If x 0, is xy > 0? (1) x > 0 (2) 1/x < y

Hello,

For xy >0 both x an y should be of the same sign either both positive or both negative. Our job is to find whether both carries same sign or opposite.

Statement1 : X is positive. No information on Y, it can take both positive and negative sign hence not sufficient
Statement 2 : 1/x<y . In this equation x can be positive making 1/x +ive or X can be negative making 1/x -ive. Y is greater than 1/x hence it can be both positive and negative.

Combining both statements are sufficient.
From statement 1 we get to know that x is postive and hence 1/x is +ive which results in Y being positive.
From both statements we know that both x and y are positive so xy>0. Sufficient
Answer C

Question : Is xy > 0?

for xy to be greater than zero, both x and y must have same sign so the question can be rephrased as

Question : Do x and y have same sign?

Statement 1: x > 0

But this doesn't provide any information of y nor does it provide any relation of x with y

hence, NOT SUFFICIENT

Statement 2: 1/x < y

i.e. If y is Negative, x Must be negative because 1/x will be defined as less than negative value (i.e. y)
and If y is Positive, x May be Positive or negative because 1/x will be defined as less than Positive value (i.e. y) e.g. x=1, y=2 OR x=-1, y=2

hence, NOT SUFFICIENT

Combining the two statements

x>0 and 1/x < y
for x>0, 1/x MUST be Positive
and Since, 1/x(positive value) is lass than y, therefore y must be a POSITIVE value as well

hence, SUFFICIENT

Answer: Option

MANHATTAN GMAT OFFICIAL SOLUTION:

(1) INSUFFICIENT: This tells us nothing about the sign of y.

In evaluating Statement (2), you might be tempted to assume that x must be positive. After all, we just read information in Statement (1) that tells us that x is positive. Besides, it is natural to assume that a given variable will have a positive value, because positive numbers are much more intuitive than negative numbers.

Instead, if we follow Principle #4, we will actively try to violate Statement (1), helping us expose the trick in this question.

(2) INSUFFICIENT: If we contradict Statement (1) to consider the possibility that x is negative, we would realize that it is necessary to flip the sign of the inequality when we cross multiply. That is, if x < 0, then 1/x < y means that 1 > xy, and the answer to the question is MAYBE.

(1) & (2) SUFFICIENT: If x is positive, then statement (2) says that 1 < xy (we do not flip the sign when cross multiplying). Thus, xy > 0.

The correct answer is C.

I would go for c.

Statement 1: insufficient coz no info about y.
For example
X=5, y=1 so xy=5 (yes to main question)
Or X=5, y=-1 so xy=-5 (NO to main question)

STATEMENT 2: insufficient
Case 1: (1/5)<1
X=5, y=1 so xy=5 (yes to main question)

Case 2: (1/-2)<1
X=-2, y=1 so xy=-2 (NO to main question)

COMBINE
Since x is positive (in statement 1), (1/x) must be positive.

And since y is greater than (1/x) which is positive, y must be positive.

So, xy must be positive.

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