Inequality

If -2x > 3y then either y is negative or x is negative
(if you aren't sure about this, graph -2x = 3y and shade in the area below the line to represent -2x).

So,

1) y > 0
So, if y is positive, then x must be negative = sufficient

2) 2x + 5y -20 = 0
rephrase the equation to solve for 3y and you get 3y = -6/5x + 12

Now substitute into the stem equation of -2x > 3y
and you get
-2x > -6/5x + 12
-4/5x > 12

For -4/5 times something to be greater than a positive number, it must be times a negative, therefore X is negative and 2 = sufficient also.

Answer is D

-Carrie

aroon7 wrote:If -2x > 3y, is x negative?

1) y>0
2) 2x + 5y - 20 = 0

(1) If y is positive and -2x > 3y, then -2x > 0. Therefore, x must be negative: sufficient.

(2) 2x + 5y = 20. So, at least one of x and y must be positive (for two numbers to have a positive sum, at least one must be positive, since neg + neg = neg).

Well, if y is positive, then as we saw from statement (1), x must be negative... so we can get a "yes" answer.

Part of me wants to say that we should be able to get a positive x too, but a bigger part of me thinks that the ratio of x:y in statement (2) makes it impossible for a positive value of x (which would lead to a negative value of y due to the inequality) to hold true. So my gut is saying that (2) is also sufficient on its own, although I'm having trouble proving it!

Someone feel free to prove me right or wrong!

Good solution above, hit enter before I did!

gaggleofgirls wrote:
2) 2x + 5y -20 = 0
rephrase the equation to solve for 3y and you get 3y = -6/5x + 12

Now substitute into the stem equation of -2x > 3y
and you get
-2x > -6/5x + 12
-4/5x > 12

For -4/5 times something to be greater than a positive number, it must be times a negative, therefore X is negative and 2 = sufficient also.

Answer is D

-Carrie

This is how I say that 2 is sufficient on its own.


You say "Well, if y is positive, then as we saw from statement (1), x must be negative... so we can get a "yes" answer. "

But once you know that 1) is sufficient, then there is no point looking at whether 1) and 2) are sufficient, they will always be. The only question is if 2) alone is sufficient, so I try to totally block 1) out of my head for a sec and look at 2) only.

-Carrie

The statement 2 is sufficient.

2x + 5y -20 = 0 can be rewritten as -2x=5y-20

Since -2x > 3y, we can rewrite this as 5y-20>3y, which can be rewritten as 2y>20 or y>10. Since y is a positive number greater than 10, x must be a negative number.

Hope this helps.