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Length of a Longer Piece?

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by Ahmed MS » Sat Oct 29, 2011 8:46 pm
Q: A wooden rod cut into two pieces. What is the length of the longer piece?

1. One of the piece is 20 inch longer than other.

2. The length of the shorter piece is 1/3 length of longer piece.

My answer is D but OA is C. Can anyone help me to find out my mistake?


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Source: — Data Sufficiency |
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by shankar.ashwin » Sat Oct 29, 2011 9:18 pm
From (1) we know Longer = Shorter + 20
Since we are asked specific length, it could be any combination. (60,80)(100,120) and so on

From (2) Longer = 3* shorter
Again multiple possibilities (10,30)(30,90) and so on

Together; L=S+20 and L=3S

2S = 20; S=10 and L=30 Only one possibility. C
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by Ahmed MS » Sat Oct 29, 2011 10:39 pm
Well my approach was,

1. Short = X, Long= X+20
Let the rod is 100 feet,
so, X+X+20=100
2X=80, X= 40, S=40, L=60 Sufficient.

2. S=X and L=3X, again X+3X=100
So X= 25, S= 25, L= 75. Sufficient.


But the problem is that the values of S and L are not the same for both 1 and 2. Does the value has to be the same? If YES, C is the right answer and if NO then D is the right answer. I am confused about that!


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by shankar.ashwin » Sun Oct 30, 2011 3:16 am
You need to find a distinct/unique solution for a problem.
You have assumed the length as 100 here, someone would assume 200. There could be infinite solutions using both statements alone. For a unique solution you need both together. GMAT would never have problems which have different answers using two statements in DS
Ahmed MS wrote:Well my approach was,

1. Short = X, Long= X+20
Let the rod is 100 feet,
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