Question from MGMAT CAT 1

[thinkblue]

If x and y are integers and xy does not equal 0, is xy < 0?

(1) y = x^4 - x^3

(2) x is to the right of y on the number line


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Question is asking if x, y have different signs.

For 1) y = x^3(x-1)

if x < 0, x^3 < 0 and x-1 < 0. So y is positive.
if x > 0, x^3 > 0 and x-1 > 0. So y is positive.

Hence INSUFF.

For 2) x > y. This doesn't tell us anything.

So taking the two together...

y > 0 and x > y

BUT this isn't possible!?

x > y (=x^3(x-1))

x > x^3(x-1)
x>0 so

1 > x^2 (x-1)

there is no solution to this inequality where x is an int and greater than 0. So the answer should be INSUFF??

[esledge]

Good catch, thinkblue! You are absolutely right. I will forward this one to our curriculum director for review.

Another way to prove your point:
(2) x > y
(1) y = x^4 - x^3
(combined)
x > x^4 - x^3
0 > x^4 - x^3 - x
0 > x (x^3 - x^2 - 1)
Since x is a positive integer, you can plug in 1, 2, 3, etc. to see that (x^3 - x^2 - 1) will never be negative.

It's invalid for the statements to say things that couldn't be true. This wouldn't make the answer INSUFF, it would just never happen on the GMAT. There are always theoretically possible value(s)/answer(s)...insufficiency just means you can't determine with certainty what they are.

I think one simple fix to this one is to change (2) to read: "y is to the right of x on the number line," though that would change the answer to (E), as positive y can be the result of either:

positive x: e.g. 2^4-2^3 = 16 - 8 = 8 > 2
negative x: e.g. (-2)^4 - (-2)^3 = 16 - (-8) = 24 > -2.

[esledge]

Update: This question has been corrected as follows.

If x and y are integers and xy does not equal 0, is xy < 0?

(1) y = x^4 - x^3
(2) x is to the right of 0 on the number line.

The correct answer is C.