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 500,000 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:

Set S contains seven distinct integers. The median of set S is the [#permalink]

Show Tags

18 Nov 2009, 21:35

13

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

75% (hard)

Question Stats:

42% (00:44) correct
58% (00:31) wrong based on 314 sessions

HideShow timer Statistics

Set S contains seven distinct integers. The median of set S is the integer m, and all values in set S are equal to or less than 2m. What is the highest possible average (arithmetic mean) of all values in set S ?

Re: Set S contains seven distinct integers. The median of set S is the [#permalink]

Show Tags

18 Nov 2009, 21:51

kairoshan wrote:

Set S contains seven distinct integers. The median of set S is the integer m, and all values in set S are equal to or less than 2m. What is the highest possible average (arithmetic mean) of all values in set S ? m 10m/7 10m/7 – 9/7 5m/7 + 3/7 5m

10m/7 -9/7

lets consider m = 7 and set as [4,5,6,7,12,13,14] all distinct and will give highest possible average

1. m is median --> x x x m x x x 2. 2m is the maximum value. x x x m x x 2m 3. because integers are distinct, we should find as large integers as we can under above restrictions:

x x (m-1) m x (2m-1) 1m (m-3) (m-2) (m-1) m (2m-2) (2m-1) 2m Sum = 10m-9 Average = 10/7m-9/7

Re: Set S contains seven distinct integers. The median of set S is the [#permalink]

Show Tags

19 Nov 2009, 06:20

walker wrote:

1. m is median --> x x x m x x x 2. 2m is the maximum value. x x x m x x 2m 3. because integers are distinct, we should find as larger integers as we can under above restrictions:

x x (m-1) m x (2m-1) 1m (m-3) (m-2) (m-1) m (2m-2) (2m-1) 2m Sum = 10m+9 Average = 10/7m-9/7

Re: Set S contains seven distinct integers. The median of set S is the [#permalink]

Show Tags

27 May 2010, 01:53

Set S contains seven distinct integers. The median of set S is the integer m, and all values in set S are equal to or less than 2m. What is the highest possible average (arithmetic mean) of all values in set S ?

m 10m/7 10m/7 – 9/7 5m/7 + 3/7 5m
_________________

press kudos, if you like the explanation, appreciate the effort or encourage people to respond.

Re: Set S contains seven distinct integers. The median of set S is the [#permalink]

Show Tags

29 May 2010, 02:11

Set S contains seven distinct integers. The median of set S is the integer m, and all values in set S are equal to or less than 2m. What is the highest possible average (arithmetic mean) of all values in set S ?

m 10m/7 10m/7 – 9/7 5m/7 + 3/7 5m

mean of 7 numbers = (Sum of 7 numbers)/7 To find the highest mean we need to maximise the numerator.

since m in the median and we've 7 numbers so m will take the 4th position i.e. the Set S must have(for max avg)

m, m, m, m, 2m, 2m, 2m

Max avg mean = (m + m + m + m + 2m + 2m + 2m)/7 = 10m/7

Re: Set S contains seven distinct integers. The median of set S is the [#permalink]

Show Tags

30 May 2010, 04:34

OA is C

But why cant the set be

m,m,m,m,2m,2m,2m

it is a set and m can be the median, and average will be more than

m-3,m-2,m-1,m,2m-2,2m-1,2m

Amiman wrote:

Set S contains seven distinct integers. The median of set S is the integer m, and all values in set S are equal to or less than 2m. What is the highest possible average (arithmetic mean) of all values in set S ?

m 10m/7 10m/7 – 9/7 5m/7 + 3/7 5m

mean of 7 numbers = (Sum of 7 numbers)/7 To find the highest mean we need to maximise the numerator.

since m in the median and we've 7 numbers so m will take the 4th position i.e. the Set S must have(for max avg)

m, m, m, m, 2m, 2m, 2m

Max avg mean = (m + m + m + m + 2m + 2m + 2m)/7 = 10m/7

Re: Set S contains seven distinct integers. The median of set S is the [#permalink]

Show Tags

30 May 2010, 12:44

BlueRobin wrote:

OA is C

But why cant the set be

m,m,m,m,2m,2m,2m

it is a set and m can be the median, and average will be more than

m-3,m-2,m-1,m,2m-2,2m-1,2m

Amiman wrote:

[highlight]Set S contains seven distinct integers[/highlight]. The median of set S is the integer m, and all values in set S are equal to or less than 2m. What is the highest possible average (arithmetic mean) of all values in set S ?

m 10m/7 10m/7 – 9/7 5m/7 + 3/7 5m

mean of 7 numbers = (Sum of 7 numbers)/7 To find the highest mean we need to maximise the numerator.

since m in the median and we've 7 numbers so m will take the 4th position i.e. the Set S must have(for max avg)

m, m, m, m, 2m, 2m, 2m

Max avg mean = (m + m + m + m + 2m + 2m + 2m)/7 = 10m/7

Note that "Set S contains seven distinct integers".

Re: Set S contains seven distinct integers. The median of set S is the [#permalink]

Show Tags

30 May 2010, 13:09

Fistail wrote:

BlueRobin wrote:

OA is C

But why cant the set be

m,m,m,m,2m,2m,2m

it is a set and m can be the median, and average will be more than

m-3,m-2,m-1,m,2m-2,2m-1,2m

Amiman wrote:

[highlight]Set S contains seven distinct integers[/highlight]. The median of set S is the integer m, and all values in set S are equal to or less than 2m. What is the highest possible average (arithmetic mean) of all values in set S ?

m 10m/7 10m/7 – 9/7 5m/7 + 3/7 5m

mean of 7 numbers = (Sum of 7 numbers)/7 To find the highest mean we need to maximise the numerator.

since m in the median and we've 7 numbers so m will take the 4th position i.e. the Set S must have(for max avg)

m, m, m, m, 2m, 2m, 2m

Max avg mean = (m + m + m + m + 2m + 2m + 2m)/7 = 10m/7

Note that "Set S contains seven distinct integers".

Yeah thanks for point zzzzzzzzzzzz that out, i am awake now.
_________________

Re: Set S contains seven distinct integers. The median of set S is the [#permalink]

Show Tags

01 Dec 2014, 10:04

walker wrote:

1. m is median --> x x x m x x x 2. 2m is the maximum value. x x x m x x 2m 3. because integers are distinct, we should find as large integers as we can under above restrictions:

x x (m-1) m x (2m-1) 1m (m-3) (m-2) (m-1) m (2m-2) (2m-1) 2m Sum = 10m-9 Average = 10/7m-9/7

So, C

Had the integers not been distinct would it have been like this: m m m m 2m 2m 2m And the median would still have been m trying to clarify an imp concept P.S. I'm a technology handicap so please dont beat your head at my posts' misplacements and redundancies

1. m is median --> x x x m x x x 2. 2m is the maximum value. x x x m x x 2m 3. because integers are distinct, we should find as large integers as we can under above restrictions:

x x (m-1) m x (2m-1) 1m (m-3) (m-2) (m-1) m (2m-2) (2m-1) 2m Sum = 10m-9 Average = 10/7m-9/7

So, C

Had the integers not been distinct would it have been like this: m m m m 2m 2m 2m And the median would still have been m trying to clarify an imp concept P.S. I'm a technology handicap so please dont beat your head at my posts' misplacements and redundancies

Yes, that's correct.

Set S contains seven distinct integers. The median of set S is the integer m, and all values in set S are equal to or less than 2m. What is the highest possible average (arithmetic mean) of all values in set S ?

A. m B. 10m/7 C. 10m/7 – 9/7 D. 5m/7 + 3/7 E. 5m

If a set has odd number of terms the median of a set is the middle number when arranged in ascending or descending order; If a set has even number of terms the median of a set is the average of the two middle terms when arranged in ascending or descending order.

So median of S, which contains seven terms is 4th term when arranged in ascending order;: \(median=4th \ term=m\).

Now, to maximize the mean we should maximize the terms. As numbers in S are distinct integers and the highest number in S could be equal to \(2m\), then maximum values of the terms would be: \(m-3\), \(m-2\), \(m-1\), \(median=m\), \(2m-2\), \(2m-1\), \(2m\).