Is xy 3y (2) x 0

Question

Is  xy < 1 ?

(1)  \frac{2}{x} > 3y

(2)  x > 0

GMATinsight · Answer

Question : Is xy < 1? Statement 1: 2/x > 3y @x=1, y can be 1/3 i.e. xy(1/3) < 1 @x=-1, y can be -3 i.e. xy(3) > 1 Hence, NOT SUFFICIENT Statement 2: x > 0 No information about y Hence, NOT SUFFICIENT Combining the two statements 2/x > 3y and x>0 Since x is positive, therefore we can re-write the expression of first statement as 2 > 3xy i.e. xy < 2/3 i.e. xy is always less than 1 Hence, SUFFICIENT Answer: Option C

Bunuel · Answer

MANHATTAN GMAT OFFICIAL SOLUTION:

Statement (1) might imply that xy < 2/3, but only if x is positive. If it is negative, we would need to flip the sign: xy > 2/3.

Thus we cannot answer the question without knowing the sign of x—information that is provided in Statement (2).  The correct answer is C.

These types of questions may have an A or B trap, in that you might fail to realize that you have to set up negative and positive cases when you multiply or divide an inequality by a variable.

Watch out! In some GMAT problems, you  can  assume the sign of the variables, because the variables represent countable quantities of physical things. In those cases, you can assume that the variables are positive, and you can cross-multiply inequalities involving those variables at will.

nikitamishra25 · Answer

1- x could be negative so we cant cross multiply as there is a possibility of sign reversal. NS
2-given x is greater than 0, but y could be negative

BOTH: we can take the x to other side of inequality. this gives us xy less than .66

so C

YB10 · Answer

Bunuel is the below approach right? Statement 1) multiply x^2 on both sides, results in 2x-3yx^2>0 x(2-3xy)>0 Case 1: X>0, xy<2/3 Case 2: X<0, xy>2/3 (could be 1 or more) Not sufficient Statement 2: Not sufficient, just says x is positive Combine Gives case 1, hence xy<2/3 Sufficient Posted from my mobile device

Is xy < 1? (1) 2/x > 3y (2) x > 0

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