GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 25 Jun 2018, 02:42

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

Five pieces of wood have an average (arithmetic mean) length of 124

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

4 KUDOS received
Intern
Intern
User avatar
Joined: 01 Aug 2009
Posts: 28
Location: Australia
Five pieces of wood have an average (arithmetic mean) length of 124 [#permalink]

Show Tags

New post 04 Aug 2009, 23:38
4
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

71% (01:17) correct 29% (01:34) wrong based on 763 sessions

HideShow timer Statistics

Five pieces of wood have an average (arithmetic mean) length of 124 centimeters and a median length of 140 centimeters. What is the maximum possible length, in centimeters, of the shortest piece of wood?

A. 90
B. 100
C. 110
D. 130
E. 140

_________________

The three most significant times in your life are:
1. When you fall in love
2. The birth of your first child
3. When you prepare for your GMAT

1 KUDOS received
Manhattan Prep Instructor
User avatar
Joined: 28 Aug 2009
Posts: 153
Location: St. Louis, MO
Schools: Cornell (Bach. of Sci.), UCLA Anderson (MBA)
Re: Five pieces of wood have an average (arithmetic mean) length of 124 [#permalink]

Show Tags

New post 30 Jun 2010, 13:42
1
For questions with a fixed sum (here 5*avg = 620), if you need to maximize one term, then you minimize all the others. Likewise, if asked to minimize one term, you maximize all the others.

I find it useful to create placeholders for the terms on paper, filling in with numbers/variables:

(In order, smallest to largest)
x / x / 140 / 140 / 140 = sum of 620
_________________


Emily Sledge | Manhattan GMAT Instructor | St. Louis

Manhattan GMAT Discount | Manhattan GMAT Course Reviews | Manhattan GMAT Reviews

Expert Post
2 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 46334
Five pieces of wood have an average (arithmetic mean) length of 124 [#permalink]

Show Tags

New post 23 Sep 2010, 05:50
2
1
Five pieces of wood have an average (arithmetic mean) length of 124 centimeters and a median length of 140 centimeters. What is the maximum possible length, in centimeters, of the shortest piece of wood?

A. 90
B. 100
C. 110
D. 130
E. 140

Given: 5 peices of wood have an average length of 124 centimeters --> total length = 124*5=620. Also median = 140.

If a set has odd number of terms the median of a set is the middle number when arranged in ascending or descending order;
If a set has even number of terms the median of a set is the average of the two middle terms when arranged in ascending or descending order.


As we have odd # of pieces then 3rd largest piece \(x_3=median=140\).

So if we consider the pieces in ascending order of their lengths we would have \(x_1+x_2+140+x_4+x_5=620\).

Question: what is the MAX possible length of the shortest piece of wood? Or \(max(x_1)=?\)

General rule for such kind of problems:
to maximize one quantity, minimize the others;
to minimize one quantity, maximize the others.

So to maximize \(x_1\) we should minimize \(x_2\), \(x_4\) and \(x_5\). Min length of the second largest piece of wood, \(x_2\) could be equal to \(x_1\) and the min lengths of \(x_4\) and \(x_5\) could be equal to 140 --> \(x_1+x_1+140+140+140=620\) --> \(x_1=100\).

Answer: B.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Expert Post
Veritas Prep GMAT Instructor
User avatar
P
Joined: 16 Oct 2010
Posts: 8105
Location: Pune, India
Re: Five pieces of wood have an average (arithmetic mean) length of 124 [#permalink]

Show Tags

New post 09 Apr 2011, 21:01
AnkitK wrote:
5 pieces of wood have an average length of 124 cm and a median of 140 cm .what is the maximum possible length in cm of the shortest piece of wood?
A.90
B.100
C.110
D.130
E.140


It is a nice question, a GMAT type question i.e. fun to work out, can be reasoned out fairly quickly but needs you to think a little. Follow my train of thought here (which finally takes just a few seconds when you start doing it on your own)

First thing that comes to mind - Median is the 3rd term out of 5 so the lengths arranged must look like:

___ _____ 140 _______ __________

The mean is given and I need to maximize the smallest number. Basically, it should be as close to the mean as possible. Which means the greatest number should be as close to the mean as possible too.
If this doesn't make sense, think of a set with mean 20:
19, 20, 21 (smallest number very close to mean, greatest very close to mean too)
10, 20, 30 (smallest number far away, greatest far away too)

Using the same logic, lets make the greatest number as small as possible. The two greatest numbers should both be at least 140 (since 140 is the median)

___ _____ 140 140 140

Since the mean is 124, the 3 greatest numbers are already 16 each more than 124 i.e. total 16*3 = 48 more than the mean. So the two smallest numbers should be a total of 48 less than mean, 124. To make the smallest number as great as possible, both the small numbers should be 24 each less than the mean i.e. they should be 100.
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for $199

Veritas Prep Reviews

Director
Director
avatar
Status: Impossible is not a fact. It's an opinion. It's a dare. Impossible is nothing.
Affiliations: University of Chicago Booth School of Business
Joined: 03 Feb 2011
Posts: 800
Reviews Badge
Re: Five pieces of wood have an average (arithmetic mean) length of 124 [#permalink]

Show Tags

New post 10 Apr 2011, 06:18
Karishma
I don't know if the key word "shortest" means the second. It means the least. So the answer should be 99 practically because of the need to differentiate the first from the second- and be compatible with keyword. Your thoughts on this?

Posted from my mobile device
Expert Post
1 KUDOS received
Veritas Prep GMAT Instructor
User avatar
P
Joined: 16 Oct 2010
Posts: 8105
Location: Pune, India
Re: Five pieces of wood have an average (arithmetic mean) length of 124 [#permalink]

Show Tags

New post 10 Apr 2011, 07:51
1
1
gmat1220 wrote:
Karishma
I don't know if the key word "shortest" means the second. It means the least. So the answer should be 99 practically because of the need to differentiate the first from the second- and be compatible with keyword. Your thoughts on this?

Posted from my mobile device


Hey gmat1220,

Smallest just means the smallest element. It doesn't necessarily mean that there should be a unique 'smallest number'.

Say {1, 2, 5, 9, 1, 3, 9}
Which is the smallest number here? 1 right? It doesn't matter even if it appears twice. If I arrange them in ascending order {1, 1, 2, 3 ....} .. the first and the second both are smallest (or shortest length).
So two pieces of wood could have the shortest length. It would be maximized only if their lengths are equal and both have a length of 100.
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for $199

Veritas Prep Reviews

Expert Post
2 KUDOS received
GMAT Tutor
avatar
S
Joined: 24 Jun 2008
Posts: 1345
Re: Five pieces of wood have an average (arithmetic mean) length of 124 [#permalink]

Show Tags

New post 12 Sep 2011, 20:54
2
1
socalboy429 wrote:
Five pieces of wood have an average (arithmetic mean) length of 124 centimeters and a median length of 140 centimeters. What is the maximum possible
length, in centimeters, of the shortest piece of wood:

A. 90
B. 100
C. 110
D. 130
E. 140


Say we list the lengths of our pieces of wood in increasing order:

S, a, 140, b, L

We know that the sum of these lengths is 5*124 = 620. Now, we want to make S, the smallest length, as big as possible. To do that, we want the other unknown lengths to 'use up' as little of the sum of 620 as possible. That is, the smaller we make a, b and L, the larger we can make S. Since b and L must be at least as large as the median, the smallest possible values for b and L are 140. That gives us this set:

S, a, 140, 140, 140

The three largest values now add to 420, so the two smallest values must add to 620-420 = 200. Since making them equal will make a as small as possible (a cannot be less than S), the largest possible value of S is 200/2 = 100.
_________________

GMAT Tutor in Toronto

If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com

11 KUDOS received
Manager
Manager
avatar
Joined: 20 Aug 2011
Posts: 135
Re: Five pieces of wood have an average (arithmetic mean) length of 124 [#permalink]

Show Tags

New post 20 Nov 2011, 07:21
11
1
Sum of lengths is 124*5=620

Median is 140
Sum of the lengths of other four pieces= 620-140=480

The lengths of pieces-

L1, L2, 140, L4, L5

The sum of the four pieces is constant.

L4 and L5 have to be minimum for L1 to be maximum but median length must be 140.

The minimum possible values of L4 and L5 could be 140, hence the L1+L2 = 620 - 420 = 200.
The maximum possible value of L1 = 100= L2
_________________

Hit kudos if my post helps you.
You may send me a PM if you have any doubts about my solution or GMAT problems in general.

Expert Post
12 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 46334
Re: Five pieces of wood have an average (arithmetic mean) length of 124 [#permalink]

Show Tags

New post 05 Feb 2012, 15:50
12
13
Five pieces of wood have an average (arithmetic mean) length of 124 centimeters and a median length of 140 centimeters. What is the maximum possible length, in centimeters, of the shortest piece of wood?

A. 90
B. 100
C. 110
D. 130
E. 140

Given: 5 peices of wood have an average length of 124 centimeters --> total length = 124*5=620. Also median = 140.

If a set has odd number of terms the median of a set is the middle number when arranged in ascending or descending order;
If a set has even number of terms the median of a set is the average of the two middle terms when arranged in ascending or descending order.


As we have odd # of pieces then 3rd largest piece \(x_3=median=140\).

So if we consider the pieces in ascending order of their lengths we would have \(x_1+x_2+140+x_4+x_5=620\).

Question: what is the MAX possible length of the shortest piece of wood? Or \(max(x_1)=?\)

General rule for such kind of problems:
to maximize one quantity, minimize the others;
to minimize one quantity, maximize the others.

So to maximize \(x_1\) we should minimize \(x_2\), \(x_4\) and \(x_5\). Min length of the second largest piece of wood, \(x_2\) could be equal to \(x_1\) and the min lengths of \(x_4\) and \(x_5\) could be equal to 140 --> \(x_1+x_1+140+140+140=620\) --> \(x_1=100\).

Answer: B.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 46334
Re: Five pieces of wood have an average (arithmetic mean) length of 124 [#permalink]

Show Tags

New post 14 Jun 2013, 05:27
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE

All DS Min/Max Problems to practice: search.php?search_id=tag&tag_id=42
All PS Min/Max Problems to practice: search.php?search_id=tag&tag_id=63

_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Manager
Manager
avatar
Joined: 26 Feb 2013
Posts: 166
Re: Five pieces of wood have an average (arithmetic mean) length of 124 [#permalink]

Show Tags

New post 25 Aug 2013, 03:21
Bunuel wrote:
enigma123 wrote:
Apologies blink005, if I am getting this wrong. But how did you get this?

The minimum possible values of L4 and L5 could be 140, hence the L1+L2 = 620 - 420 = 200.


Below is step by step analysis of this question. Hope it helps.

5 peices of wood have an average length of 124 inches and a median of 140 inches. What is the MAX possible length of the shortest piece of wood?
A. 90
B. 100
C. 110
D. 130
E. 140

Given: 5 peices of wood have an average length of 124 inches --> total length = 124*5=620. Also median = 140.

If a set has odd number of terms the median of a set is the middle number when arranged in ascending or descending order;
If a set has even number of terms the median of a set is the average of the two middle terms when arranged in ascending or descending order.


As we have odd # of pieces then 3rd largest piece \(x_3=median=140\).

So if we consider the pieces in ascending order of their lengths we would have \(x_1+x_2+140+x_4+x_5=620\).

Question: what is the MAX possible length of the shortest piece of wood? Or \(max(x_1)=?\)

General rule for such kind of problems:
to maximize one quantity, minimize the others;
to minimize one quantity, maximize the others.

So to maximize \(x_1\) we should minimize \(x_2\), \(x_4\) and \(x_5\). Min length of the second largest piece of wood, \(x_2\) could be equal to \(x_1\) and the min lengths of \(x_4\) and \(x_5\) could be equal to 140 --> \(x_1+x_1+140+140+140=620\) --> \(x_1=100\).

Answer: B.


Why couldn't x4 and x5 be bigger than 140 and thus making x1 and x2 even smaller?
Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 46334
Re: Five pieces of wood have an average (arithmetic mean) length of 124 [#permalink]

Show Tags

New post 25 Aug 2013, 06:46
Skag55 wrote:
Bunuel wrote:
enigma123 wrote:
Apologies blink005, if I am getting this wrong. But how did you get this?

The minimum possible values of L4 and L5 could be 140, hence the L1+L2 = 620 - 420 = 200.


Below is step by step analysis of this question. Hope it helps.

5 peices of wood have an average length of 124 inches and a median of 140 inches. What is the MAX possible length of the shortest piece of wood?
A. 90
B. 100
C. 110
D. 130
E. 140

Given: 5 peices of wood have an average length of 124 inches --> total length = 124*5=620. Also median = 140.

If a set has odd number of terms the median of a set is the middle number when arranged in ascending or descending order;
If a set has even number of terms the median of a set is the average of the two middle terms when arranged in ascending or descending order.


As we have odd # of pieces then 3rd largest piece \(x_3=median=140\).

So if we consider the pieces in ascending order of their lengths we would have \(x_1+x_2+140+x_4+x_5=620\).

Question: what is the MAX possible length of the shortest piece of wood? Or \(max(x_1)=?\)

General rule for such kind of problems:
to maximize one quantity, minimize the others;
to minimize one quantity, maximize the others.

So to maximize \(x_1\) we should minimize \(x_2\), \(x_4\) and \(x_5\). Min length of the second largest piece of wood, \(x_2\) could be equal to \(x_1\) and the min lengths of \(x_4\) and \(x_5\) could be equal to 140 --> \(x_1+x_1+140+140+140=620\) --> \(x_1=100\).

Answer: B.


Why couldn't x4 and x5 be bigger than 140 and thus making x1 and x2 even smaller?


We want to maximize \(x_1\), not to minimize.

Next, \(x_4\) and \(x_5\) cannot be less than the median, which is 140.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

BSchool Forum Moderator
User avatar
D
Joined: 12 Aug 2015
Posts: 2642
GRE 1: 323 Q169 V154
GMAT ToolKit User Premium Member
Re: Five pieces of wood have an average (arithmetic mean) length of 124 [#permalink]

Show Tags

New post 15 Dec 2016, 14:17
Here is my solution to this Great Official Question =>

Let W1,W2,W3,W4,W5 be the 5 wooden pieces in increasing order of length.
Given Mean = 124

\(Mean = Sum/#\)

Hence Sum(5) = 124*5 = 620
Now Median = 140
As #=5
Hence median => 3rd term => W3
Hence W3=140

Now to maximise the smallest piece that is W1 we must minimise all the other pieces keeping in mind the following things =>
All values To the left of median must be either less than or equal to it.
All values to the right of median must be greater than or equal to it.
All values in set must be greater than or equal W1
All values in set must be less than or equal to W5


Hence W1+W1+140+140+140 = 620
W1=100
Hence Maximum length of smallest piece of food is 100 inches

Hence B

_________________


MBA Financing:- INDIAN PUBLIC BANKS vs PRODIGY FINANCE!

Getting into HOLLYWOOD with an MBA!

The MOST AFFORDABLE MBA programs!

STONECOLD's BRUTAL Mock Tests for GMAT-Quant(700+)

AVERAGE GRE Scores At The Top Business Schools!

Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 7060
Premium Member
Re: Five pieces of wood have an average (arithmetic mean) length of 124 [#permalink]

Show Tags

New post 14 Jan 2018, 13:54
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Re: Five pieces of wood have an average (arithmetic mean) length of 124   [#permalink] 14 Jan 2018, 13:54
Display posts from previous: Sort by

Five pieces of wood have an average (arithmetic mean) length of 124

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.