Bunuel wrote:
Are x and y both positive?
(1) 2x-2y=1
(2) x/y>1
(1) 2x-2y=1. Well this one is clearly insufficient. You can do it with number plugging OR consider the following: x and y both positive means that point (x,y) is in the I quadrant. 2x-2y=1 --> y=x-1/2, we know it's an equation of a line and basically question asks whether this line (all (x,y) points of this line) is only in I quadrant. It's just not possible. Not sufficient.
(2) x/y>1 --> x and y have the same sign. But we don't know whether they are both positive or both negative. Not sufficient.
(1)+(2) Again it can be done with different approaches. You should just find the one which is the less time-consuming and comfortable for you personally.
One of the approaches:
\(2x-2y=1\) --> \(x=y+\frac{1}{2}\)
\(\frac{x}{y}>1\) --> \(\frac{x-y}{y}>0\) --> substitute x --> \(\frac{1}{y}>0\) --> \(y\) is positive, and as \(x=y+\frac{1}{2}\), \(x\) is positive too. Sufficient.
Answer: C.
Hello Bunuel,
I am preparing for GMAT and you are a master in quantitatives,I salute you. However this problem I did not understand why it is C.I got E by plugging in numbers.
Considerin Stmt (1)
2x-2y=1
Means x-y=1/2
Now i used 2 numbers x=2,y=1.5 and x= -1.5 and y= -2
So (1) is insufficient as both x and y can be both +ve or -ve.
Stmt(2)
x/y > 1
Means x >y
If i use the above numbers x=2,y=1.5 and x= -1.5 and y= -2
then this holds true but cannot determine if x and y are both positive or negetive.
Combining (1) and (2) I still cannot determine if x and y are both positive or negetive .
So for me answer is E .
Please let me know what am I missing here.
Thanks
As stated above, x= -1.5 and y= -2 does not satisfy the second statement, hence you cannot use these values when plugging numbers.