enigma123 wrote:

If xy < 5, is x < 1 ?

(1) |y| > 5

(2) \frac{x}{y}> 0

I got the answer is C which is correct but it was a guess work. So here is how I did this question:

Statement 1

|y| > 5 i.e. y > 5 and y > -5 or y > 5 and y < -5.

As this statement doesn't say anything about x, its clearly insufficient.

Statement 2

x/y> 0 --> This statement only tells that x and y have the same sign. Therefore insufficient.

After this I struggled to complete the question, and guessed answer C as correct answer. Can someone please help?

|y| > 5 means that y<-5 or y>5.

If xy < 5, is x < 1 ?(1)

|y| > 5 --> if

y=10 and

x=0 then the answer is YES but if

y=-10 and

x=2 then the answer is NO. Not sufficient.

(2)

\frac{x}{y}>0 -->

x and

y have the same sign. Still insufficient: if

y=-2 and

x=-1 then the answer is YES but if

y=2 and

x=2 then the answer is NO. Not sufficient.

(1)+(2) From (2)

x and

y have the same sign. Now, if from (1)

y>5 then

0<x<1 (in order

xy<5 to hold true) and if from (1)

y<-5 then

-1<x<0 (again in order

xy<5 to hold true). So in both cases

x<1. Sufficient.

Answer: C.

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