Problem

[candygal79]

An auction charges a commission 15 % on the first $50,000 of the sale price of an item, plus 10% on the amount of the sale price in excess of $50,000. What was the sale price of a painting for which the auction house charged a total commission of $ 24,000 ?

[abhasjha]

(x-50000)*.10+ 50000*15=24000
0.10x-5000+7500=24000
0.10x=21500
x= 21500/0.10= 215000

[Abhishek009]

An auction charges a commission 15 % on the first $50,000 of the sale price of an item, plus 10% on the amount of the sale price in excess of $50,000. What was the sale price of a painting for which the auction house charged a total commission of $ 24,000 ?

The auction house charges 15% of 50,000 = 7,500

Further it is given that -

10% on the amount of the sale price in excess of $50,000.

We calculated that commission for the item is 7500 for price up to 50,000

So the commission remaining will be charged at 10% rate , commission left is 24000-7500 = 16500

This 16500 is 10 of the amount exceeding 50,000 so 100% of the amount is 16500*10 = 1,65,000


Hence the total selling price of the item is - 165000 + 50000 => 215000

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Hi candygal79,

In these types of GMAT Problem Solving questions, the five answer choices would be numbers, so you would be able to TEST THE ANSWERS.

Both abhasjha and Abhishek009 have offered "math" explanations that are valid, but they really had no choice but to do math. GMAT questions (both Quant and Verbal) are usually written in such as way so as to give Test Takers multiple ways to get to the correct answer. Keep your mind open to other possibilities and be prepared to use the answer choices to your advantage.

GMAT assassins aren't born, they're made,
Rich