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Help me solve this

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Intern
Joined: 15 Apr 2011
Posts: 32

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15 Oct 2011, 19:30
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)8/15

d)3/5

e)1/2
Current Student
Joined: 08 Jan 2009
Posts: 326
GMAT 1: 770 Q50 V46
Re: Help me solve this [#permalink]

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15 Oct 2011, 19:40
1
KUDOS
Mark off a number line in 3rds and 5ths:

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

Note that 0/3 = 0/5 = 0, and 3/3 = 5/5 = 1

If we put the above on common denominators:
0/15, 3/15, 6/15, 9/15, 12/5, 5/15, 10/15, 15/15

Order:
0/15, 3/15, 5/15, 6/15, 9/15, 10/15, 12/5, 15/15

The gaps between each piece is:
3, 2, 1, 3, 1, 2, 3

So we remove one of each distinct gap:
3, 2, 1, 3

We have (3 + 2 + 1 + 3) / 15 remaining

9/15 = 3 / 5

D)
Intern
Joined: 15 Apr 2011
Posts: 32
Re: Help me solve this [#permalink]

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15 Oct 2011, 19:53
Aahhhh... Common denominator, y did not I get tat in my head???

Thank u Pike .. That was an excellent explanation..
Re: Help me solve this   [#permalink] 15 Oct 2011, 19:53
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