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Help me solve this [#permalink] New post 15 Oct 2011, 18:30
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
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Re: Help me solve this [#permalink] New post 15 Oct 2011, 18:40
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Mark off a number line in 3rds and 5ths:

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

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)
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Re: Help me solve this [#permalink] New post 15 Oct 2011, 18:53
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, 18:53
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