MGMAT Test 5 - Is x a negative number?

[boazkhan]

Is x a negative number?

(1) x^2 is a positive number.

(2) x × |y| is not a positive number.


OA after discussion.

[albatross86]

Is x < 0 ?

1. x^2 > 0

eg 1. x = 2; x^2 = 4
2. x = -2; x^2 = 4

INSUFFICIENT

2. x * |y| is NOT a positive number

Remember: Zero is not considered a positive number either, so we need to count that in.

eg 1. x = -2, |y| = 4 => x*|y| = -8
2. x = 0, |y| = 3 => x*|y| = 0
3. x = 3, |y| = 0 => x*|y| = 0

INSUFFICIENT

Both 1 and 2:

This tells us that x cannot equal zero. However it could still be positive or negative, and satisfy both statements.

INSUFFICIENT.

Pick E.

[boazkhan]

Hi Albatross,
Thanks for your reply though I am still not very clear...When we take both statements together doesn't it mean that X is not zero because according to Statement 1 we have X^2 > 0 which means X can be positive or negative and since according to Statement 2 the product is NOT positive that only leaves us with a negative value of X?

I DO see how evaluating B alone we have X=0 as the 3rd case but together I am not too sure.

[Rahul@gurome]

Statement (1) alone is obviously not sufficient.

Consider just statement (2).
x X lyl is not a positive number implies x X lyl can be zero or negative.
If x X lyl is 0, then either x is zero or y is zero or both are zero.
If x is zero then we know, it is not negative.
If y is zero, x can be negative, zero or positive.
If x X lyl is negative, then since lyl cannot be negative, x has to be negative.
Since we cannot say anything definite about x, (2) alone is not sufficient.

Next combine both the statements and check.
Since x^2 > 0, x is not 0.
Still x X lyl can be zero or negative.
If x X lyl is zero, y has to be zero and x can be negative or positive.
If x X lyl is negative, obviously, x has to be negative.
So on combining what we have is if x X lyl is zero, then x can be positive or negative,
and if x X lyl is negative, then x is negative.
So we cannot say definitely whether x can be negative or not.
Or both the statements together are not sufficient to answer the question.

The correct answer is hence (E).

[albatross86]

Hi Albatross,
Thanks for your reply though I am still not very clear...When we take both statements together doesn't it mean that X is not zero because according to Statement 1 we have X^2 > 0 which means X can be positive or negative and since according to Statement 2 the product is NOT positive that only leaves us with a negative value of X?

I DO see how evaluating B alone we have X=0 as the 3rd case but together I am not too sure.

Yeah I know what you mean, actually when we take both statements together, we do not consider x = 0

I only said that x could be positive or negative. But remember, |y| could very well be = 0

Thus,

eg 1. x = 2, |Y| = 0 => x*|y| = 0 which is not a positive number.
and x=-2 , |y| = 4 => x*|y| = -2 which is not a positive number.

Thus x could be positive or negative.

[boazkhan]

Thanks! Got it!

[backtoschool11]

I was having a hard time understanding why C wasn't the answer, but the lightbulb went off when I realized I wasn't thinking about the possibility of Y being zero.

Great problem.

[BastiG]

Is x a negative number?

(1) x^2 is a positive number.

(2) x × |y| is not a positive number.


OA after discussion.

I think that this is a very good question because it seems very easy but has dirty little traps in it. I think that the two main traps are:

1) "not a positive number"

This means that it restricts just the positive numbers but not zero.

2) considerung that zero is not restricted
X can be either positive or negative because y can also be zero. So the two statements are together not sufficient as the previous posters pointed out.

[J N]

for statement 2

x [y] <= 0

is it permissible to divide by absolute y since it is always positive??

thus x <= 0

[Imsukhi]

IMO E