Data Sufficiency

Is XY>0?

(1) X-Y > -2
(2) X-2y > -6

IMO C

Stmt 1 -

x-y>-2

Let x = 4 y = -2, x-y = 6 > -2 but xy < 0
Let x = 4 y = 2, x-y = 2 > -2 but xy > 0

Hence insufficient

Stms 2 -

x-2y > -6

Let x = 10 y = 2 x-2y = 6 > -6 but xy>0
Let x= 10 y = -2 x-2y = 14 > -6 but xy< 0

Hence insufficient

Stmt 1 and Stmt 2 -

subtracting both the stmt - y > 4
Let say y = 5, substitute this value in stmts 2
=>x > 4

Since both x and y are positive, xy has to be positive.

Hence sufficient.

crazy4gmat wrote:Is XY>0?

(1) X-Y > -2
(2) X-2y > -6

Let's start by rephrasing the question.

When will xy be greater than 0? When x and y are the same sign. So, we can ask:

Do x and y have the same sign?

(Note: if either one equals 0, we get an automatic "no" answer to the question.)

Let's look at the statements in general using some basic number properties rules.

If x is positive and y is negative, each statement reduces to:

(positive - negative) > (negative)

Since subtracting a negative is the same as adding a positive, we can rewrite this as:

(positive + positive) > (negative)

which is, of course, always true.

So, we can definitely pick a positive x and a negative y to get a "NO" answer to the original question.

Next we have to see if can get a "YES" answer to the original question, i.e. can we make them both positive or both negative.

Both negative is probably easier, so let's start there.

We're subtracting y from x in both statements, so let's pick a "big" negative y and a "small" negative x.

If x = -1 and y = -100, we get:

1) -1 - (-100) > -2

-1 + 100 > -2

99 > -2.

This inequality is true, so -1 and -100 are permissible numbers. Is (-1)(-100)>0? YES.

2) -1 - 2(-100) > -6

-1 + 200 > -6

199 > -6

This inequality is true, so -1 and -100 are permissible numbers. Is (-1)(-100)>0? YES.

So, even after combining, we can pick two negatives OR a negative and a positive: insufficient, choose (E).

pradeepsarathy wrote:IMO C

Stmt 1 -

x-y>-2

Let x = 4 y = -2, x-y = 6 > -2 but xy < 0
Let x = 4 y = 2, x-y = 2 > -2 but xy > 0

Hence insufficient

Stms 2 -

x-2y > -6

Let x = 10 y = 2 x-2y = 6 > -6 but xy>0
Let x= 10 y = -2 x-2y = 14 > -6 but xy< 0

Hence insufficient

Stmt 1 and Stmt 2 -

subtracting both the stmt - y > 4
Let say y = 5, substitute this value in stmts 2
=>x > 4

Since both x and y are positive, xy has to be positive.

Hence sufficient.

I don't think you can simply subtract both statements because:

a > b
c > d

do not mean a - c > b - d

For example, 4 > -4 & 3 > -6 but 4-3 < -4 -(-6).

So far, Stuart's solution is the only solution I can think of. Don't know if there is a better way than number testing because I can see myself spending a lot of time on number testing.