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An auction house charges a commission of 15% on the first

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An auction house charges a commission of 15% on the first [#permalink] New post 28 May 2012, 18:37
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Question Stats:

81% (02:20) correct 19% (01:17) wrong based on 113 sessions
An auction house charges a commission of 15% on the first $50,000 of the sale price of an item, plus 10% on the amount of of the sale price in excess of $50,000. What was the price of a painting for which the house charged a total commission of $24,000?

A. $115,000
B. $160,000
C. $215,000
D. $240,000
E. $365,000
[Reveal] Spoiler: OA

Last edited by Bunuel on 28 May 2012, 23:22, edited 2 times in total.
Edited the question and added the OA
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Re: An auction house charges a commission of 15% on the first [#permalink] New post 28 May 2012, 23:28
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Smita04 wrote:
An auction house charges a commission of 15% on the first $50,000 of the sale price of an item, plus 10% on the amount of of the sale price in excess of $50,000. What was the price of a painting for which the house charged a total commission of $24,000?

A. $115,000
B. $160,000
C. $215,000
D. $240,000
E. $365,000


Say the price of the house was $x, then 0.15*50,000+0.1*(x-50,000)=24,000 --> x=$215,000 (15% of $50,000 plus 10% of the amount in excess of $50,000, which is x-50,000, should equal to total commission of $24,000).

Answer: C.
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Re: An auction house charges a commission of 15% on the first [#permalink] New post 06 Sep 2012, 17:37
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Re: An auction house charges a commission of 15% on the first [#permalink] New post 06 Sep 2012, 18:54
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carcass wrote:
Bunuel I would ask one thing if I can: in this kind of problem algebra (set up an equation) is faster than for instance backsolving in general, or always depends on you ??

Thanks


It Always depends on you!

For this question i did in this way.

50000 - 10 % = 7500
Then commission for remaining amount will be 24000-7500=16500

Then amount which gives this 16500 as 10% should be 165000.


Therefore summing up 165000+50000 = 215000

This was the way i felt easy for me. :-D
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Re: An auction house charges a commission of 15% on the first [#permalink] New post 05 Oct 2013, 09:34
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Re: An auction house charges a commission of 15% on the first [#permalink] New post 05 Oct 2013, 09:42
Quote:
It Always depends on you!
For this question i did in this way.
50000 - 10 % = 7500
Then commission for remaining amount will be 24000-7500=16500
Then amount which gives this 16500 as 10% should be 165000.

Therefore summing up 165000+50000 = 215000

This was the way i felt easy for me. :-D


This is the way i did it. With several parts to the equation, I kind of tackled it one part at time instead of developing an equation. That's the way my mind works. I could have derived the equation after the fact but that would have been pointless since once you get the answer you are done.
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Re: An auction house charges a commission of 15% on the first   [#permalink] 05 Oct 2013, 09:42
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