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# A piece of string is marked in segments of one-fourth the

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A piece of string is marked in segments of one-fourth the [#permalink]  02 Nov 2008, 02:13
A piece of string is marked in segments of one-fourth the length of the string and also in segments of one third the length of the string. If the string is then cut at each mark, which of the following expresses all the different lengths of the bits of string, in fractions of the original length?

A) 1/12 and 1/4 only

B) 1/4 and 1/3 only

C) 1/6, 1/4 and 1/3

D) 1/12, 1/6, and 1/4

E) 1/12, 1/6, and 1/3
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Re: strings [#permalink]  07 Nov 2008, 14:02
a quick draw on paper suggests

there should be atleast one 1/4 length, and a total of 3 different lengths..Doing the Process of Elim, you get C and D remaining. upon further solving, you know that atleast one has to be 1/2 in length. So my pick for an answer is D
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Re: strings [#permalink]  07 Nov 2008, 14:08
sorry a small correction to my last post. Atleast one should be 1/12 and not 1/2 as posted.
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Re: strings [#permalink]  07 Nov 2008, 14:12
--1/4--1/3--1/2—2/3---3/4--1

1/4-0 = 1/4
1/3-1/4 = 1/12
1/2-1/3 = 1/6
2/3-1/2 = 1/6
3/4-2/3 = 1/12
1 -3/4 = 1/4

Therefore 1/4,1/6,1/12 --> D
Re: strings   [#permalink] 07 Nov 2008, 14:12
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