guerrero wrote:In the year 2001, a company's sales increased by x percent from the year 2000. In 2002, sales decreases x percent from the year 2001. If the sales in 2002 is 9 percent less than that in 2000, what is x?
20
30
40
50
60
I've added answer choices, which an actual GMAT question would provide.
Let the sales in 2000 = 100.
We can plug in the answers for the value of x.
Answer choice C: 40
Sales in 2001 = 100 + .4(100) = 140.
Sales in 2002 = 140 - .4(140) = 84.
From 100 to 84 is a decrease of 16%.
Since the decrease is supposed to be only 9%, the value of x must be smaller.
Eliminate C, D and E.
Answer choice B: 30
Sales in 2001 = 100 + .3(100) = 130.
Sales in 2002 = 130 - .3(130) = 91.
From 100 to 91 is a decrease of 9%.
Success!
The correct answer is
B.
If a value increases by x% and then decreases by y%, the total percent change = x - y - xy/100.
Thus:
If a value increases by x% and then decreases by x%, the total percent change = x - x - x²/100 = -x²/100.
Here, the total percent change = -9%.
Thus:
-x²/100 = -9
x² = 900
x = 30.
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