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Five peices of wood have an average length of 124 inches and

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Director
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Status: Preparing for the 4th time -:(
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Five peices of wood have an average length of 124 inches and [#permalink] New post 20 Nov 2011, 04:49
00:00
A
B
C
D
E

Difficulty:

  25% (low)

Question Stats:

73% (02:25) correct 26% (01:27) wrong based on 130 sessions
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

Even though I got the correct answer (B) by doing maths, but it was a total guess work. This is how I did.

Let say shortest piece be x

x+x+3*140=5*124
2x+420=620
2x=200
x=100

I have no idea how I did it. So can someone be please kind enough to let me know the mathematical approach and the concept ?
[Reveal] Spoiler: OA

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E.

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Re: 5 pieces of wood [#permalink] New post 20 Nov 2011, 06:21
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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
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Director
Director
Status: Preparing for the 4th time -:(
Joined: 25 Jun 2011
Posts: 563
Location: United Kingdom
Concentration: International Business, Strategy
GMAT Date: 06-22-2012
GPA: 2.9
WE: Information Technology (Consulting)
Followers: 11

Kudos [?]: 129 [0], given: 217

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Re: 5 pieces of wood [#permalink] New post 20 Nov 2011, 21:32
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.
_________________

Best Regards,
E.

MGMAT 1 --> 530
MGMAT 2--> 640
MGMAT 3 ---> 610 :-(

3 KUDOS received
Math Expert
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Re: 5 pieces of wood [#permalink] New post 05 Feb 2012, 14:50
3
This post received
KUDOS
Expert's post
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.
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Re: Five peices of wood have an average length of 124 inches and [#permalink] New post 14 Jun 2013, 04:27
Expert's post
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

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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

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Re: 5 pieces of wood [#permalink] New post 25 Aug 2013, 02:21
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?
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Re: 5 pieces of wood [#permalink] New post 25 Aug 2013, 05:46
Expert's post
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 MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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?
25 extra-hard Quant Tests

Re: 5 pieces of wood   [#permalink] 25 Aug 2013, 05:46
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Five peices of wood have an average length of 124 inches and

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