GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 19 Oct 2019, 05:28 GMAT Club Daily Prep

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

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.  Set S contains seven distinct integers. The median of set S

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

Hide Tags

Manager  Joined: 25 Jul 2010
Posts: 93
Set S contains seven distinct integers. The median of set S  [#permalink]

Show Tags

7
45 00:00

Difficulty:   95% (hard)

Question Stats: 45% (02:19) correct 55% (01:44) wrong based on 698 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 ?

A. m
B. 10m/7
C. 10m/7 – 9/7
D. 5m/7 + 3/7
E. 5m
Math Expert V
Joined: 02 Sep 2009
Posts: 58449
Re: Highest possible all values in set S  [#permalink]

Show Tags

14
7
Orange08 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 ?
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: $$m-3$$, $$m-2$$, $$m-1$$, $$median=m$$, $$2m-2$$, $$2m-1$$, $$2m$$.

$$Mean=\frac{(m-3)+(m-2)+(m-1)+m+(2m-2)+(2m-1)+2m}{7}=\frac{10m-9}{7}$$.

_________________
General Discussion
Intern  Status: Getting ready for the internship summer
Joined: 07 Jun 2009
Posts: 33
Location: Rochester, NY
Schools: Simon
WE 1: JPM - Treasury
Re: Highest possible all values in set S  [#permalink]

Show Tags

Seven distinct integers, the highest value is equal to twice the median. To achieve the highest possible mean you need the following seven integers:

Set S = $${2m, 2m - 1, 2m - 2, m, m - 1, m - 2, m - 3}$$

$$10m-\frac{9}{7}$$= $$\frac{10m}{7} - \frac{9}{7}$$

Manager  Joined: 20 Jul 2010
Posts: 191
Re: Highest possible all values in set S  [#permalink]

Show Tags

2
I had missed reading distinct and made the set as m,m,m,m,2m,2m,2m and came with option B.

Phuf...why they keep such answer choices _________________
If you like my post, consider giving me some KUDOS !!!!! Like you I need them
Manager  Joined: 25 Oct 2013
Posts: 142
Re: Set S contains seven distinct integers. The median of set S  [#permalink]

Show Tags

To maximize the average we need to maximize all the distinct integers in the set.

the numbers then will be

m-3, m-2, m-1,m,2m-2,2m-1, 2m average is sum of these divided by 7.

$$\frac{(10m-9)}{7} = \frac{10m}{7}- \frac{9}{7}$$

C.
_________________
Click on Kudos if you liked the post!

Practice makes Perfect.
Director  Joined: 07 Aug 2011
Posts: 502
Concentration: International Business, Technology
GMAT 1: 630 Q49 V27 Re: Set S contains seven distinct integers. The median of set S  [#permalink]

Show Tags

Orange08 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 ?

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

$$Mean=\frac{(m-3)+(m-2)+(m-1)+(m)+(2m-2)+(2m-1)+(2m)}{7} = \frac{10m-9}{7}$$
Manager  S
Joined: 22 Jan 2014
Posts: 170
WE: Project Management (Computer Hardware)
Re: Set S contains seven distinct integers. The median of set S  [#permalink]

Show Tags

Orange08 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 ?

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

just assume m = 7 (median)

now since each term is distinct and max is 2m, to achieve max sum ... terms should be 4,5,6,7,12,13,14
mean = 61/7

by options, C is satisfied. so C.
_________________
Illegitimi non carborundum.
Senior Manager  Joined: 12 Aug 2015
Posts: 280
Concentration: General Management, Operations
GMAT 1: 640 Q40 V37 GMAT 2: 650 Q43 V36 GMAT 3: 600 Q47 V27 GPA: 3.3
WE: Management Consulting (Consulting)
Re: Set S contains seven distinct integers. The median of set S  [#permalink]

Show Tags

looks like picking numbers won't help and one should solve with algebra
_________________
KUDO me plenty
Intern  Joined: 01 Feb 2016
Posts: 9
Location: Viet Nam
GMAT 1: 500 Q49 V15 GMAT 2: 680 Q49 V34 WE: Real Estate (Real Estate)
Re: Set S contains seven distinct integers. The median of set S  [#permalink]

Show Tags

Hi, i got the right answer but i am a bit concern. The question says all all values in set S are equal to or less than 2m. So is that the maximum value should be 2m-1 because it obviouly says the value is less then 2m. Plz help me. I put 2m-1 for the first time and it is not in the showed answer, so i have to take 2m as a maximum value. Thanks
Current Student B
Joined: 26 Feb 2015
Posts: 26
Location: Thailand
Concentration: Entrepreneurship, Strategy
GMAT 1: 630 Q49 V27 GMAT 2: 680 Q48 V34 GPA: 2.92
WE: Supply Chain Management (Manufacturing)
Re: Set S contains seven distinct integers. The median of set S  [#permalink]

Show Tags

one word that change the whole game . . "distinct"
Target Test Prep Representative D
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8109
Location: United States (CA)
Re: Set S contains seven distinct integers. The median of set S  [#permalink]

Show Tags

Orange08 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 ?

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

Since there are 7 distinct integers, there are 3 integers below the median and 3 above. Furthermore, since we want the largest possible average of these integers, we want the integers to be as large as possible. Thus we can let the largest integer be 2m, the second largest (2m - 1), and the third largest (2m - 2). The fourth largest is the median, so it must be m. The fifth, sixth, and seventh (or the smallest) integers will be (m - 1), (m - 2), and (m - 3), respectively. Thus, the largest possible average is:

[2m + (2m - 1) + (2m - 2) + m + (m - 1) + (m - 2) + (m - 3)]/7

(10m - 9)/7

10m/7 - 9/7

_________________

Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

GMAT Club Legend  V
Joined: 12 Sep 2015
Posts: 4009
Re: Set S contains seven distinct integers. The median of set S  [#permalink]

Show Tags

1
Top Contributor
Orange08 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 ?

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

One approach is to TEST a value of m.

Let's say m = 5.
So, when we arrange all 7 values in ASCENDING order, 5 is the MEDIAN: _ _ _ 5 _ _ _
Since all values in set S are equal to or less than 2m, the BIGGEST value is 10.
So, we get: _ _ _ 5 _ _ 10
At this point, we are tying to MAXIMIZE the other values AND make sure all are DISTINCT.
So, we get: 2, 3, 4, 5, 8, 9, 10
The average = (2 + 3 + 4 + 5 + 8 + 9 + 10)/7 = 41/7

Now plug m = 5 into the answer choices to see which one yields an average of 41/7

A) 5 NOPE
B) 10m/7. So, we get: 10(5)/7 = 50/7 NOPE
C) 10m/7 – 9/7. So, we get: 10(5)/7 - 9/7 = 41/7 BINGO!!
D) 5m/7 + 3/7. So, we get: 5(5)/7 + 3/7 = 28/7 NOPE
E) 5m. So, we get: 5(5) = 25 NOPE

Cheers,
Brent
_________________
Intern  B
Joined: 02 Jun 2015
Posts: 20
Location: United States
Re: Set S contains seven distinct integers. The median of set S  [#permalink]

Show Tags

I used Picking Numbers to solve this question.

M= 4 Median

2M= 8 All values are equal or less than 8

This way, the 7 different integers in Set S are: 1, 2, 3, 4, 6, 7, 8

AVG = $$\frac{sum of terms}{# of terms}$$ = $$\frac{1+2+3+4+6+7+8}{7}$$ = $$\frac{31}{7}$$

When we plug M=4 in the answer choices, we have to find the match AVG = $$\frac{31}{7}$$

A) 4 not a match

B) $$\frac{40}{7}$$ not a match

C) $$\frac{40}{7}$$ - $$\frac{9}{7}$$ = $$\frac{31}{7}$$ that's a match

D) $$\frac{20}{7}$$ + $$\frac{3}{7}$$ = $$\frac{23}{7}$$ not a match

E) 20 not a match

Hence, answer C is the correct choice.

Hope it helps!

Thanks! Alecita  Re: Set S contains seven distinct integers. The median of set S   [#permalink] 30 Dec 2018, 12:13
Display posts from previous: Sort by

Set S contains seven distinct integers. The median of set S

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne  