Percent problem

[didieravoaka]

Thanks to help.

Marc.

[MartyMurray]

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

One way to bang this one out with or without using the pad is to do the following.

You know that 24,000 is more than 15% of 50,000. So just start with 15% of 50,000, which is half of 15% of 100,000. So 15% of 50,000 is 7500.

After doing that you know that the rest, 24,000 - 7500 = 16,500 is 10% of the rest of the price. So the quantity above 50,000 is 165,000.

50,000 + 165,000 = 215,000

The correct answer is C.

[[email protected]]

Hi didieravoaka,

This question can be solved by TESTing THE ANSWERS.

We're told that the commission is 15% of the first $50,000 (so that's $7,500) and 10% of the anything above $50,000. Then we're told that the total commission on an item was $24,000. We're asked for the overall price of the item.

Let's TEST Answer B: $160,000

We already know that the first $7,500 comes from the first $50,000.
10% of the remaining $110,000 = $11,000
$7500 + $11000 = $18,500 which is TOO LOW.
Eliminate Answers B and A.

Next, Let's TEST Answer D: $240,000

We already know that the first $7,500 comes from the first $50,000.
10% of the remaining $190,000 = $19,000
$7500 + $19000 = $26,500 which is TOO HIGH.
Eliminate Answers D and E.

There's only one answer left.

Final Answer: C

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

[Matt@VeritasPrep]

It also helps to write these in words first.

(15% of $50,000) + (10% of rest) = Commission

so

.15*50,000 + .10*(total - 50,000) = 24,000

then just solve for the total, and you're set! In my experience, though, that first step is a huge, huge help.