GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 06 Jul 2020, 05:08

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

A set of numbers contains 7 integers and has an average

Author Message
TAGS:

Hide Tags

Intern
Joined: 16 Jun 2018
Posts: 38
Location: India
Schools: Stern '21
GMAT 1: 700 Q49 V41
GPA: 4
Re: A set of numbers contains 7 integers and has an average  [#permalink]

Show Tags

26 Feb 2019, 07:21
Bunuel wrote:
Joy111 wrote:
A set of numbers contains 7 integers and has an average (arithmetic mean) value as well as a median value of 23. If the largest value is equal to 15 more than 4 times the smallest number, what is the largest possible range for the numbers in the set?

A. 33
B. 35
C. 38
D. 48
E. 75

The average of 7 numbers is 23 --> the sum of these numbers is 7*23=161;
The median of 7 numbers is 23 --> 23 is the middle term: {*, *, *, 23, *, *, *};
The largest value is equal to 15 more than 4 times the smallest number --> say the smallest number is x then the largest number would be 4x+15, so our set is {x, *, *, 23, *, *, 4x+15};

Now, in order to maximize the range we need to make the second and the third numbers equal to x and the fifth and sixth numbers equal to 23, so the set should be {x, x, x, 23, 23, 23, 4x+15}.

Since the sum is 161 then x+x+x+23+23+23+4x+15=161 --> x=11.

The range is (4x+15)-x=3x+15=48.

How did we consider the 5th and 6th terms as 23 too ? Can someone please elaborate the reason ?
Intern
Joined: 21 Apr 2019
Posts: 12
Re: A set of numbers contains 7 integers and has an average  [#permalink]

Show Tags

28 Jul 2019, 10:21
If we have to maximize a1 to get the largest range, why aren't we taking the median as a1?
EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 17021
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: A set of numbers contains 7 integers and has an average  [#permalink]

Show Tags

28 Jul 2019, 11:21
Hi sinkingbot,

This prompt places a number of 'restrictions' on us - the big one being that the AVERAGE has to be 23 (meaning that the SUM of the 7 terms is 161). If we made the first term 23, then that would NOT actually maximize the range (since that number - along with all of the other "lower" numbers - would make up too much of the 161 total).

To make the largest number as large as possible, we have to make EVERYTHING ELSE as small as possible. Here's how to do it:

X X X 23 23 23 (4X+15)

Summing all of these values gives us:

7X + 84 = 161
7X = 77
X = 11

So, the smallest number = 11 and the largest number = 4(11)+15 = 59

GMAT assassins aren't born, they're made,
Rich
_________________
Contact Rich at: Rich.C@empowergmat.com

The Course Used By GMAT Club Moderators To Earn 750+

souvik101990 Score: 760 Q50 V42 ★★★★★
ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★
SVP
Joined: 24 Nov 2016
Posts: 1663
Location: United States
Re: A set of numbers contains 7 integers and has an average  [#permalink]

Show Tags

03 Dec 2019, 06:26
Joy111 wrote:
A set of numbers contains 7 integers and has an average (arithmetic mean) value as well as a median value of 23. If the largest value is equal to 15 more than 4 times the smallest number, what is the largest possible range for the numbers in the set?

A. 33
B. 35
C. 38
D. 48
E. 75

n=7, avg_med=23, sum=7*23=161, tn=15+4a
minimize 'a' to find largest range: {a,a,a,md,md,md,tn}
3a+3md+tn=161…3a+3(23)+15+4a=161
7a=161-15-69;a=77/7=11
range: tn-a=15+4a-a=15+44-11=48

$$Ans (D)$$
Re: A set of numbers contains 7 integers and has an average   [#permalink] 03 Dec 2019, 06:26

Go to page   Previous    1   2   3   [ 44 posts ]