Check GMAT Club Decision Tracker for the Latest School Decision Releases https://gmatclub.com/AppTrack

 It is currently 28 May 2017, 16:48

### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# Five pieces of wood have an average length of 124cm and a

Author Message
TAGS:

### Hide Tags

Senior Manager
Joined: 07 Jul 2005
Posts: 402
Followers: 3

Kudos [?]: 57 [0], given: 0

Five pieces of wood have an average length of 124cm and a [#permalink]

### Show Tags

25 Oct 2005, 00:08
5
This post was
BOOKMARKED
00:00

Difficulty:

35% (medium)

Question Stats:

67% (02:05) correct 33% (01:13) wrong based on 254 sessions

### HideShow timer Statistics

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

a) 90
b) 100
c) 110
d) 130
e) 140

OPEN DISCUSSION OF THIS QUESTION IS HERE: five-peices-of-wood-have-an-average-length-of-124-inches-and-123513.html
[Reveal] Spoiler: OA
Intern
Joined: 01 Aug 2009
Posts: 29
Location: Australia
Followers: 1

Kudos [?]: 17 [4] , given: 3

Re: Mean, Median and 5 pieces of wood [#permalink]

### Show Tags

04 Aug 2009, 23:38
4
KUDOS
The median of 5 pieces is 140. Therefore, there are 2 pieces >=140.
Since, we want to maximize the smallest piece, we want to limit the largest piece(s) to the lowest value possible, because the larger the largest pieces the smaller the smallest pieces will have to be. But since the median is 140, it is the floor limit on the size of the 2 largest pieces...so the two largest pieces will have to be 140.

(A+B+140+140+140)/2 = 124 [where, A and B are the smaller pieces]

Since the question is asking for the maximum size of the smallest piece while preserving the average and median, A and B must be equal, so,
(2A+140+140+140)/2 = 124

A = 100.

Another way to think about it is, how averages are distributed among numbers. For every inch more the average, their has to be an inch less than the average. So, we have 3 numbers which are 16 each more than the average...in total 48 over the average. The two smaller pieces will have to be compensate this. And to get the maximum lowest value the compensation should be distributed evenly...each member should be 24 less than the average...124-24 = 100.
_________________

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

SVP
Joined: 29 Aug 2007
Posts: 2476
Followers: 70

Kudos [?]: 774 [2] , given: 19

Re: Five pieces of wood GMAT Prep PS [#permalink]

### Show Tags

18 Mar 2009, 18:52
2
KUDOS
Accountant wrote:
Five pieces of wood have an average length of 124cm and a median lenght of 140cm. What is maximum possible length in cm of the shortest piece of wood

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

Is plugging in answers the shortest way to solve this?

Not really. That is too time consuming.

The logic is: Make the distribution of the lengths close to the median.
Since median > avg, the max. shortest valu cannot be the avg.

So it is: (124x5 - 140x3)/2 = (620 - 420)/2 = 100
_________________

Gmat: http://gmatclub.com/forum/everything-you-need-to-prepare-for-the-gmat-revised-77983.html

GT

Math Expert
Joined: 02 Sep 2009
Posts: 39037
Followers: 7750

Kudos [?]: 106472 [2] , given: 11626

Re: Mean, Median and 5 pieces of wood [#permalink]

### Show Tags

23 Sep 2010, 05:50
2
KUDOS
Expert's post
robertrdzak wrote:
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

I see no ambiguity in this question.

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 --> $$x_1+x_1+140+140+140=620$$ --> $$x_1=100$$.

Hope it's clear.
_________________
GMAT Tutor
Joined: 24 Jun 2008
Posts: 1179
Followers: 438

Kudos [?]: 1606 [2] , given: 4

### Show Tags

12 Sep 2011, 20:54
2
KUDOS
Expert's post
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

VP
Joined: 22 Aug 2005
Posts: 1113
Location: CA
Followers: 1

Kudos [?]: 111 [1] , given: 0

### Show Tags

25 Oct 2005, 00:20
1
KUDOS
3
This post was
BOOKMARKED
B. 100

sum of all lengths of all 5 pieces of wood = 124 * 5 = 620

3rd piece (sorted in increasing length) length = 140 (median)

for sum of first 2 wood length to become max, last two should be least.
let 4th, 5th wood also have length 140 each.

total of last 3 = 140 * 3 = 420
sum of first 2 = 620 - 420 = 200

each of these 2 will have length 200/2 = 100
VP
Joined: 30 Sep 2004
Posts: 1482
Location: Germany
Followers: 6

Kudos [?]: 349 [1] , given: 0

### Show Tags

25 Oct 2005, 00:21
1
KUDOS
how can the shortest piece have maximum length ? when all other pieces have a min value. thats 100 100 140 140 140. B)...
_________________

If your mind can conceive it and your heart can believe it, have faith that you can achieve it.

Senior Manager
Joined: 19 Mar 2008
Posts: 352
Followers: 1

Kudos [?]: 62 [1] , given: 0

### Show Tags

28 Jul 2008, 08:30
1
KUDOS
singaks wrote:
. Five pieces of wood have an average length of 124 cm and a median length of 140cm. what is the maximum possible length of the shortest piece of wood?

Need help. Thanks

Five pieces of wood in order of increasing length:
A,B,C,D,E
A+B+C+D+E = 124*5 = 620
C is the median and equals to 140
Because Maximum (A+B) occurs when D and E at their minimum; and D and E cannot be lower than 140, so min. D and E = 140
So max. A+B = 620 - 3*140 = 200
A+B = 200 and B > A
So, max A = 99 when B = 101
if B=A is acceptable, max. A = 100
Senior Manager
Joined: 31 Aug 2009
Posts: 417
Location: Sydney, Australia
Followers: 9

Kudos [?]: 295 [1] , given: 20

Re: Mean, Median and 5 pieces of wood [#permalink]

### Show Tags

28 Sep 2009, 19:05
1
KUDOS
tejal777 wrote:
Phew..NOT clear at all..
I struggled and made it through robertrdzak explanation but not clear in the last part of each pc being 100 and 100..why cant it be 90 and 110??

The smallest two pieces COULD be 90, 110. They could also be 80, 120. However, the question stem asks for what the MAX length could be for the smallest piece of wood. In both these situations the smallest piece is 90 and 80 i.e not maximised.

So {100, 100, 140, 140, 140} and {90,100,140,140,140} and many other sets satisfy the conditions for mean and median.
But in order to maximise the smallest piece 100 would be the only option. Hope that makes sense.
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7380
Location: Pune, India
Followers: 2291

Kudos [?]: 15147 [1] , given: 224

### Show Tags

10 Apr 2011, 07:51
1
KUDOS
Expert's post
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

Senior Manager
Joined: 20 Feb 2006
Posts: 373
Followers: 1

Kudos [?]: 29 [0], given: 0

### Show Tags

21 Feb 2006, 06:43
Five pieces of wood have an average (arithmetic mean) length of 124cm and a median length of 140 cm. What is the maximum possible length, in centimetres, of the smallest piece of wood?

a) 90

b) 100

c) 110

d) 130

e) 140
Senior Manager
Joined: 11 Jan 2006
Posts: 269
Location: Chennai,India
Followers: 1

Kudos [?]: 4 [0], given: 0

### Show Tags

21 Feb 2006, 07:00
A ) 90

here is my explanation

x-140 , y-140, 140 , z+140 , m+140
______________________________ = 124
5

x-140 + y-140 + 140 + z+140 + m+140 = 600

x-140 + y-140 + z+140 + m +140 = 460

now i assumed z & m == 1 ----> x-140+ y-140 = 460 - 280 = 180

so the loewst value can be 180/2 = 90
_________________

vazlkaiye porkalam vazltuthan parkanum.... porkalam maralam porkalthan maruma

Director
Joined: 13 Nov 2003
Posts: 789
Location: BULGARIA
Followers: 1

Kudos [?]: 53 [0], given: 0

### Show Tags

21 Feb 2006, 07:10
think there is something wrong with this Q. If the median is 140cm and AVRG is 124 then the total lenght of the woods is 620cm.Since median is 140cm the values above the median should be > or = to the median.Their minimum value is 140x3=420cm.The max possible lenght of the shortest piece is 200-124=76cm
May be i am wrong
Director
Joined: 06 Feb 2006
Posts: 898
Followers: 3

Kudos [?]: 112 [0], given: 0

### Show Tags

21 Feb 2006, 07:24
1
This post was
BOOKMARKED

The average of 5 pieces is 124, this means the total length of all pieces=620

We now the median is 140, which gives us that 140 is the middle value of all the fives pieces... which means two pieces are below 140 and two pieces above 140....

To get the maximum length of the smallest piece of wood we must minimize the length of the two largest pieces....

Remember we have the total length of 620... and the middle value 140... all we need is to distribute 380 (i.e. 620-140) in such a way that two of the values would be below 140 and two at least 140... so 100+100+140+140+140=620, the maximum value of the smallest piece is 100, since if we chose 110, two other values would only yield 130 which cannot be the case...

Hope i wrote it in understandable way...

Last edited by SimaQ on 21 Feb 2006, 07:49, edited 1 time in total.
Director
Joined: 06 Feb 2006
Posts: 898
Followers: 3

Kudos [?]: 112 [0], given: 0

### Show Tags

21 Feb 2006, 07:26
BG wrote:
think there is something wrong with this Q. If the median is 140cm and AVRG is 124 then the total lenght of the woods is 620cm.Since median is 140cm the values above the median should be > or = to the median.Their minimum value is 140x3=420cm.The max possible lenght of the shortest piece is 200-124=76cm
May be i am wrong

Everything is perfect with your reasoning... you got that 3 values must be at least 140*3=420cm so we need to distribute 200 among the rest pieces (i.e 2) which would equal 100...
Director
Joined: 13 Nov 2003
Posts: 789
Location: BULGARIA
Followers: 1

Kudos [?]: 53 [0], given: 0

### Show Tags

21 Feb 2006, 07:36
Thanx SimaQ for your help, what was i thinking of!!!???
Manager
Joined: 16 Sep 2005
Posts: 62
Followers: 1

Kudos [?]: 2 [0], given: 0

### Show Tags

21 Feb 2006, 07:51
I would select 100.

The way I solved the question as follows.
Median is 140
Average is 124
Total length is 620
Now based on the available information 2 Lengths <= 140 <= remaining two lengths.

Sum of these 4 lengths has to be 620 - 140 = 480
To maximize the shortest length, I considered that two short lengths are equal is size = x and remaining two lengths equal in size = 140 so now the addition of two short lengths is
2X = 480 - (140 + 140)
2X = 200
X = 100

I hope this makes sense.
_________________

Thanks

Senior Manager
Joined: 11 Jan 2006
Posts: 269
Location: Chennai,India
Followers: 1

Kudos [?]: 4 [0], given: 0

### Show Tags

21 Feb 2006, 08:33
yeah guys i calculated as 600 , it is 620 , then it will be 100... thnks
_________________

vazlkaiye porkalam vazltuthan parkanum.... porkalam maralam porkalthan maruma

Manager
Joined: 23 May 2007
Posts: 107
Followers: 1

Kudos [?]: 14 [0], given: 0

### Show Tags

09 Jun 2007, 21:15
Five pieces of wood have an average length of 124 cm and median length 140 cm. What is the maximum length in cm of the shortest peice of wood.

1.90
2.100
3.110
4.130
5.140
Director
Joined: 30 Nov 2006
Posts: 591
Location: Kuwait
Followers: 15

Kudos [?]: 291 [0], given: 0

### Show Tags

09 Jun 2007, 21:25
We already know that the middle piece, when ordering the pieces from longest to shortest, is 140 cm long [the median of five pieces is the middle one]

To result in a maximum length for the shortest piece, the two longest pieces must have minimum possible length --> both 140 cm

Now we have 3 pieces with 140 and two other pieces <140> the two short pieces must have equal length [ call it X ]

[2X + (3x140)] / 5 = 124
[2X + 420] = 5 x 124 = 620
2X = 620 - 420 = 200 --> X = 100 cm

09 Jun 2007, 21:25

Go to page    1   2   3   4   5    Next  [ 87 posts ]

Similar topics Replies Last post
Similar
Topics:
3 Seven pieces of wood have an average length of 100 cm and a median len 4 15 Dec 2016, 14:31
9 Five logs of wood have an average length of 100 cm and a median length 5 11 Dec 2016, 00:23
230 Seven pieces of rope have an average (arithmetic mean) lengt 43 17 Dec 2016, 20:25
49 Five peices of wood have an average length of 124 inches and 12 15 Dec 2016, 14:17
11 A rectangular tabletop consists of a piece of laminated wood 9 11 May 2016, 13:26
Display posts from previous: Sort by