If -3x > 4y, is x < 0? (1) y > 0 (2) 3x + 5y – 20 = 0

IMO A

since we dont know the sign of y in statement 2 so we can say anything about answer being D

look, it's been mentioned in the question stem that 3x+4y<0 but how come 3x + 4y +y =20 ? It means that the negative part (3x+4y) ought to be added with a positive 'y' in order to make the expression equals 20 , you see

A. -3x>4y - statement 1 - y>0, means -3x>a where a is 4y which is a positive value and for -3x to be greater than the positive value x shall be < 0. Hence sufficient.
Statement 2 - 3x+5y=20 which is also an equation of a decreasing line as the slope is negative and the values for the (x,y) pair can be (-10,10), (-5,7), (0,4), (5,1), (10,-2) where can be negative or less than zero but it can also be positive but for all positive values of x the equation -3x>4y will not be satisfied hence x can only be <0. Hence statement 2 is sufficient. So answer is D

sorry missed an important point there so updated the response. correct answer is D.

Sent from my SM-N920G using GMAT Club Forum mobile app

Given -3x>4y

Find is x<0 i.e is 'x'-ve

Now -3x > 4y
=> OR 3x < -4y
=> OR x < \(\frac{-4}{3}\)*y ---(1)
=> Therefore from (1) x<0 FOR SURE if y>0

Statement 1 y>0
=> Since y>0, Therefore x<0 SUFFICIENT

Statement 2 3x+5y-20=0
=> 3x+5y=20 ------------- (2)
=> Given 3x<-4y
=> OR 3x+4y<0
=> OR 3x+4y+y<0+y
=> OR 3x+5y<y
=> OR 20<y ------- from (2)
=> OR y>20
=> Since y>20 i.e y>0
=> Therefore 'x' is -ve i.e x<0
=> SUFFICIENT

Therefore 'D'

Thanks
Dinesh

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.