If xy≠0, what is the value of (2x + y)/(x - 2y)?

First of all, please format questions properly. The question reads:

If xy≠0, what is the value of (2x + y)/(x - 2y)?

(1) x/(x + y) = 2
(2) x - 2y = 4

As Mike from Magoosh puts it "those parenthesis are not garnish, not extra decorative elements --- they are absolute essential pieces of mathematical equipment, and you are setting yourself up for mistake if you casually ignore their tremendous importance".

If \(xy\neq{0}\), what is the value of \(\frac{2x + y}{x - 2y}\) ?

(1) \(\frac{x}{x + y} = 2\) --> \(x=2x+2y\) --> \(x=-2y\) --> \(\frac{2x + y}{x - 2y}=\frac{-4y+y}{-2y-2y}=\frac{-3y}{-4y}=\frac{3}{4}\). Sufficient.

(2) \(x - 2y = 4\) --> \(x=2y+4\) --> \(\frac{2x + y}{x - 2y}=\frac{2y+4+y}{4}=\frac{3y+4}{4}\) --> we don't know the value of \(y\), hence we can not calculate numerical value of this fraction. Not sufficient.

Answer: A.

Hope it's clear.
_________________

If xy≠0, what is the value of (2x + y)/(x - 2y)?

(1) x/(x + y) = 2
(2) x - 2y = 4

1.
x =2x+2y
x =-2y

(-4y + y)/(-2y - 2y)

We can get a value

(2) x - 2y = 4

(2x + y)/4 No single value so A

1. {x-2(x+y)}/(x+y)=0
{-x-2y}/(x+y)=0
-x=2y or x=-2y

(2x+y)/(x-2y)
=(-4y+y)/(-2y-2y)
=-3y/-4y
=3/4 (SUFFICIENT)

2. (2x+y)/(x-2y)
= {2(2y+4)+y} /(x-2y)
= {5y+8}/4
NOT SUFFICIENT

FINAL ANSWER IS A

We can get a value

(2) x - 2y = 4

(2x + y)/4 No single value so A

Posted from my mobile device

Asked: If xy≠0, what is the value of (2x + y)/(x - 2y)?

(1) x/(x + y) = 2
x/y = -2
(2x + y)/(x - 2y) = (-3)/(-4) = 3/4
SUFFICIENT

(2) x - 2y = 4
Since (2x + y) is unknown
NOT SUFFICIENT

IMO A
_________________

Question data : xy≠0, given so that the term in the denominator is NOT zero. Typical of a GMAT type of question.
This is a value kind of DS question where we have to find the value of the given expression.

From statement I alone, \(\frac{x }{ (x+y)}\) = 2.

Cross multiplying and simplifying, we have, x = -2y. This value can now be plugged into the expression to find out its value.

\(\frac{(2x + y) }{ (x – 2y)}\) = \(\frac{(-4y + y) }{ (-2y – 2y)}\) = ¾.

Statement I alone is sufficient to find the value of the expression. Answer options B, C and E can be eliminated. Possible answer options are A or D.

From statement II alone, x – 2y = 4. We cannot compute either the values of the variables x and y OR the value of the expression.
Statement II alone is insufficient. Answer option D can be eliminated.

The correct answer option is A.

Hope that helps!
Aravind B T
_________________

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.
_________________