Is xy< 0 ?

[VJesus12]

Is xy< 0 ? $$\left(1\right)\ xy^2 < y^2$$ $$\left(2\right)\ y^2 < y$$ The OA is the option E.

Could someone give me some help here? I think that the first statement is sufficient. <i class="em em-confused"></i>

[Jay@ManhattanReview]

Is xy< 0 ? $$\left(1\right)\ xy^2 < y^2$$ $$\left(2\right)\ y^2 < y$$ The OA is the option E.

Could someone give me some help here? I think that the first statement is sufficient. <i class="em em-confused"></i>

We are given that xy < 0.

If xy < 0, one of x and y must be postive and the other must be negative.

Let's see each statenment one by one.

(1) xy^2 < y^2

Since y^2 is a positive quantity, we can cancel it.

=> x < 1

=> x can be positive (for example, x = 1/2), 0, or negative (for example, x = -1). We are sure about the nature of x as well as y. Insufficient.

(2) y^2 < y

Since y^2 is a positive quantity and y is greater than y^2, y must be a positive quantity. However, we do not know about x. Insufficient.

(1) and (2) together

Even after combining the statements, we cannot be sure wether xy < 0 as x can be positive or negative.

The correct answer: E

Hope this helps!

-Jay
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Hi VJesus12,

We're asked if (X)(Y) is less than 0. This is a YES/NO question and can be solved by TESTing VALUES.

1) (X)(Y^2) < Y^2

IF....
X=0 and Y=1 then (X)(Y) = (0)(1) = 0 and the answer to the question is NO.
X= -1 and Y=1 then (X)(Y) = (-1)(1) = -1 and the answer to the question is YES.
Fact 1 is INSUFFICIENT.

2) Y^2 < Y

The inequality in Fact 2 proves that Y must be a positive fraction (0 < Y < 1), but tells us NOTHING about the value of X.
Fact 2 is INSUFFICIENT.

Combined, we know:
(X)(Y^2) < Y^2
Y is a positive fraction (0 < Y < 1)

Since Y must be positive...
If X= 0, then the answer to the question is NO.
If X = negative, then the answer to the question is YES.
Combined, INSUFFICIENT

Final Answer: E

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