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M12 Q35

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Senior Manager
Joined: 16 Apr 2009
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21 Apr 2010, 17:39
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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Joined: 08 Apr 2010
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21 Apr 2010, 23:48
ichha148 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 the price is P initially.
the increase from 2001 to 2002 is x% so new price is P + P*x/100
the increase from 2002 to 2003 is y% so new price is P(1+ x/100)(1+ y/100)
= P(1+ (x+y)/100 + xy/10000) = (P/10000) (10000 + (x+y)*100 + xy)

statement xy = 30 gives a single value which is not sufficient alone
statement 100x + 100y + xy = 800 when put into the expression derived above gives the value P/100*100 (10000 + 800) = 1.08 P
hence the %age increase from 2001 to 2003 is 8%

so statement 2 is alone sufficient to solve this.
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fivezero7

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26 Apr 2010, 21:32
Thanks for clear cut explaination
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Re: M12 Q35   [#permalink] 26 Apr 2010, 21:32
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M12 Q35

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