GMAT Tip: Maximize/Minimize Statistics Problems » Clear Admit: MBA Admissions Consultants Blog

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Dawna Clarke (Tuck)
Rose Martinelli (Chicago)
Judith Hodara (Wharton)
Sara Neher (Darden)
Soojin Kwon Koh (Michigan)
Randall Sawyer (Cornell)
Beth Flye (Kellogg)
David Simpson (LBS)
Liz Riley Hargrove (Duke)
Linda Meehan (Columbia)
Bruce DelMonico (Yale)
Peter Johnson (Berkeley)
Isser Gallogly (NYU)
Mae Jennifer Shores (UCLA)
J.J. Cutler (Wharton)
Jake Cohen (INSEAD)
Rod Garcia (MIT Sloan)

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Application Deadlines
Below are the upcoming deadlines for admission to top-tier schools.
Feb 10: INSEAD R3
Mar 1: Michigan / Ross R3
Mar 3: CBS
Mar 3: LBS R3
Mar 4: Kellogg R3
Mar 8: Cambridge / Judge R4
Mar 8: CMU / Tepper R3
Mar 9: Duke / Fuqua R3
Mar 9: Penn / Wharton R3
Mar 10: Berkeley / Hass R4
Mar 10: Chicago Booth R3
Mar 10: Yale SOM R3
Mar 15: NYU / Stern R3
Mar 17: UCLA / Anderson R3
Mar 19: UNC / Kenan-Flagler R4
Mar 30: Cornell / Johnson R4
Mar 31: UVA / Darden R3
Mar 31: INSEAD R4
Apr 1: UT-Austin / McCombs
Apr 2: Dartmouth / Tuck R3
Apr 2: Oxford / Saїd R3
Apr 7: Stanford GSB R4
Apr 8: Harvard R3
Apr 14: CBS

Essay Topic Analysis
Below are links to our comments on some of the top programs' essay topics.
The Career Goals Essay
Berkeley / Haas*
Chicago Booth*
CMU / Tepper*
Columbia*
Cornell / Johnson*
Dartmouth / Tuck*
Duke / Fuqua*
Harvard*
Indian School of Business*
INSEAD*
London Business School*
MIT / Sloan*
Michigan / Ross*
Northwestern / Kellogg*
NYU / Stern*
Oxford / Said*
Penn / Wharton*
Stanford GSB*
UCLA / Anderson*
UNC / Kenan-Flagler*
USC / Marshall*
UT Austin / McCombs*
UVA / Darden*
Yale SOM*
* denotes '09-'10 commentary

Categories
Use categories to access all that has been written on each of the topics. We have categorized by school and by subject matter.

Interview Reports
A selection of interview field reports from fellow applicants posted to the MBA Admissions Wiki. Add your reports when you are finished with your interviews.
Chicago
Columbia
Dartmouth / Tuck
Duke / Fuqua
Harvard
Kellogg
Michigan / Ross
MIT / Sloan
Stanford
UNC / Chapel Hill
Virginia / Darden
Wharton
London Business School

GMAT Resources
MBA.com
Manhattan GMAT
GMAT Club
Princeton Review
Test Prep New York
Kaplan
Beat The GMAT
Knewton

Writing Resources
Guide to Grammar and Writing
The Internet Grammar of English
English Usage, Style and Composition
The Economist Style Guide
Paradigm Online Writing Assistant

School Rankings
Rankings are a good way to start your research on various MBA Programs. Keep in mind each uses a different methodology.
Business Week
Economist
Financial Times
Forbes
USNews
Wall Street Journal

Career Guides
The following resources should be useful to those who want to research the careers open to them after (or before) earning an MBA.
Vault.com
Wetfeet

Business School Resources
The following are business resources offered by a variety of leading Business Schools. It's useful to subscribe to these resources, especially for the schools to which you are applying.

MBA Programs: North America
If an MBA Program is not listed, please e-mail and we will be happy to list it.
Berkeley / Haas
Boston College / Carroll
Carnegie Mellon / Tepper
Chicago
Columbia
Concordia
Cornell / Johnson
Dartmouth / Tuck
Duke / Fuqua
Emory / Goizueta
Harvard
HEC Montreal
Indiana / Kelley
Michigan
MIT / Sloan
Northwestern / Kellogg
New York / Stern
North Carolina / Kenan Flagler
Notre Dame / Mendoza
Pennsylvania / Wharton
Queens
Stanford
Syracuse / Whitman
Texas / McCombs
Thunderbird
Toronto
USC / Marshall
UCLA / Anderson
Vanderbilt / Owen
Virginia / Darden
Washington University in St. Louis / Olin
Western Ontario / Ivey
Yale

MBA Programs: Rest of the World
As there is some variety in the length of international MBA programs, we have denoted the length of the program next to its name (1 = one year; 2 = 2 years). If an MBA Program is not listed, please e-mail and we will be happy to list it.
AGSM (Australia) 2
Cambridge / Judge (UK) 1
CIEBS (China) 2
Cheung Kong Graduate School of Business (China) 1
Cranfield School of Mgmt (UK) 1
ESADE (Spain) 1 or 2
HEC (France) 2
Hult (UK) 1
IESE (Spain) 2
IMD (Switzerland) 1
INCAE (Costa Rica) 2
INSEAD (France) 1
IPADE (Mexico)
ISB (India) 1
London Business School (UK) 2
Manchester Bus. School (UK) 2
Melbourne (Australia) 2
Oxford / Said (UK) 1
Rotterdam (Netherlands) 1
Tsinghua IMBA (China) 2
University of St. Gallen (Switzerland) 1

Additional Resources
Here we link a host of additional resources available across the web. E-mail info@clearadmit.com to have resources added to this list.
AACSB International
Association of MBAs
Beyond Grey Pinstripes
EFMD
gradschools.com (worldwide)
Infozee
International Student Loans
mba.com (GMAT Scores)
MBAInfo
mbaleague.blogspot.com
MBAzone
MBA Jungle
TOEFL
Top MBA

MBA Tipline
We encourage admissions officers, students and applicants to alert us of interesting news and developments, please send an email to news@clearadmit.com so we can blog it.

Blog Archive

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Saturday, November 28, 2009

GMAT Tip: Maximize/Minimize Statistics Problems

Today’s GMAT tip comes from our friends at ManhattanGMAT. In this article, ManhattanGMAT instructor Stacey Koprince offers explanations to sample GMATPrep® max/min questions:

This week, we’re going to tackle two GMATPrep® questions, this time from the quant side of things. My students have been asking (really, complaining!) about maximize / minimize questions lately. A lot of students aren’t sure about the most efficient approach to these kinds of questions. We’ll tackle these two GMATPrep® questions this week in order to learn how to master max/min questions in general.

Let’s start with a sample problem. Set your timer for 2 minutes…. and… GO!

*Three boxes of supplies have an average (arithmetic mean) weight of 7 kilograms and a median weight of 9 kilograms. What is the maximum possible weight, in kilograms, of the lightest box?

(A) 1

(B) 2

(D) 4

(E) 5

The most important thing to notice here is the word “maximum.” This one word is going to be the determining factor in how we set this problem up, right from the very beginning.

Most of the time, when we’re asked to maximize something, we will need to minimize the remaining variables in the problem. Conversely, if the problem asks us to minimize something, we will usually need to maximize the remaining variables. (There are times, though, when we will need to minimize some other variable in order to minimize the desired thing or maximize some other variable in order to maximize the desired thing – so we do need to pay attention.)

This time, they’re asking us to maximize one figure: the lightest box.

If three items have an average weight of 7, then collectively, the three items have a weight of 7×3 = 21. If three items have a median weight of 9, then the middle of the three items is actually 9. This one isn’t a variable; we can’t change this number. The first (or lightest) of the three, therefore, has to be equal to or less than 9 (because it is to the left of the median). Check the answers quickly – in this case, unfortunately, that information doesn’t help us to eliminate any answers.

If the middle box is actually 9, then we can subtract that from 21 to get the combined weight for the other two boxes. 21 – 9 = 12. So the lightest and heaviest boxes have to add up to 12.

Now, do we want to minimize or maximize the weight of the heaviest box?

The heaviest box has to be equal to or greater than 9 (because it is to the right of the median). We want to minimize the weight of this box in order to maximize the weight of the lightest box. So, the smallest possible weight for the heaviest box is 9.

If the heaviest box is minimized to 9, and the heaviest and lightest add up to 12, then the maximum weight for the lightest box is 3. The correct answer is C.

Make sense? If you’re sure you’ve got it, try this harder one. Set your timer for 2 minutes!

*A certain city with a population of 132,000 is to be divided into 11 voting districts, and no district is to have a population that is more than 10 percent greater than the population of any other district. What is the minimum possible population that the least populated district could have?

(A) 10,700

(B) 10,800

(D) 11,000

(E) 11,100

In this case, there are 11 voting districts, each with some number of people. We’re asked to find the minimum possible population in the least populated district – or the smallest population that any one district could possibly have.

Let’s say that we’re going to minimize the population in District 1. Because all 11 districts have to add up to 132,000 people, we want to maximize the population in Districts 2 through 10. How can we do that? Now, we need more information from the problem:

“no district is to have a population that is more than 10 percent greater than the population of any other district”

So, if the smallest district has 100 people, then the largest district could have 110 people but can’t have any more than that. If the smallest district has 500 people, then the largest district could have 550 people but can’t have any more than that. How did we calculate those numbers? In each case, we take 10% of the original number and add that figure to the original number to give us our maximum.

In the given problem, we don’t know the number of people in the smallest district, so let’s call that x. If the smallest district is x, then calculate 10% and add that figure to x: x + 0.1x = 1.1x. So the largest district could be 1.1x but can’t be any larger than that.

We want to maximize all of the 10 remaining districts, so we should assume that all 10 districts are equal to 1.1x. As a result, we have (1.1x)(10) = 11x people in the 10 maximized districts (Districts 2 through 10), as well as our original x people in the minimized district (District 1).

The problem told us that all 11 districts add up to 132,000, so write that out mathematically:

11x + x = 132,000

12x = 132,000

x = 11,000

The correct answer is D.

Key Takeaways for Max/Min Problems:

(1) figure out what variables are “in play” (what figures we can manipulate in the problem)

(2) figure out whether each variable needs to be maximized or minimized in order to achieve the desired outcome (the thing the problem asks us to do)

(3) do the work (carefully, as always!)

* GMATPrep® questions courtesy of the Graduate Management Admissions Council. Usage of this question does not imply endorsement by GMAC.

For more information on ManhattanGMAT, download Clear Admit’s independent guide to the leading test preparation companies here. This FREE guide includes coupons for discounts on test prep services at nine different firms!

# posted by Clear Admit @ 9:00 am in GMAT - Quantitative, GMAT News, GMAT Practice Problem, GMAT Test Prep Company Series, GMAT Tips

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Stanford
Virginia / Darden
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INSEAD
London Business School

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Independent blog with content by Vanderbilt MBA students.

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