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q 35 discussion

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Intern
Joined: 02 Jul 2010
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29 Aug 2010, 07:12
I don't understand this answer. where in the world did the 800 go?

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. $$100X + 100Y + XY = 800$$

(C) 2008 GMAT Club - m12#35

* Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient
* Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient
* BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
* EACH statement ALONE is sufficient
* Statements (1) and (2) TOGETHER are NOT sufficient

Statement (1) by itself is insufficient.

Statement (2) by itself is sufficient. $$\text{Percentage increase} = 100\frac{\text{(price in 2003)}}{\text{(price in 2001)}} - 100 = (1 + \frac{X}{100})(1 + \frac{Y}{100})100 - 100 = X + Y + \frac{XY}{100}$$
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30 Aug 2010, 07:51
Let me try to explain.
Lets take price in 2003 as P2003 and price in 2001 as p2001
Question asks about percentage rise from 2001 to 2003. This would be ((P2003 - P2001)/P2001) * 100.
But, as per question P2003 = P2001(1+X/100)(1+Y/100)
Substituting, %rise = ((P2001(1+X/100)(1+Y/100) - P2001)/P2001) * 100
= ((1+X/100)(1+Y/100) - 1) * 100
= X + Y + XY/100.
Now,
Option 1 gives XY=30. This is not sufficient to get the answer.
Option 2 gives 100X+100Y+XY = 800. Hence % rise = 8. This is sufficient to get the answer.

Please let me know if you have any queries on the explanation.
_________________

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Re: q 35 discussion   [#permalink] 30 Aug 2010, 07:51
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q 35 discussion

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