xy ds prob

[tj123]

Are x and y both positive?
1) 2x-2y = 1
2) (x/y) > 1

I chose E.
Answer is c

I did the following:
2(x-y)=1
x-y=1/2

Even with x>y, its still insufficient in my opinion since it could be :
1-.5 = 1/2
or even
.25- (-.25) = 1/2

Please explain

[gaggleofgirls]

Here's what I get:

2 is easier, so x/y >1 so x and y must both be pos or both be neg, so insuficient.

1)
2x-2y = 1
2(x-y)=1
x-y = 1/2
You can come up with examples here of x,y both pos; y,x both ned and pos/neg or neg/pos, so it doesn't help us with sign at all on it's own, therefore insuff.

Together, they are still insuff in that we don't know any more together than we did in just 1).

So, I believe the Answer is E

-Carrie

[Zipper]

We do get more info for both.

x>y and they are both the same sign

so

x-y=1/2

x and y can't both be negative so they are both positive.
and we can't have +x -y or -x +y anymore coz they must be the same sign.

Hence, C

[aroon7]

from 1 we have x-y = 1/2

we have 3 possibilities for X and Y with respect to their signs :
+ -
+ +
- -

x = 1/4;y = -1/4; x-y = 1/2
x = 1;y = 1/2; x-y = 1/2
x = -1;y = -3/2;x-y = 1/2

so (1) is insuff

2) says x/y >1
we can know both X and Y have same sign
Insuff

combining both,

only X = +ve and Y = +ve will satisfy the condition
in the above examples, (-1)/(-3/2) yields answer less than 1, while (1)/(1/2) is greater than 1

So C

[gaggleofgirls]

Whey can't x and y both be negative?

x=-1/4
y = -3/4
-1/4 - -3/4 = 1/2

-Carrie

[aroon7]

Whey can't x and y both be negative?

x=-1/4
y = -3/4
-1/4 - -3/4 = 1/2

-Carrie

I missed it carrie. thanks!
still (-1/4)/(-3/4) is less than 1.
still C

Edited: i didn miss it. it the third row in my example...

[gaggleofgirls]

Arron - It was Zipper who said that they can't both be negative.

But I do see my mistake. I didn't pull enough information from 2)
Not only must x,y be both pos or both neg, but x>y (if it had been x/y >0, then the answer would be E).

With x,y both pos or both neg AND x > y, then the only way to solve for 1) x-y = 1/2 is for them both to be positive becuase there is no way for a neg number less than another negative number to also be greater than it.

so, yes, the answer is C.

-Carrie

[tj123]

what about these options:

let x = 1
and y = .5


1-.5 = .5

x and y are both positive and its sufficient to answer the question.
HOWEVER now

let x = .25
and y = -.25

.25- (-.25)= .5

x and y are not both positive but it satisfies statement 2 with x>y

The answer should be E

[Alara533]

tj123 there is a small correction here.

x/y > 1 means |x| > |y| and not exactly x > y.

From first equation we have y = x - (1/2)
so different values of (x,y) can be (1, 1/2), (1/2,0), (1/4,-1/4), (0,-1/2), (-1/4, -3/4). Here we have both positive x,y values, both negative x,y values and mixed x,y values. Hence in sufficient.

From second we have |x| > |y|. Which is insufficient.

Together, we have

y = x - (1/2) and |x| > |y|

Now from y = x - 1/2, for any -ve value of x, we will get a -ve value of y such that |x| < |y|.

Hence for |x| to be greater than |y| and satisfy y = x - 1/2, x and y should be positive.

Answer C