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

(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.


Hope it's clear.

The key here is knowing whether Y is positive or negative. If Y is positive, then X MUST be negative.
If Y=1, then in order for -2x = 3(1) = 3, then X must be a negative number.

If Y is negative, well - X could go either way. For example, if Y = -2, then x could = 2, in which case you would get

-2X > 3Y
-2X > 3(-2)
-2X > -6
x < 3

But the major point here is that if Y is positive, then X MUST be negative.
We already know (1) is good.
But with (2), what info do we know?

Well, if you combine
-2X > 3Y
with
2X + 5Y > 20

then the 2X cancels the -2X, bring the 3Y to the left and negate it and combine it with 5Y.

5Y - 3Y gets you to 2Y

So you get 2Y > 20
Y>10

OK, so what does that tell you? Well, it tells you that Y is positive! It's essentially a subset of statement (1) where Y>0. So both (1) and (2) basically say that Y is positive. That alone is enough info to answer the original question.

Therefore, when both (1) and (2) are good, we pick answer choice (D).

See more GMAT Pill material for Data Sufficiency.

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 \(2y=20+(+ve)\)

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

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

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

In the original condition, there are 2 variables(x,y) and 1 equation(-2x>3y), which should match with the number of equations. So you need 1 equation. For 1) 1 equation, for 2) 1 equation, which is likely to make D the answer. For 1), when y>0, it becomes 3y>2y. That is, -2x>3y>2y, -2x>2y. -x>y --> -x>y>0, -x>0 therefore x<0, which is yes and sufficient.
For 2), substitute y=(-2/5)x+4 to the equation. It becomes -2x>3(-2/5)x+4 and multiply 5 to both equations. Divide -10x>-6x+20, -4x>20 with -4 and x<-5<0 is also yes and sufficient. Therefore, the answer is D.


-> For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.

Given: -2x > 3y

St1: y > 0
If y is positive --> RHS is positive --> For the condition, -2x > 3y, to hold true LHS must be positive --> x must be negative
Sufficient

St2: 2x + 5y - 20 = 0 --> x = (20 - 5y)/2
Substitute x in the given equation
-2((20 - 5y)/2) > 3y

5y - 20 > 3y

2y > 20

y > 10

Since y > 10, -2x > 3y will hold true only if x is negative.
Sufficient

Answer: D

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

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

Answer:
RELATED VIDEO

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.

Answer D

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.