 2} > mean=1=median. So, if a set is evenly spaced, then mean=median, but if mean=median, then it's not necessary the set to be evenly spaced. Does this make sense? Thanks Bunnel. I understood it now.



NonHuman User
Joined: 09 Sep 2013
Posts: 7010

Re: What is the median of the numbers 4, 5, 6, 7, 9, and x? [#permalink]
Show Tags
25 Nov 2017, 01:07
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: What is the median of the numbers 4, 5, 6, 7, 9, and x?
[#permalink]
25 Nov 2017, 01:07






