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

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Math Expert
Joined: 02 Aug 2009
Posts: 7199
Re: If -2x > 3y, is x negative?  [#permalink]

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21 Jun 2016, 06:42
1
Shrivathsan wrote:
If -2x > 3y, is x negative?
(1) y > 0
(2) 2x + 5y - 20 = 0

Hi,
-2x > 3y...
(a)If y<0, x can be both +ive and -ive..
(b)if y>0, x will have to be +ive as 3y is positive and -2x , to be positive, has to have x as -ive..

now lets see the choices..

(1) y > 0
If y>0, x is -ive as proved in (b) above... suff

(2) 2x + 5y - 20 = 0..
this can be written as 2x+3y + 2y -20=0..
now 2x+3y<0, so 2y>20... or y is +ive and therefore x is -ive.... suff

ans D
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Joined: 01 May 2015
Posts: 39
Re: If -2x > 3y, is x negative?  [#permalink]

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29 Jun 2016, 23:38
Question says x < -1.5y

(1) is sufficient becuase if y is positive and x < -1.5y then clearly, x will be negative.

(2) y = (20 - 2x)/5
Substituting in -2x > 3y
-2x > 3(20 - 2x)/5
-10x > 60 - 6x
x < -15
So, from (2) alone also, we know that x is negative.
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Joined: 11 Sep 2015
Posts: 3326
Re: If -2x > 3y, is x negative?  [#permalink]

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29 Sep 2016, 07:33
1
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dimitri92 wrote:
If -2x > 3y, is x negative?

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

Target question: Is x negative?

Given: -2x > 3y

Statement 1: y > 0
In other words, y is POSITIVE
This means that 3y is POSITIVE
It is given that -2x > 3y
Since 3y is POSITIVE, we can write: -2x > SOME POSITIVE #
If -2x is greater than SOME POSITIVE #, we know that -2x is POSITIVE
If -2x is POSITIVE, then x must be negative
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: 2x + 5y - 20 = 0
IMPORTANT: It is given that -2x > 3y
So, let's take 2x + 5y - 20 = 0 and rewrite it as 5y - 20 = -2x [I have isolated -2x, just like we have in the GIVEN information]
Now, we'll take -2x > 3y, and replace -2x with 5y - 20 to get: 5y - 20 > 3y
Subtract 3y from both sides: 2y - 20 > 0
Add 20 to both sides: 2y > 20
Solve: y > 10
This means that y is POSITIVE
We already saw in statement 1, that when y is positive, x must be negative
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

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Re: If -2x > 3y, is x negative?  [#permalink]

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04 Mar 2017, 11:11
1
sitagupta385 wrote:
If -2x > 3y, is x negative?

(1) y > 0

(2) 2x + 5y - 20 = 0

Hi

(1) Simple and sufficient, if y>0 then x should be <0.

(2) 2x + 5y = 20

2x = 20 - 5y

2x = 5(4 - y)

x=5n, y = 4 - 2n

We are not done yet, still need to consider main restriction -2x>3y. Putting above values into inequality we'll get:

-2*5n > 3(4 - 2n)

-10n > 12 - 6n

n < -3

x = 5n and n<-3 then our x<0. Sufficient.

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Re: If -2x > 3y, is x negative?  [#permalink]

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19 Mar 2018, 06:55
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Re: If -2x > 3y, is x negative? &nbs [#permalink] 19 Mar 2018, 06:55

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