If xy0, what is the value of (2x + y)/(x - 2y)?

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

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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

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