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If -2x > 3y, is x negative? [#permalink]
23 May 2010, 01:49

1

This post received KUDOS

Expert's post

If -2x>3y , is x negative

Given: -2x>3y. Question: is x<0? (Note here that if y is any positive number then we would have -2x>positive, and in order that to be true x must be some negative number).

(1) y>0 --> -2x>3y>0 --> x<0. Sufficient.

(2) 2x+5y-20=0 --> 2x=20-5y --> -20+5y>3y --> y>10. The same as above: x<0. Sufficient.

Re: If -2x > 3y, is x negative? (1) y > 0 (2) 2x + 5y - 20 = 0 [#permalink]
29 Jun 2013, 06:45

1

This post received KUDOS

fozzzy wrote:

In statement 2 we can write the equation 2x+3y+2y = 20 we know 2x+3y is positive and we get y = 10 hence same as statement 1 is this approach correct?

If -2x > 3y, is x negative?

(1) y > 0 -2x > +ve number, hence x is negative. Sufficient

(2) 2x + 5y - 20 = 0 The area defined by -2x > 3y is the area under the red line. If we know that 2x + 5y - 20 = 0 (blue line) (given the initial condition) we can say that x is negative because they intersect when x is negative. (refer to the image) Sufficient

Your approach is correct. We know that 2x+3y is negative (typo I think), so 2x + 3y +2y= 20 can be seen as -ve +2y=20 so y is positive for sure as 2y=20+(+ve)

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Given: -2x>3y. Q: is x<0? (Note here that if y is any positive number than we would have -2x>positive, and in order that to be true x must be some negative number).

(1) y>0 --> -2x>3y>0 --> x<0. Sufficient.

(2) 2x+5y-20=0 --> 2x=20-5y --> -20+5y>3y --> y>10. Same as above: x<0. Sufficient.

Answer: D.

Can you please explain stmt. 2 again. Unable to understand the following stmt---

-20+5y>3y _________________

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Given: -2x>3y. Q: is x<0? (Note here that if y is any positive number then we would have -2x>positive, and in order that to be true x must be some negative number).

(1) y>0 --> -2x>3y>0 --> x<0. Sufficient.

(2) 2x+5y-20=0 --> 2x=20-5y --> -20+5y>3y --> y>10. Same as above: x<0. Sufficient.

Answer: D.

Can you please explain stmt. 2 again. Unable to understand the following stmt---

-20+5y>3y

(2) 2x+5y-20=0 --> 2x=20-5y --> given -2x>3y, substitute 2x --> -(20-5y)>3y --> -20+5y>3y --> y>10 --> y=positive, as discussed above if y is any positive number then x must be some negative number: x<0. Sufficient.

Re: If -2x > 3y, is x negative [#permalink]
24 Aug 2013, 23:04

SUNGMAT710 wrote:

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

-2x > 3y 2x + 3y<0 -----(1)

Statement 1 If y>0 & 2x + 3y<0

Then x must be Negative. Sufficient

Statement 2 2x + 5y - 20 = 0 2x + 5y = 20 (2x + 3y) + 2y=20 We can write 2y + some negative no = 20 2y = 20 + some Positiveno y = 10 + some Positiveno/2 This mean that y>10

2x + 3y<0 2x< -3y x < -1.5 (Positive no) because y is positive

Then x must be Negative. Sufficient

Answer D _________________

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