• NEW! FREE Beat The GMAT Quizzes
Hundreds of Questions Highly Detailed Reporting Expert Explanations
• 7 CATs FREE!
If you earn 100 Forum Points

Engage in the Beat The GMAT forums to earn
100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## Z is a set of positive numbers. The median of Z is greater ##### This topic has 1 expert reply and 0 member replies ### Top Member ## Z is a set of positive numbers. The median of Z is greater ## 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 ### GMAT/MBA Expert GMAT Instructor Joined 22 Aug 2016 Posted: 1770 messages Followed by: 28 members Upvotes: 470 Top Reply 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 Hour Free BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • 5 Day FREE Trial Study Smarter, Not Harder Available with Beat the GMAT members only code • 5-Day Free Trial 5-day free, full-access trial TTP Quant Available with Beat the GMAT members only code • Award-winning private GMAT tutoring Register now and save up to$200

Available with Beat the GMAT members only code

• Get 300+ Practice Questions

Available with Beat the GMAT members only code

• Free Trial & Practice Exam
BEAT THE GMAT EXCLUSIVE

Available with Beat the GMAT members only code

• Magoosh
Study with Magoosh GMAT prep

Available with Beat the GMAT members only code

• FREE GMAT Exam
Know how you'd score today for \$0

Available with Beat the GMAT members only code

• Free Practice Test & Review
How would you score if you took the GMAT

Available with Beat the GMAT members only code

• Free Veritas GMAT Class
Experience Lesson 1 Live Free

Available with Beat the GMAT members only code

### Top First Responders*

1 fskilnik@GMATH 55 first replies
2 GMATGuruNY 52 first replies
3 Brent@GMATPrepNow 52 first replies
4 Jay@ManhattanReview 42 first replies
5 Rich.C@EMPOWERgma... 23 first replies
* Only counts replies to topics started in last 30 days
See More Top Beat The GMAT Members

### Most Active Experts

1 Scott@TargetTestPrep

Target Test Prep

203 posts
2 fskilnik@GMATH

GMATH Teacher

164 posts
3 Brent@GMATPrepNow

GMAT Prep Now Teacher

96 posts
4 Max@Math Revolution

Math Revolution

91 posts
5 GMATGuruNY

The Princeton Review Teacher

75 posts
See More Top Beat The GMAT Experts