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
Whenever you're given an average, determine the sum.
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
