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Math-Fraction Problem

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by screwdriver » Sun Jun 26, 2011 11:27 am
Hi,

I have a issue in understanding this problem.

Kim finds a 1-meter tree branch and marks it off in thirds and fifths. She then breaks the branch along all the markings and removes one piece of every distinct length. What fraction of the original branch remains?


(A)2/5
(B)7/15
(C)1/2
(D)8/15
(E)3/5

Can some one please explain how we can solve this problem?

Thanks in advance.
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by goalevan » Sun Jun 26, 2011 4:23 pm
I started by drawing a sketch of a line and breaking it into fifths and thirds.

You'll will find each label in order from 0 to 1 as follows:

0, 1/5, 1/3, 2/5, 3/5, 2/3, 4/5, 1

The problem asks what the length of the 1-meter branch remains after removing one piece of each distinct length.

Length 1: 1/5-0 = 1/5, distinct so far.
Length 2: 1/3-1/5 = (5-3)/15 = 2/15, distinct so far.
Length 3: 2/5-1/3 = (6-5)/15 = 1/15, distinct so far.
Length 4: 3/5-2/5 = 1/5, NOT distinct.

At this point you should notice from your sketch that the rest of the branch is symmetrical to what you've already calculated.

We can rephrase the question now as "What is 1 - (1/5 + 2/15 + 1/15)?"
= 1 - ((3+2+1)/15) = 1 - 6/15

Answer is 9/15, or 3/5, E

Notice that answer choice A is a prime example of a trap answer. You will get this question wrong if you counted the 4th length as distinct, or if you forget to subtract the sum of distinct lengths from 1. Both easy errors to make.
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by GMATGuruNY » Sun Jun 26, 2011 8:18 pm
screwdriver wrote:Hi,

I have a issue in understanding this problem.

Kim finds a 1-meter tree branch and marks it off in thirds and fifths. She then breaks the branch along all the markings and removes one piece of every distinct length. What fraction of the original branch remains?


(A)2/5
(B)7/15
(C)1/2
(D)8/15
(E)3/5

Can some one please explain how we can solve this problem?

Thanks in advance.
I posted a solution here:

https://www.beatthegmat.com/tree-branche ... tml#380520
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