• PrepScholar GMAT
    5 Day FREE Trial
    Study Smarter, Not Harder

    Available with Beat the GMAT members only code

    MORE DETAILS
    PrepScholar GMAT
  • Veritas Prep
    Free Veritas GMAT Class
    Experience Lesson 1 Live Free

    Available with Beat the GMAT members only code

    MORE DETAILS
    Veritas Prep
  • EMPOWERgmat Slider
    1 Hour Free
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    EMPOWERgmat Slider
  • Varsity Tutors
    Award-winning private GMAT tutoring
    Register now and save up to $200

    Available with Beat the GMAT members only code

    MORE DETAILS
    Varsity Tutors
  • e-gmat Exclusive Offer
    Get 300+ Practice Questions
    25 Video lessons and 6 Webinars for FREE

    Available with Beat the GMAT members only code

    MORE DETAILS
    e-gmat Exclusive Offer
  • Kaplan Test Prep
    Free Practice Test & Review
    How would you score if you took the GMAT

    Available with Beat the GMAT members only code

    MORE DETAILS
    Kaplan Test Prep
  • Target Test Prep
    5-Day Free Trial
    5-day free, full-access trial TTP Quant

    Available with Beat the GMAT members only code

    MORE DETAILS
    Target Test Prep
  • Magoosh
    Magoosh
    Study with Magoosh GMAT prep

    Available with Beat the GMAT members only code

    MORE DETAILS
    Magoosh
  • The Princeton Review
    FREE GMAT Exam
    Know how you'd score today for $0

    Available with Beat the GMAT members only code

    MORE DETAILS
    The Princeton Review
  • Economist Test Prep
    Free Trial & Practice Exam
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    Economist Test Prep

Z is a set of positive numbers. The median of Z is greater

This topic has 1 expert reply and 0 member replies

Z is a set of positive numbers. The median of Z is greater

Post

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

Difficult



Z is a set of positive numbers. The median of Z is greater than the mean of Z. Which of the following must be true?

I. At least 50% of the numbers in Z are smaller than the median.
II. Less than 50% of the numbers in Z are greater than the median.
III. The median of Z is greater than the average of the largest and smallest numbers in Z.

A. I only
B. II only
C. III only
D. I and III only
E. None of the above

OA E

Source: https://gmat.economist.com/btg?gsrc=btg

  • +1 Upvote Post
  • Quote
  • Flag
Post
BTGmoderatorDC wrote:
Z is a set of positive numbers. The median of Z is greater than the mean of Z. Which of the following must be true?

I. At least 50% of the numbers in Z are smaller than the median.
II. Less than 50% of the numbers in Z are greater than the median.
III. The median of Z is greater than the average of the largest and smallest numbers in Z.

A. I only
B. II only
C. III only
D. I and III only
E. None of the above

OA E

Source: Economist GMAT
Since this is a roman numeral question and each of the three statements are independent of each other, we must think of Set Z such that the statements are challenged.

Let's see each statement one by one.

I. At least 50% of the numbers in Z are smaller than the median.

Say Z : {0, 2, 2, 4, 6, 6, 6}
Median = 4; Mean = 26/7 = 3.7...; we see that Median (4) > Mean (3.7), so this is a valid set.
The numbers smaller than Median (4) are 0, 2, and 2; there are 3 out of 7 numbers (3/7 * 100% < 50%) smaller than Median.
Statement I must not be true.

II. Less than 50% of the numbers in Z are greater than the median.

Say Z : {0, 1, 1, 3, 3, 3}
Median = (1 + 3)/2 = 2; Mean = 11/6 = 1.8...; we see that Median (2) > Mean (1.8), so this is a valid set.
The numbers greater than Median (2) are 3, 3, and 3; there are 3 out of 6 numbers (3/6 * 100% = 50%) greater than Median.
Statement II must not be true.

III. The median of Z is greater than the average of the largest and smallest numbers in Z.

Say Z : {0, 1, 1, 3, 3, 3}
Median = (1 + 3)/2 = 2; Mean = 11/6 = 1.8...; we see that Median (2) > Mean (1.8)
The the average of the largest and smallest numbers = (0 + 3)/2 = 2 = Median (2)
Statement III must not be true.

The correct answer: E

Hope this helps!

-Jay
_________________
Manhattan Review GRE Prep

Locations: GRE Classes Los Angeles | GMAT Prep Course Singapore | GRE Prep Orlando | SAT Prep Courses Toronto | and many more...

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

  • +1 Upvote Post
  • Quote
  • Flag

Top First Responders*

1 Jay@ManhattanReview 84 first replies
2 Brent@GMATPrepNow 73 first replies
3 fskilnik 50 first replies
4 GMATGuruNY 37 first replies
5 Rich.C@EMPOWERgma... 16 first replies
* Only counts replies to topics started in last 30 days
See More Top Beat The GMAT Members

Most Active Experts

1 image description fskilnik

GMAT Teacher

199 posts
2 image description Brent@GMATPrepNow

GMAT Prep Now Teacher

166 posts
3 image description Scott@TargetTestPrep

Target Test Prep

118 posts
4 image description Jay@ManhattanReview

Manhattan Review

98 posts
5 image description Max@Math Revolution

Math Revolution

95 posts
See More Top Beat The GMAT Experts