BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

A set of 11 positive integers have an average of 25. Which

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Source: — Problem Solving |

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 3008
Joined: Mon Aug 22, 2016 6:19 am
Location: Grand Central / New York
Thanked: 470 times
Followed by:34 members

by Jay@ManhattanReview » Wed Feb 06, 2019 2:11 am
BTGmoderatorLU wrote:Source: EMPOWERgmat

A set of 11 positive integers have an average of 25. Which of the following is the greatest possible value for the median of this set?

A. 25
B. 30
C. 36
D. 45
E. 46

The OA is D
Given the average of 11 positive integers is 25, we have the sum of the 11 positive integers = 11*25 = 275.

Again, given that there are 11 numbers in the set, the median would be the 6th number.

Since we need to maximize the median, we must have the values of 1st to 5th numbers smallest. The smallest possible values of 1st to 5th numbers would be 1 each.

Again, since median would be the 6th numbers, let's assume that 6th to 11th numbers are same.

So, the 11 numbers would be 1, 1, 1, 1, 1, M, M, M, M, M, M

Thus, the sum of 11 numbers = 5*1 + 6*M = 275

=> M = 45.

The correct answer: D

Hope this helps!

-Jay
_________________
Manhattan Review GMAT Prep

Locations: GMAT Classes Austin | GMAT Tutoring Denver | GRE Prep Los Angeles | TOEFL Prep Classes Las Vegas | and many more...

Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 8086
Joined: Sat Apr 25, 2015 10:56 am
Location: Los Angeles, CA
Thanked: 43 times
Followed by:29 members

by Scott@TargetTestPrep » Wed Feb 06, 2019 6:32 pm
BTGmoderatorLU wrote:Source: EMPOWERgmat

A set of 11 positive integers have an average of 25. Which of the following is the greatest possible value for the median of this set?

A. 25
B. 30
C. 36
D. 45
E. 46

The OA is D
The sum of the 11 positive integers is 11 x 25 = 275. If we let m = smallest integer and n = largest integer, we can have 5 values of m and 6 values of n such that the median is n. Since we want the median to be as large as possible, we want the 5 values of m to be as small as possible. Since the smallest positive integer is 1, we can let m be 1. Thus, we have:

5 x 1 + 6n = 275

6n = 270

n = 45

Answer: D

Scott Woodbury-Stewart
Founder and CEO
[email protected]

Image

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

ImageImage
Top
Post new topic Post Reply
• Page 1 of 1