Inequality

[Uri]

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

OA: [spoiler](D)[/spoiler]
Forgotten the source. Sorry :roll:
Please explain the logic.

[splendentsky]

The answer is D.

My analysis:

1. if -2x>3y, and if y>0, then x must be negative.
For Example, if y=1, -2x must > 3. In order for -2x equals to a positive number, x must be a negative number, in this example, x must >-1.5. So A itself is correct.
At this point, we can already eliminate C or E.

Let's see Data2.
2. Given: 2x+5y-20=0. Also given: -2x>3y.
(a)2x+5y=20
(b)-2x-3y>0
Add (a) and (b) together, gives us 2y>20, which also equals to y>10.
If y is positive, from the Data 1's analysis, x must be negative.

Therefore, D.

Hope this helps.

[Uri]

well done, splendentsky! are you sure that we can add equality and inequality as you have done for st. 2?

Another approach:
Given, (2x+3y)<0
St1:
If y>0, then 3y>0. So, to make 2x+3y negative, x must be negative. So, sufficient.
St 2:
Substituting the value of y obtained from this equation in (2x+3y)<0 we find that x<-15. So, x is obviously negative. Hence sufficient.

[cramya]

Lets try something a little different in statement II

Stmt I

-2x>3y => 0 > 2x+3y i.e 2x+3y is negative

2x+5y = 20

(2x+3y)+2y = 20

-ve + 2y = 20 means y is positive >0

SUFF

Different ways to skin a cat so go with what works best for u....

Regards,
CR

[cubicle_bound_misfit]

cramya....

thanks a bunch for the fur from the cat