Aaring23 wrote:Hey guys, I am stuck on this problem. If someone could help me out I would appreciate it very much.
An auction house charges a commission of 15 percent on the first $50,000 of the sale price of an item, plus 10 percent on the amount of of the sale price in excess on $50,000. What was the sale price of a painting for which the auction house charged a total commission of $24,000?
$115,000
$160,000
$215,000 *correct*
$240,000
$365,000
Great question for backsolving!
Using Kaplan's backsolving method, we first ask if any answers just don't make sense. On this question, it's unlikely you can quickly eliminate any of them. So, we start with either (b) or (d). Each looks similarly easy to use, so let's just pick (b).
(b) 160,000
We know that the auction house gets 15% of the first 50k, so that's 7500.
We know that it takes 10% of the remainder. 10% of 110,000 is 11000.
So, on a sale of 160,000, the take would be 18500. We want the take to be 24000, so eliminate (b). To increase the take, we need to increase the sale price, so also eliminate (a).
On to (d)!
(d) 240,000
Base take of 7500 from the first $50000 is the same.
10% of 190,000 is $19000.
$7500 + $19000 = $26000... too much! Eliminate (d) and (e).
We've eliminated a, b, d and e: choose (c).
* * *
We can backsolve if we have word problems or equations and answer choices that are numbers (i.e. no variables).
On a question like this, if the algebra jumps out at you, then an algebraic approach will almost always be faster than backsolving. However, if you don't see the equations in the first 10 seconds, you're better off using a method that you know will work rather than staring at the screen and praying for inspiration to strike.
