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If the price increased by x% from 2001 to 2002 and by y% fro

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If the price increased by x% from 2001 to 2002 and by y% fro [#permalink] New post 18 Jan 2010, 00:29
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If the price increased by x% from 2001 to 2002 and by y% from 2002 to 2003, what is the percentage increase from 2001 to 2003?

(1) xy = 30
(2) 100x + 100y + xy = 800
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Re: Percentage problem [#permalink] New post 18 Jan 2010, 04:54
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Price in 2002=(1+x)*Price-in-2001

Price in 2003=(1+y)*Price-in-2002=(1+x)(1+y)*Price-in-2001=(1+x+y+xy)*Price-in-2001

So basically, we need to determine (1+x+y+xy), where x=X/100, y=Y/100. 1+X/100+Y/100+XY/10,000


St1: XY=30 - > Clearly Insufficient

St2: 100X+100Y+XY=800; => X+Y+XY/100 = 8 => X/100+Y/100+XY/10,000 = 0.08 That's what we wanted. Sufficient


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Re: Percentage problem [#permalink] New post 18 Jan 2010, 08:16
Many thanks for the explanation!!
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Re: If the price increased by x% from 2001 to 2002 and by y% fro [#permalink] New post 20 Sep 2013, 10:58
Expert's post
amitanand wrote:
If the price increased by x% from 2001 to 2002 and by y% from 2002 to 2003, what is the percentage increase from 2001 to 2003?

(1) xy = 30
(2) 100x + 100y + xy = 800


m12 q35

If the price increased by x% from 2001 to 2002 and by y% from 2002 to 2003, what is the percentage increase from 2001 to 2003?

The price in 2001 - p;
The price in 2002 - p*(1+\frac{x}{100});
The price in 2003 - p*(1+\frac{x}{100})(1+\frac{y}{100})=p(1+\frac{y}{100}+\frac{x}{100}+\frac{xy}{10,000});

The percentage increase from 2001 to 2003 is \frac{2003-2001}{2001}*100=x+y+\frac{xy}{100}.

(1) xy = 30. Not sufficient.

(2) 100x + 100y + xy = 800 --> divide both sides by 100: x+y+\frac{xy}{100}=8, directly gives the answer. Sufficient.

Answer: B.

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Re: If the price increased by x% from 2001 to 2002 and by y% fro [#permalink] New post 22 Sep 2013, 02:17
amitanand wrote:
If the price increased by x% from 2001 to 2002 and by y% from 2002 to 2003, what is the percentage increase from 2001 to 2003?

(1) xy = 30
(2) 100x + 100y + xy = 800


Let price, P be 100.

after x% increase, price P1 = 100+x

After y% further increase, price P2 = 100+x + (100+x)*(y/100)

% increase = Increase in price / original price = (p2-p)*100/p = (100 X +100Y+xy)/100.

B gives numerator value. so sufficient but A is not.

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Re: If the price increased by x% from 2001 to 2002 and by y% fro   [#permalink] 22 Sep 2013, 02:17
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