if 2/x + 3/y=4 and xy=5, then 3x + 2y= A) 1/5 B) 1/4

Question

if 2/x + 3/y=4 and xy=5, then 3x + 2y=

A) 1/5

B) 1/4

C) 4/5

D) 4

E) 20

don't understand how to do this problem.

SigEpUCI · Answer

Make the denominator the same so you can add the two


2y/xy + 3x/xy = (2y + 3x)/xy

(2y + 3x)/xy = 4
(2y + 3x)/5 = 4
2y + 3x) = 20

E

ywilfred · Answer

Striaghtfoward. 2/x + 3/y = (2y+3x)/xy = 4
 3x+2y = 4xy = 4*5 = 20
 
 
(E) is the anwer.

ian7777 · Answer

ditto all that.

Here's my "let's learn something from this" comment:

Whenever the GMAT asks for the value of several variables together, rather than a particular variable, it's likely that you'll find a way to solve for the group without having to solve for them individually. 

In this example, they ask for 3x + 2y, not x and y individually. You can get their individual values if you want, you'd still get 20, but probably you don't have to. Notice that when we get the answer, we still have no idea what x and y are. That doesn't matter at all.

So this is the "red flag". Many variables in a single question usually points to a trick somehow.

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if 2/x + 3/y=4 and xy=5, then 3x + 2y= A) 1/5 B) 1/4

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