Data Sufficiency

Is x + y > 0?

(1) x - y > 0

(2) x2 - y2 > 0

iwillsurvive101 wrote:Is x + y > 0?

(1) x - y > 0

(2) x2 - y2 > 0

Hi!

We want to know if the sum of x and y is positive. So, we either need the individual values of x and y or information about the expression "x+y".

(1) x - y > 0

We know nothing about x and y individually, so (1) is insufficient.

If the concepts don't jump out at you, then pick numbers to see if you can get both a YES and a NO answer.

if x = 5 and y = 3, then x-y>0. Is 5+3>0? YES
if x = 5 and y = -6, then x-y>0. Is 5 + (-6) > 0? NO

Since we can get both a yes and no answer, (1) is insufficient: eliminate A and D.

(2) x^2 - y^2 > 0

The GMAT loves to test us on special quadratics - here we have a difference of squares. We can rewrite (2) as:

(x+y)(x-y) > 0

For any product of two terms to be positive, the signs of the two terms must be the same (i.e. both + or both -). So, (2) tells us that:

x+y and x-y are both positive;
OR
x+y and x-y are both negative.

So, do we know if x+y is positive? NO - it could be positive or negative. Insufficient: eliminate B.

Since neither statement was sufficient alone, we have to combine them. So, now we know that:

x+y and x-y are both the same sign;
AND
x-y is positive.

Accordingly, x+y must be positive as well. Together sufficient: choose C!

can you pls help with the following similar problem as well?

Is |a| > |b|?

(1) b < -a

(2) a < 0

iwillsurvive101 wrote:can you pls help with the following similar problem as well?

Is |a| > |b|?

(1) b < -a

(2) a < 0

Sure!

We want to know if the absolute value of a is greater than the absolute value of b. In other words, is the magnitude of a greater than the magnitude of b? (I.e. is a further from 0 on the number line than is b?)

As always, let's start with the simpler of the two statements (that way if we get stuck, at least we'll have eliminated some choices).

(2) a < 0. No information about b, so insufficient. Eliminate B and D.

(1) b < -a

adding a to both sides, we get:

b + a < 0

We now know that a+b is negative. Does this tell us anything about the relative values of a and b? NO - so insufficient: eliminate A.

Since neither statement was sufficient alone, we have to combine.

So, we know that:

a + b < 0

and

a < 0.

Does this tell us which of a or b has a greater magnitude? NO! For example, we could pick:

a = -2, b = -1

which fit both statements. Now we ask:

Is |-2| > |-1|? YES

However, we could also pick:

a = -2, b = -1000

which fit both statements.

Is |-2| > |-1000|? NO

Since we can still get both a yes and a no answer, even after combining we still don't have enough information to answer the question: choose E!

Thank you very much Stuart! I appreciate your help.