My answer is C.

Is that correct ?

I just have a small confusion !!

The q says : Are x and y both positive ?
1. 2x-2y=1
2. x/y>1

In statement 2 we have x/y >1 => x > y
then pluggin some valus of x and y we can have results like :

x=3; y=2 so x/y >1 (both are positive)
x=-3; y=-2 so x/y >1( but x is smaller than y, which contradicts the inequality condition !!)
x=1/2 and y=1/3then x/y >1 (both are positive and x>y)
x=-1/2 and y= -1/3 then x/y >1 (x is smaller than y here)

So for me seems like , it can be concluded both are positive under this condition !!

Can anybody throw some light !!

Any expert's solution for this confusion....


I request Stuart/Ron can you please help !!


regards,
Amit

amitansu wrote:I just have a small confusion !!

In statement 2 we have x/y >1 => x > y

Can anybody throw some light !!

Your problem stems from your manipulation of this inequality.

We have to be VERY careful when we manipulate inequalities. Remember, if you multiple or divide both sides by a negative, you need to reverse the inequality.

So:

x/y > 1

To get to "x > y", you actually multiply both sides by "y". So, we get two solutions:

if y > 0, then x > y

However, if y < 0, we actually get x < y.

So, we are allowed to pick x = -3 and y = -2, since:

-3/-2 = 1.5 > 1

Hey Stuart,

In this question, aren't there 2 situations?

1) x and y - Both positive
2) x and y - Both negative

x/y > 1

Now, if y is positive, then x>y, however, if y is negative, then, x<y.

Therefore how is the answer c?

aditikedia wrote:Hey Stuart,

In this question, aren't there 2 situations?

1) x and y - Both positive
2) x and y - Both negative

x/y > 1

Now, if y is positive, then x>y, however, if y is negative, then, x<y.

Therefore how is the answer c?

My previous post didn't even address the whole question, I was just responding the manipulation of statement (2).

Looking at the statements together, we know that:

(1) x - y = 1/2

and

(2) if y is negative, y > x; and
if y is positive, then x > y.

We can rewrite (1) as:

x - y = 1/2
x = y + 1/2

If x = y + 1/2, then x MUST be greater than y, which means it's no longer possible for x and y to both be negative (since when that happens, y > x).

Therefore, if both statements are true, x and y must both be positive.

Thanks Stuart!

what level question would you say this is ?
Also are there any other approaches to solve this one ?

Thanks.

from statement 1----x/y - 1 = 0.5 * 1/y (divide by y both sides)

from statement 2----x/y>1

Combine both--- x/y -1 must be positive number.This implies RHS must be positive.This further implies 1/y must be positive.

therefore x & y must be positive.