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

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If a rope is cut into three pieces of unequal length, what [#permalink] New post 26 Feb 2006, 06:20
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.
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 [#permalink] New post 26 Feb 2006, 07:18
E .

say x is smallest and z is longest and y is the middle one

from 1 y+z = 12 ... insufficient data

from 2 x+y =11 ..... in sufficient data

adding both x +2y+z = 23 .... insufficient data

so Ans E

P.S also from 1 and 2 you can see that there is 2 equation with 3 unknown variables ... so no solution
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 [#permalink] New post 26 Feb 2006, 07:22
Yes E is correct since we have 3 variables and 2 equations. Cheers!!

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 [#permalink] New post 26 Feb 2006, 18:37
1) We do not know the lenght of the rope, so we can't tell the length of the shortest piece x-24. Insufficient.

2) We do not now the lenght of the two pieces, so we can't deduce the lenght of the shortest piece. Insufficient.

Using 1) and 2)
Assume the three piece are x,y and z in descending order of lenght

x+y = 12
y+z = 11

x and y cannot be equal lengths since the question stem tells us all three are unequal pieces.

But if x = 7, y and z will have the wrong relationship. So we know x must be between 6 and 7.

If x = 6.1, y = 5.9 and z = 5.1
If x = 6.2, y = 5.8 and z = 5.2

We can have many possibilities.

Insufficient.

Ans E
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 [#permalink] New post 27 Feb 2006, 00:13
E.

We need more info. like the total length of the rope, "equal" pieces of rope etc...
  [#permalink] 27 Feb 2006, 00:13
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