A step by step approach for this please :
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
Ans b
GMAT Prep Q - Stats
This topic has expert replies
-
- Legendary Member
- Posts: 1337
- Joined: Sat Dec 27, 2008 6:29 pm
- Thanked: 127 times
- Followed by:10 members
five pieces of wood with an average make up the total wood length --> w1+w2+w3+w4+w5=124*5
the median length is w3 in the set {w1+w2+w3+w4+w5} and w3=140, find the shortest piece of wood-?
if we take three values from the right side, namely w5,w4,w3 and keep them equal to 140 median length, then we are left with w1 and w2 of which total length should be equal to (124*5 -140*3)=200. Now we can calculate w1 and w2 as being equal to 100. This must be an official answer, BUT I certainly would prefer choice A to make distinction between two short pieces and make the ONE shortest as 90
IOM B
the median length is w3 in the set {w1+w2+w3+w4+w5} and w3=140, find the shortest piece of wood-?
if we take three values from the right side, namely w5,w4,w3 and keep them equal to 140 median length, then we are left with w1 and w2 of which total length should be equal to (124*5 -140*3)=200. Now we can calculate w1 and w2 as being equal to 100. This must be an official answer, BUT I certainly would prefer choice A to make distinction between two short pieces and make the ONE shortest as 90
IOM B
tito1545 wrote:A step by step approach for this please :
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
Ans b
My knowledge frontiers came to evolve the GMATPill's methods - the credited study means to boost the Verbal competence. I really like their videos, especially for RC, CR and SC. You do check their study methods at https://www.gmatpill.com
GMAT/MBA Expert
- Anurag@Gurome
- GMAT Instructor
- Posts: 3835
- Joined: Fri Apr 02, 2010 10:00 pm
- Location: Milpitas, CA
- Thanked: 1854 times
- Followed by:523 members
- GMAT Score:770
tito1545 wrote:A step by step approach for this please :
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
Ans b
Solution:
Let the length of the pieces of wood in increasing order be l1, l2, l3, l4, l5.
So, l3 = 140.
Also, l1+l2+l3+l4+l5 = 124*5 = 620.
Or l1+l2+l4+l5 = 620 - 140 = 480.
If l1 has to be maximum, l2, l4 and l5 have to be minimum.
Now l4 and l5 have to be more than or equal to median.
So, their minimum value is 140 each.
Also, l2 has to be more than or equal to l1.
So the minimum value of l2 is l1.
Or l2 >= l1.
l4 >= 140.
l5 >= 140.
So, l1+l2+l4+l5 >= 2l1+280.
Or 480 >= 2l1 + 280.
Or 200 >= 2l1.
Or l1 <= 100.
Or the maximum value of l1 is 100.
Anurag Mairal, Ph.D., MBA
GMAT Expert, Admissions and Career Guidance
Gurome, Inc.
1-800-566-4043 (USA)
Join Our Facebook Groups
GMAT with Gurome
https://www.facebook.com/groups/272466352793633/
Admissions with Gurome
https://www.facebook.com/groups/461459690536574/
Career Advising with Gurome
https://www.facebook.com/groups/360435787349781/
GMAT Expert, Admissions and Career Guidance
Gurome, Inc.
1-800-566-4043 (USA)
Join Our Facebook Groups
GMAT with Gurome
https://www.facebook.com/groups/272466352793633/
Admissions with Gurome
https://www.facebook.com/groups/461459690536574/
Career Advising with Gurome
https://www.facebook.com/groups/360435787349781/
- GMATGuruNY
- GMAT Instructor
- Posts: 15539
- Joined: Tue May 25, 2010 12:04 pm
- Location: New York, NY
- Thanked: 13060 times
- Followed by:1906 members
- GMAT Score:790
Whenever you're given an average, determine the sum.tito1545 wrote:A step by step approach for this please :
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
Ans b
Sum = (number of things) * (average) = 5 * 124 = 620.
Median = 140 centimeters.
Let's call the 5 pieces, from shortest to longest: w, x, 140, y, z.
Since we want to maximize w, we need to minimize y and z. Let y=140 and z=140.
Thus, the 5 pieces are: w, x, 140, 140, 140.
Thus, w+x = 620 - 3*140 = 200.
Now we can plug in the answer choices for w (the shortest piece of wood). Since the median is 140, and the average is 124, w and x must each be less than 124. Eliminate D and E.
Answer choice C: w=110
If w =110, then x = 200-110 = 90. Doesn't work because x cannot be less than w.
Eliminate C.
Answer choice B: w=100
If w=100, then x = 200-100 = 100. This works. The 5 pieces will be 100, 100, 140, 140, 140.
The correct answer is B.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3