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.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 350,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

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.

Re: What is the median of the numbers 4, 5, 6, 7, 9, and x? [#permalink]
01 Nov 2012, 15:10

2

This post received KUDOS

Expert's post

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. _________________

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.

Re: What is the median of the numbers 4, 5, 6, 7, 9, and x? [#permalink]
24 Oct 2013, 06:21

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?

Re: What is the median of the numbers 4, 5, 6, 7, 9, and x? [#permalink]
24 Oct 2013, 06:35

Expert's post

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.

Re: What is the median of the numbers 4, 5, 6, 7, 9, and x? [#permalink]
24 Oct 2013, 09:36

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.

gmatclubot

Re: What is the median of the numbers 4, 5, 6, 7, 9, and x?
[#permalink]
24 Oct 2013, 09:36

This week went in reviewing all the topics that I have covered in my previous study session. I reviewed all the notes that I have made and started reviewing the Quant...

I was checking my phone all day. I wasn’t sure when I would receive the admission decision from Tepper. I received an acceptance from Goizueta in the early morning...

I started running as a cross country team member since highshcool and what’s really awesome about running is that...you never get bored of it! I participated in...