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# If a rope is cut into three pieces of unequal length, what

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Intern
Joined: 29 Nov 2004
Posts: 8
If a rope is cut into three pieces of unequal length, what [#permalink]

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29 Nov 2004, 20:12
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If a rope is cut into three pieces of unequal length, what is the length of the shortest of these pieces of rope?
(1) The combined length of the longer two pieces of rope is 12 meters.
(2) The combined length of the shorter two pieces of rope is 11 meters.
Intern
Joined: 26 Nov 2004
Posts: 47

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29 Nov 2004, 20:32
E, there is no way to figure out the three individual lengths.
Intern
Joined: 29 Nov 2004
Posts: 8

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29 Nov 2004, 20:35
I thought that

6.2
5.8
5.2

was the only possibility
Intern
Joined: 26 Nov 2004
Posts: 47

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29 Nov 2004, 20:42
use variables when solving these kind of problems, they will help.
Manager
Joined: 15 Jul 2004
Posts: 75
Location: London

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30 Nov 2004, 02:39
E

Letâ€™s call the fragments a, b, c where a>b>c

(1) a + b =12

(2) b + c = 11

Therefore c â€“ a = 1

There are many solutions(6.1, 5.9, 5.1 or 6.3, 5.7, 5.3, etc), but Iâ€™ve plugged in and realised that a,b,c canâ€™t have any possible value. The only possible values have to fulfil the conditions above and be within certain ranges:

6<a<6.5
5.5<b<6
5<c<5.5
DS More   [#permalink] 30 Nov 2004, 02:39
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