Algebra practice

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tonebeeze: Master | Next Rank: 500 Posts; Posts: 158; Joined: Mon Nov 02, 2009 5:49 pmFollowed by: 3 members; Thanked: 2 times

by tonebeeze » Mon May 16, 2011 3:55 pm

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

OA = E

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Source: Beat The GMAT — Problem Solving | Mon May 16, 2011 3:55 pm

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Mon May 16, 2011 5:07 pm

tonebeeze wrote: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

OA = E

This is a wonderful question, since it tests whether you can spot "xy" and "3x+2y" hiding in the given equation 2/x + 3/y = 4

We'll find these expressions hiding in the given equation if we combine the fractions on the left-hand-side.

To do this, we must rewrite 2/x and 3/y with a common denominator of xy.

(2/x)(y/y) = 2y/xy
(3/y)(x/x) = 3x/xy

So, 2/x + 3/y = 4 is the same as
2y/xy + 3x/xy = 4, which is the same as
(2y + 3x)/xy = 4
Since we're told that xy=5, we can rewrite the equation as
(2y + 3x)/5 = 4

From here we can see that (2y + 3x) must equal 20, which means the answer is E

Brent Hanneson - Creator of GMATPrepNow.com

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Mon May 16, 2011 6:30 pm

tonebeeze wrote: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

OA = E

Another approach would be to multiply the two equations:

xy*(2/x + 3/y) = 5*4.
2y + 3x = 20.

The correct answer is E.

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