Is xy x/y? (1) xy 0 (2) y

Question

Is xy > x/y?

(1) xy > 0
(2) y < 0

Bunuel · Accepted Answer

Is xy > x/y? Is xy > \frac{x}{y} ? Is \frac{xy^2-x}{y}>0 ? Is \frac{x(y^2-1)}{y}>0 ? Is \frac{x(y+1)(y-1)}{y}>0 ? This above inequality holds true when: A. x>0 and y>1 or -1 0 --> x and y have the same sign. Not sufficient. (2) y < 0. Not sufficient. (1)+(2) Both x and y are negative, so we are in scenario B, though we still need more precise range for y (if y<-1 then the answer will be YES but if -10 ? and as y<0 then the question reduces whether y<-1 . But we don't know that and thus even taken together statements are not sufficient. Answer: E.

maddy2u · Answer

(1) => Both should either be positive or negative . 
 5 * 2  > \frac{5}{2}  (yes)
-5*-2 > -5/-2 (Yes)
 0.5 *0.5  >  0.5/0.5  (No)  Insufficient

(2) => y<0 ; x can be positive or negative  Insufficient

(1) + (2) => 
 -5*-2  >  -5/-2 (Yes)
 -0.5 * -0.5 >  -0.5/-0.5  (No)

Hence , Clearly   E   .

fluke · Answer

Bunuel, how did you deduce A and B above(the range for x and y) from given inequality and how did you appropriately put "and" and "or" to the respective places? I always get confused at this. Could you please show me your way of thinking for that?
thanks

Bunuel · Answer

To check when \frac{x(y+1)(y-1)}{y}>0 holds true consider expressions with x and y separately: the product of two multiples (x and (y+1)(y-1)/y) to be positive they must have the same sign. So either: x>0 AND \frac{(y+1)(y-1)}{y}>0 , which is true when y>1 OR -1everything-is-less-than-zero-108884.html, hilit=extreme#p868863, here: inequalities-trick-91482.html, xy-plane-71492.html?hilit=solving%20quadratic#p841486, data-suff-inequalities-109078.html); Or: x<0 AND \frac{(y+1)(y-1)}{y}<0 , which is true when 0

gmat1220 · Answer

Well the first statement told that its not gonna help. The second does not add any information. How can you expect to see the answer? mark E and move on !

1) statement just tells x and y are same sign. Insuff
2) statement tells me y is -ve. What about x? Is x = 0? Insuff
Combine 1) + 2) 
No new information received. 
x/y : numerator can be -1<x<0 or denominator can be -1<x<0. Inequality can face both ways. E

Avinashs87 · Answer

Couple of questions:

1. How can we multiply both sides by y when we do not know if y is +ve or -ve.
2. I did not understand  xy > \frac{x}{y} ? --> is  \frac{xy^2-x}{y}>0 ? why is there a y in the denominator?

Bunuel · Answer

We do not multiply by y. We re-arrange xy > x/y as xy - x/y > 0 by subtracting x/y from both sides.

Mo2men · Answer

Is xy > x/y?

(1) xy > 0

x=-1 & y=-2.........2>1/2...........Answer is yes

x=-2 & y=-1.........2>2..............Answer is No

Note : I used negative numbers by spotting statement 2. Both statements do not contradict each other.

Insufficient

(2)   y < 0

No info about x..........clearly Insufficient

Combining 1 & 2:

No Need for further evidence as example above illustrates the situation in the two statements.

Answer: E

bumpbot · Answer

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

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