Since you're being asked about x, isolate x in the inequality in the question stem. What we know is that
2x < -3y
x < -3/2y.

Stat. (1) says that y is positive, meaning that -3/2*positive is negative. X is smaller than a negative quantity, which by definition means that x is negative and the answer to the question stem is "yes". Sufficient.

Stat (2) says that 2x=-5y+20
x = -5/2y+10

Plug this into the inequality in the question stem:

-5/2y + 10 < -3/2y /+5/2y
10 < y

Again, this means that y is positive, so x<-3/2y must be smaller than a negative quantity, and must therefore also be negative. The answer is a definite "yes", and also sufficient.

Therefore, answer is D.

Though agree to ur point , however wanted to have a clarification on my approach

Q.) If -2x > 3y, is x negative ?
1) y > 0
2) 2x + 5y -20 = 0


Statement 1 : Lets take y=1 and subsitute -2x > 3 that means x has to be negative and <- 1, in second attempt lets take y=2, -2x > 6 that means x has to be negative and <-3.... so x to be '-' range is varying ...don't we count range too in DS questions ?

ArpanaAmishi wrote:Though agree to ur point , however wanted to have a clarification on my approach

Q.) If -2x > 3y, is x negative ?
1) y > 0
2) 2x + 5y -20 = 0


Statement 1 : Lets take y=1 and subsitute -2x > 3 that means x has to be negative and <- 1, in second attempt lets take y=2, -2x > 6 that means x has to be negative and <-3.... so x to be '-' range is varying ...don't we count range too in DS questions ?

There are two sub-types of DS questions: your "what is the value" type questions (for example, "what is the price of a shirt"), and your "yes/no" type questions (not "what is the value of x", but rather "is x <0?"). For the second type, the only possible answers for the question stem are "yes", "no" or "maybe", and a statement is sufficient if it limits the answer to the question to a single answer. If a statement fixes it so that x is always negative, then the answer to the question stem is a definite "yes", and is sufficient - range is irrelevant here, since we're not asked for the value of x.

The only way a statement in a DS Yes/No question will be insufficient is if it allows both a yes and a no - in this case, if a statement has said that y<5, that would've allowed both a negative and positive x, so both a yes and a no.

the first step you do when looking at a DS question is to determine for yourself exactly what sub-type it is - either a "what is the value" (in which case the answer you;re looking for is a single numerical answer" - or a "yes/No" (in which case the answers are in the form of "yes" / "no" / "Maybe"). For a yes no question, take the additional step of defining to yourself what a yes - or a no - look like for this particular question.