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:

Re: Given the ascending set of positive integers {a, b, c, d, e, [#permalink]
04 Aug 2012, 15:32

5

This post received KUDOS

Expert's post

3

This post was BOOKMARKED

Given the ascending set of positive integers {a, b, c, d, e, f}, is the median greater than the mean?

The median of a set with even number of elements is the average of two middle elements when arranged in ascending/descending order. Thus, the median of {a, b, c, d, e, f} is \(\frac{c+d}{2}\).

So, the question asks: is \(\frac{c+d}{2}>\frac{a+b+c+d+e+f}{6}\)? --> is \(3c+3d>a+b+c+d+e+f\)? --> is \(2(c+d)>a+b+e+f\)?

(1) a + e = (3/4)(c + d) --> the question becomes: is \(2(c+d)>b+f+\frac{3}{4}(c + d)\)? --> is \(\frac{5}{4}(c + d)>b+f\)? Not sufficient.

(2) b + f = (4/3)(c + d). The same way as above you can derive that this statement is not sufficient.

(1)+(2) The question in (1) became: is \(\frac{5}{4}(c + d)>b+f\)? Since (2) says that \(b + f = \frac{4}{3}(c + d)\), then the question becomes: is \(\frac{5}{4}(c + d)>\frac{4}{3}(c + d)\)? --> is \(\frac{1}{12}(c+d)<0\)? --> is \(c+d<0\)? As given that \(c\) and \(d\) are positive numbers, then the answer to this question is definite NO. Sufficient.

Re: Given the ascending set of positive integers {a, b, c, d, e, [#permalink]
04 Aug 2012, 17:37

Bunuel Is this not a GMAT type question ?

Bunuel wrote:

Given the ascending set of positive integers {a, b, c, d, e, f}, is the median greater than the mean?

The median of a set with even number of elements is the average of two middle elements when arranged in ascending/descending order. Thus, the median of {a, b, c, d, e, f} is \(\frac{c+d}{2}\).

So, the question asks: is \(\frac{c+d}{2}>\frac{a+b+c+d+e+f}{6}\)? --> is \(3c+3d>a+b+c+d+e+f\)? --> is \(2(c+d)>a+b+e+f\)?

(1) a + e = (3/4)(c + d) --> the question becomes: is \(2(c+d)>b+f+\frac{3}{4}(c + d)\)? --> is \(\frac{5}{4}(c + d)>b+f\)? Not sufficient.

(2) b + f = (4/3)(c + d). The same way as above you can derive that this statement is not sufficient.

(1)+(2) The question in (1) became: is \(\frac{5}{4}(c + d)>b+f\)? Since (2) says that \(b + f = \frac{4}{3}(c + d)\), then the question becomes: is \(\frac{5}{4}(c + d)>\frac{4}{3}(c + d)\)? --> is \(\frac{1}{12}(c+d)<0\)? --> is \(c+d<0\)? As given that \(c\) and \(d\) are positive numbers, then the answer to this question is definite NO. Sufficient.

Re: Given the ascending set of positive integers {a, b, c, d, e, [#permalink]
12 Feb 2013, 13:29

1

This post received KUDOS

if all of the integers are positive, then how come c+d<o ? question system contradicts with the solution... You are right Bunuel.. not an air tight question.

Re: Given the ascending set of positive integers {a, b, c, d, e, [#permalink]
13 Feb 2013, 00:17

Expert's post

mbhussain wrote:

if all of the integers are positive, then how come c+d<o ? question system contradicts with the solution... You are right Bunuel.. not an air tight question.

The question is fine in that respect.

After some manipulations the question became "is c+d<0?" So, c+d<0 is not a statement, it's a question and since we know that c and d are positive numbers, then the answer to this question is NO.

Re: Given the ascending set of positive integers {a, b, c, d, e, [#permalink]
07 Mar 2014, 10:00

Bunuel wrote:

mbhussain wrote:

if all of the integers are positive, then how come c+d<o ? question system contradicts with the solution... You are right Bunuel.. not an air tight question.

The question is fine in that respect.

After some manipulations the question became "is c+d<0?" So, c+d<0 is not a statement, it's a question and since we know that c and d are positive numbers, then the answer to this question is NO.

Hope it's clear.

Bunuel, you have an algebra mistake in your solution, as the statements 1) and 2) combined boil down to:

\(1/2 (c+d) > 37/72 (c+d)\).

This seems like a perfectly reasonable GMAT question.

Re: Given the ascending set of positive integers {a, b, c, d, e, [#permalink]
08 Mar 2014, 06:36

Expert's post

speedilly wrote:

Bunuel wrote:

mbhussain wrote:

if all of the integers are positive, then how come c+d<o ? question system contradicts with the solution... You are right Bunuel.. not an air tight question.

The question is fine in that respect.

After some manipulations the question became "is c+d<0?" So, c+d<0 is not a statement, it's a question and since we know that c and d are positive numbers, then the answer to this question is NO.

Hope it's clear.

Bunuel, you have an algebra mistake in your solution, as the statements 1) and 2) combined boil down to:

1/2 (c+d) > 37/72 (c+d)

This seems like a perfectly reasonable GMAT question.

What mistake are you talking about? _________________

Re: Given the ascending set of positive integers {a, b, c, d, e, [#permalink]
09 Mar 2014, 19:55

1

This post received KUDOS

We don't have to do any calculations here. For mean, we have to have the sum of the all the numbers in the set while for for the median c and d are sufficient. Since both the options together can give us the mean in terms of c+d, we can compare that against the mean which is also in terms of c+d. So C should be the right choice. _________________

Re: Given the ascending set of positive integers {a, b, c, d, e, [#permalink]
11 May 2015, 15:40

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. _________________