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If the price increased by X% from 2001 to 2002 and by Y%

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If the price increased by X% from 2001 to 2002 and by Y% [#permalink] New post 21 Mar 2011, 21:16
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57% (01:48) correct 42% (01:30) wrong based on 0 sessions
If the price increased by X% from 2001 to 2002 and by Y% from 2002 to 2003,what is the % increase from 2001 to 2003?
1. XY = 30
2. 100X + 100Y + XY = 800
[Reveal] Spoiler: OA
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Re: percent problem [#permalink] New post 21 Mar 2011, 22:13
This is a trap called "lone wolf". Wolves are loner. The question will imply that you will need two equations to solve since there are two variables. However we don't need two equations. Back to the question. If you consider the general formula for percentage change is
X+y+xy/100
S2 reduces to this form . Hence sufficient
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Re: percent problem [#permalink] New post 21 Mar 2011, 22:36
Thanks again.
Illustrated the general formula with values...can understand now.
Will have to memorize the formula...
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Re: percent problem [#permalink] New post 21 Mar 2011, 22:36
Assume price in 2001 = 100
--> price in 2002 = 100(1+x/100) =100 + x
--> price in 2003 = (100+x)(1+y/100) = 100 + x + y + xy/100

from 2) x + y + xy/100 =8 --> sufficient.
1) is not sufficient.

it would of course be faster if one remembered the formula.
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Re: percent problem [#permalink] New post 21 Mar 2011, 23:35
asmit123 wrote:
If the price increased by X% from 2001 to 2002 and by Y% from 2002 to 2003,what is the % increase from 2001 to 2003?
1. XY = 30
2. 100X + 100Y + XY = 800

Price 2001 =P
=>Price in 2002, P + x% of P = P + Px/100 = P(1 + x/100)
=> Price in 2003, P(1 + x/100)(1 + y/100)

Percentage Increase =>(P ((1 + x/100)(1 + y/100) -1)/P) *100
=>(((1+X/100)(1+Y/100))-1 ) *100
=>(100+X)(100+Y)-100
=>100X+100Y+XY+10000-100
=>800+10000-100

Hence B
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Re: percent problem [#permalink] New post 22 Mar 2011, 01:54
%age increase = {P(1+x/100)(1+y/100) - P}/P

where P is the original price.

(10000 + 100y + 100x + xy)/100000 - 1

Clearly, the answer is B.
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Re: percent problem [#permalink] New post 22 Mar 2011, 19:04
rephrasing question we have x+y+(xy/100) and thats what we need to find.

1. Not sufficient . there are different possible x and y that satisfy the given condition.

2. Sufficient . as we have the expression in similar form.

Answer is B.
Re: percent problem   [#permalink] 22 Mar 2011, 19:04
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