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percents , what is faster approach

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percents , what is faster approach

by quantskillsgmat » Wed Feb 08, 2012 1:42 am
owner of an art shop on a regular basis keeps on increasing the prices of all products by x%,then after sometime, he will reduce the price by x%. This constitute one cycle.At the end of one cycle the price of painting reduced by $441, and at the end of second such cycle he sold it at $1944.81.what was original price of painting in dollars.
a)2756.25
b)2256.25
c)2500
d)2000
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by quantskillsgmat » Wed Feb 08, 2012 3:56 am
my approach is if anything increses by x% and further decreses by x% resulting % impact is x^2/100.using this we can say 441 is x^2/100% of initial price.so we can get initial price in terms of x.furcher it can be equated with final price. but this approach is tedious. can anyone help me out n finding shorter approach.
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by quantskillsgmat » Wed Feb 08, 2012 3:58 am
my approach is if anything increses by x% and further decreses by x% resulting % impact is x^2/100.using this we can say 441 is x^2/100% of initial price.so we can get initial price in terms of x.furcher it can be equated with final price. but this approach is tedious. can anyone help me out n finding shorter approach.
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by quantskillsgmat » Thu Feb 09, 2012 2:01 am
help plz
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by pemdas » Thu Feb 09, 2012 1:01 pm
quantskillsgmat wrote:owner of an art shop on a regular basis keeps on increasing the prices of all products by x%,then after sometime, he will reduce the price by x%. This constitute one cycle.At the end of one cycle the price of painting reduced by $441, and at the end of second such cycle he sold it at $1944.81.what was original price of painting in dollars.
a)2756.25
b)2256.25
c)2500
d)2000
-(x^2)/100 each cycle's change in % (net decrease by (x^2)/100 %)
you don't need to look through the 2-nd cycle here, limit to the 1-st cycle for Price (P)
P*x^2/10,000=441, as x can be any value ignore it, P*x^2=4,410,000 and P=4,410,000/x^2
P=(2100/x)^2 and substitute every answer choice into the received expression
a) 52.5^2=(2100/x)^2 <> 52.5=2100/x, x=40%
b) 47.5^2= ... <> x=44.21%
c) 50^2= ... <> x=42%
d) 44,72^2= ... <> x=47%
Now check on
a) 2756.25 * (1.4^2 *0.6^2)=1944.81 is correct choice

I don't know of any different short-cut method here, as well as in every other post you made on BTG. All your questions are difficult and beyond the scope of GMAT. I am solving them because of my interest to problem solving area.
Success doesn't come overnight!
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