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Re: If a rope is cut into three pieces of unequal length [#permalink]
22 Aug 2014, 01:51
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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.
Explanation:
I think the question is little ambiguity,
It is understood the question can not be solved by individual statements.
Let us combine both the statements and see....
According to the date S + M + L = Total length (T), shortest (S), largest (L), Middle (M)
(1) The combined length of the longer two pieces of rope is 12 meters. i.e., M + L = 12 (2) The combined length of the shorter two pieces of rope is 11 meters. i.e., S + M = 11
If we subtract both we get L  S = 1, that is the longest of the three is 1 greater than the shortest of the three ( L = S + 1 )
Now if S + M = 11 and M + L = 12, then 5.1 + 5.9 = 11 and 5.9 + 6.1 = 12 , and 5.1 + 5.9 + 6.1 = T ( 17.1) , here the greatest number is 1 greater than the least number, and the total value is 17.1
But 5.2 + 5.8 = 11 and 5.8 + 6.2 = 12 , and 5.2 + 5.8 + 6.2 = T ( 17.2) , here the greatest number is 1 greater than the least number, and the total value is 17.2
We can also check few more decimal values 5.01 + 5.99 = 11 and 5.99 + 6.01 = 12 , and 5.01 + 5.99 + 6.01 = T ( 17.01) , here the greatest number is 1 greater than the least number, and the total value is 17.01.
In the above three cases the lease value could be 5.2, 5.1, 5.01,..... and many more, so we can not determine the least value as the total is not defined.
The correct answer is E.
