GMAT Quant Questionbank | Statistics

GMAT Sample Questions | Average | Mean & Median | Hard Math Question

This GMAT Sample Math question is a descriptive statistics question and the concept tested is finding the Arithmetic Mean & Median. A GMAT hard math question.

Question 8: Positive integers from 1 to 45, inclusive are placed in 5 groups of 9 each. What is the highest possible average of the medians of these 5 groups ?

  1. 25
  2. 31
  3. 15
  4. 26
  5. 23

Get to Q51 in GMAT Quant


Online GMAT Course
@ INR 3000


Video Explanation


GMAT Live Online Classes


Start Thu, Dec 3, 2020


Explanatory Answer

We are dividing the numbers into sets of 9.
The median of each set is the middle number when the 9 numbers are arranged in ascending order.
So, the median is the 5th number when the numbers in a set are written in ascending order.
Therefore, we will have 4 numbers that are greater than the median in each set.
We need to maximize the median in each group in order to maximize the average of all the medians.

The highest possible median is 41 as there should be 4 numbers greater than the median in a group of 9.
So, if we have a group that has a, b, c, d, 41, 42, 43, 44, 45, the median will be 41.
In this set, it is essential not to expend any more high values on a, b, c, or d as these do not affect the median.

For example, the median of a group that comprises 1, 2, 3, 4, 41, 42, 43, 44, 45 will be 41.

The next group can be 5, 6, 7, 8, 36, 37, 38, 39, 40. The median will be 36.
The first 4 numbers in any set is not of much consequence. Our focus is on the numbers upward of the median in any set.

Extrapolating the findings in the two sets listed above, to maximize medians in all the 5 groups, the medians of the 5 groups will have to be 21, 26, 31, 36 and 41.

The average of the highest possible medians will be the average of these 5 numbers = 31.

Choice B is the correct answer.

 

GMAT Online Course - Quant
Try it free!

Register in 2 easy steps and
Start learning in 5 minutes!

★ Sign up for Free

Already have an Account?

★ Login to Continue

GMAT Live Online Classes

Next Batch Dec 3, 2020

★ GMAT Live Info

GMAT Coaching in Chennai

Next Integrated (Online + Offline) Batch
Starts Thu, Dec 3, 2020

★ GMAT Class Info

GMAT Coaching in Chennai

Sign up for a Free Demo of our GMAT Classes in Chennai

★ Schedule Demo


GMAT Sample Questions | Topicwise GMAT Questions


Where is Wizako located?

Wizako - GMAT, GRE, SAT Prep
An Ascent Education Initiative
48/1 Ramagiri Nagar
Velachery Taramani Link Road.,
Velachery, Chennai 600 042. India

How to reach Wizako?

Phone: (91) 44 4500 8484
Mobile: (91) 95000 48484
WhatsApp: WhatsApp Now
Email: learn@wizako.com
Leave A Message