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

Question

If x ≠ 0, is xy > 0?

(1) x > 0
(2) 1/x < y

chetan2u · Answer

The Q asks xy>0.. which basically means :"are x and y of the same sign?" 1)statement 1 tell us that x>0.. nothing about y.. if y is +ive, then yes .. if y is -ive, ans is no... insuff 2) statement two also does not give us a clear answer.. it can take both values as negative , both positive or x -ive and y positive... if x<0, then we will have to change the inequality sign when multiplying both sides by x => 1>xy…..xy could be 0.5 or -2 But if x>0, then we will hint change the inequality sign when multiplying both sides by x => 10.. by statement 2 y will be positive for positive x.... suff C

abhinav008 · Answer

1) x >0 but Y can be > 0 or Y can be < 0 . So not sufficient. 2) Y> 1/x here Y can be +ve and X can be -ve or both X and Y can be +ve . So not sufficient . Combining 1+2 Since X>0 we can multiply by X on both sides and sign of inequality will not change => 1 < XY thus XY >0 so C

vik09 · Answer

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/x0. Sufficient Answer C :-D

GMATinsight · Answer

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 C

Bunuel · Answer

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.

BelalHossain046 · Answer

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

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