Statement 1: 2x - 2y = 1
Lets take an example: 4 - 3 = 1 OR (-4) - (-5) = 1.
Thus we can't say for sure if X and Y are positive.
Also: 1 - 0 = 1 and 0 - (-1) = 1. So, both need not be positive or negative simultaneously.
Statement 2: (x/y) > 1
This means that either both X and Y are positive (in which case X > Y) OR both X and Y are negative (in which case X < Y). Thus, we still can't say if both X and Y are positive.
Combining 1 and 2:
Firstly we eliminate 1 - 0 = 1 and 0 - (-1) = 1.
Two cases left: both are positive, and both are negative.
In the case where both numbers are negative, Y has to be less than X, but Statement 2 does not allow that. It is only in the case where both numbers are positive that both the equations hold true.
Thus C is the OA.
ps: You might want to attach a smaller file for a screen shot; 2.5 MB does take some time to download.
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Source: Beat The GMAT — Data Sufficiency |
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rdadbhawala
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Stem1:
2x-2y=1
=>x-y=1/2…………(1). NOT SUFF as it does not say about the values of x and y.
Stem2:
x/y >1………..(2). NOT SUFF as both x and y may be positive or negative.
1+2:
Start with the equation (2)
x-y = ½
x=1/2 +y
x/y = 1/2y +1 [ divide both the sides by y]
As x/y>1, 1/2y +1>1 => 1/2y>0 =>y>0.
As 1/2y>0, y is positive; and x/y>1, so, x is also positive. SUFF.
Answer is C.
2x-2y=1
=>x-y=1/2…………(1). NOT SUFF as it does not say about the values of x and y.
Stem2:
x/y >1………..(2). NOT SUFF as both x and y may be positive or negative.
1+2:
Start with the equation (2)
x-y = ½
x=1/2 +y
x/y = 1/2y +1 [ divide both the sides by y]
As x/y>1, 1/2y +1>1 => 1/2y>0 =>y>0.
As 1/2y>0, y is positive; and x/y>1, so, x is also positive. SUFF.
Answer is C.
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