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# In the year 2001, a company's sales increased by x percent from the ye

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Math Expert
Joined: 02 Sep 2009
Posts: 64096
In the year 2001, a company's sales increased by x percent from the ye  [#permalink]

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31 Jul 2019, 01:06
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Difficulty:

25% (medium)

Question Stats:

78% (02:16) correct 22% (03:18) wrong based on 37 sessions

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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?

A. 20
B. 30
C. 40
D. 50
E. 60

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Re: In the year 2001, a company's sales increased by x percent from the ye  [#permalink]

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31 Jul 2019, 01:34
Bunuel 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?

A. 20
B. 30
C. 40
D. 50
E. 60

Given: 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,

If sales in 2000 = 1
Sales in 2002 = (1+x)(1-x) = 1+x-x-x^2 = 1-x^2
x^2 = .09
x=.3 = 30%

IMO B
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Re: In the year 2001, a company's sales increased by x percent from the ye  [#permalink]

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31 Jul 2019, 01:47
Let’s say that
—sales in 2000 is 100\$;
—(increased by x percent) sales in 2001 is (100+x);
—(decreased by x percent) sales in 2002 is (100+x)—(100+x)*(x/100)=(100+x)*(1–x/100)=(100^2-x^2)/100

It says that sales in 2002 is 9 percent less than that in 2000
—> 100–9=91

(100^2–x^2)/100=91
x^2=100^2–91*100=900
x=30

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Re: In the year 2001, a company's sales increased by x percent from the ye  [#permalink]

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31 Jul 2019, 07:27
Bunuel 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?

A. 20
B. 30
C. 40
D. 50
E. 60

Lets say Sale was 100 in the year 2000 so the resultant sale in 2002 was 91.
Now try to fill the gap with options.
100 -> 120 -> (.8*120) doesn't result in 91
100 -> 130 -> (.7*130) results in 91.
IMO B.
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Re: In the year 2001, a company's sales increased by x percent from the ye  [#permalink]

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05 Aug 2019, 16:22
1
Bunuel 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?

A. 20
B. 30
C. 40
D. 50
E. 60

Let’s let n = the sales in the year 2000. We can create the equation:

0.91n = n * (100 + x)/100 * (100 - x)/100

0.91 = (10,000 - x^2)/10,000

9100 =10,000 - x^2

x^2= 900

x = 30

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Re: In the year 2001, a company's sales increased by x percent from the ye   [#permalink] 05 Aug 2019, 16:22