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by j_shreyans » Sun Sep 21, 2014 3:11 am
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

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by GMATGuruNY » Sun Sep 21, 2014 3:21 am
j_shreyans wrote: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
Ignore the given length of 1-meter.'
Since the question stem asks for a FRACTION, the total length can be ANY VALUE.

Let the total length = 15 meters.
Dividing 15 into 3rds will yield markings at 5 and 10.
Dividing 15 into 5ths will yield markings at 3, 6, 9, and 12.

Listing the markings in order:
0......3....5..6......9..10....12......15

There are only 3 distinct lengths:
1 meter --> from 5 to 6 and from 9 to 10
2 meters --> from 3 to 5 and from 10 to 12
3 meters --> from 0 to 3, from 6 to 9, and from 12 to 15

Subtracting these 3 distinct lengths from 15, we get:
Length remaining = 15-1-2-3 = 9.
Remaining length/Total length = 9/15 = 3/5.

The correct answer is E.
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by RiyaR » Fri Sep 26, 2014 12:16 pm
I didnt get the part about marking 15 in thirds will get 5's and 10's
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by [email protected] » Fri Sep 26, 2014 3:20 pm
Hi RiyaR,

The logic behind this question actually allows us to make the tree branch ANY length, so Mitch chose a length that will give us integer values when the branch is broken into pieces.

Here's how you can visualize this explanation:

1) Draw a line segment on a piece of paper; label it 15 meters wide.
2) Mark where the line would be broken into THIRDS (it should be at the 5-meter and 10-meter marks).
3) Mark where the line would be broken into FIFTHS (it should be at the 3-meter, 6-meter, 9-meter, and 12-meter marks).

Now break the branch into pieces (as the question tells us to); from here you can pick up with MItch's explanation.

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