percentages

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sl750: Master | Next Rank: 500 Posts; Posts: 496; Joined: Tue Jun 07, 2011 5:34 amFollowed by: 1 member; Thanked: 38 times

by sl750 » Wed Aug 03, 2011 11:59 am

A firm's annual revenue grows twice as fast as its costs. In 2007 it operated at a $1000 loss, it broke even in 2008, and in 2009 its revenues were 44% higher than in 2007. If the firm's revenues and costs grew at a constant rate over this period, what was its profit in 2009?

A $700

B $1000

C $1300

D $1600

E $2000

The answer is an approximation, so if you don't get the exact answer don't be alarmed. I shall post the answer after a few responses

Thanks

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Source: Beat The GMAT — Problem Solving | Wed Aug 03, 2011 11:59 am

tpr-becky: GMAT Instructor; Posts: 509; Joined: Wed Apr 21, 2010 1:08 pmFollowed by: 85 members; Location: Irvine, CA; Thanked: 199 times; GMAT Score:750

by tpr-becky » Wed Aug 03, 2011 9:09 pm

Where is this problem from? The approximation is a bit too wide for the question and a real GMAT question would clearly state the answer was an approximation. however here is how I would solve it:

First is to figure out that if the revenue increases 44% over two years that the yearly increas is 20% (20% of 120% is 144%) Which means that costs increase by 10% each year. we have the profit (R - C) for each of the first two years. I found it helpful to create a chart

R7 1.2R7 1.44R7
C7 1.1C7 1.21C7
-1000 0 ???

Now it is just about doing the algebra:

you know that 1.2R7 = 1.1C7 and that R7 - C7 = -1000

You can rewrite R7 = C7 - 1000 which means that 1.2(C7 - 1000) = 1.1C7 which simplifies to
1.2C7 - 1200 = 1.1C7

.1C7 = 1200
C7 = 12000

which means R7 = 11000.

Now you have to put that into the final column:

1.44(11000) - 1.21 (12000) = ?

15840 - 14520 = 1320

so the closest answer is 1300

Becky
Master GMAT Instructor
The Princeton Review
Irvine, CA

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