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08 Mar 2004, 12:58
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1. Time yourself
2. Solve this problem on a sheet of paper [ under 2 mins, if possible]
3. type in our solution and the time, if possible.
The owner of an art shop conducts his business in the following
manner: Every once in a while he raises his prices by X%, then a while
later he reduces all the new prices by X%. After one such up-down cycle,
the price of a painting decreased by $441. After a second up-down cycle
the painting was sold for $1944.81. What was the original price of the
painting?
a) 2756.25
b) 2256.25
c) 2500
d) 2000
2. Solve this problem on a sheet of paper [ under 2 mins, if possible]
3. type in our solution and the time, if possible.
The owner of an art shop conducts his business in the following
manner: Every once in a while he raises his prices by X%, then a while
later he reduces all the new prices by X%. After one such up-down cycle,
the price of a painting decreased by $441. After a second up-down cycle
the painting was sold for $1944.81. What was the original price of the
painting?
a) 2756.25
b) 2256.25
c) 2500
d) 2000
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08 Mar 2004, 14:12
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I just saw 23 views on this one. I am not sure if many gave up!!!
I took more than 2 minutes but gaveup. So POE made me come to answer A.
I just took 2500 as original price.
p(1-x)(1+x) = p(1-x^2)
so px^2 = 441
x^2 = 441/2500 x = 0.42
2500-441 = 2059
2059(1-0.42^2) = 1500 approx so even 2500 does not satisfy the final price. so it must be greater than 2500 and hence answer A.
I took more than 2 minutes but gaveup. So POE made me come to answer A.
I just took 2500 as original price.
p(1-x)(1+x) = p(1-x^2)
so px^2 = 441
x^2 = 441/2500 x = 0.42
2500-441 = 2059
2059(1-0.42^2) = 1500 approx so even 2500 does not satisfy the final price. so it must be greater than 2500 and hence answer A.
08 Mar 2004, 16:43
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anandnk
anandnk, you are right.
good work.
well, guyz, if you get to 50-51, i will absolutely guarantee you , you will see problems like these.not tough, just requires thinking.
The "441" solves 99% of the problem in 30 seconds....but just to give you a explanation..here goes
1st equation
Let SP be original selling price
SP*(1+ X/100) (1-X/100) = SP-441
2nd Equation
(SP-441) * (1+X/100)(1-X/100) = 1944.81 .....eqn 2
Now, from 1... (1+ X/100) (1-X/100) = SP-441 /SP
Therefore
(SP -441) * (SP-441) /SP[b]= 1944.81 .....equation 3
[b]Some Common Sense
Look at the answer choices...it cant be 2000 and 2256..because the first "round" itself reduces the price by 441 which will be less than 1944.81...so these two are incorrect.
Also 2500 gets reduced to 2059 in the first "round ".....its too close to 1944.81 in the first round itself...but just to be sure..
We'll try the largest value 2756.25 ..Lets approximate SP to 2800
and 441 to 500 ...cool? ok
(2800-500)*(2800-500) /2800 = 2300 *23/28 =52900/28 => 1889
Thats as close as you can get in 45 seconds..
Answer A
comments?
thanks
praetorian
Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Quantitative Questions Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
