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

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.

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

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.

Hi All,

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:

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

Solution:

We can create the equation where p is the price of the item:

0.15 x 50,000 + 0.1 x (p - 50,000) = 24,000

7,500 + 0.1p - 5,000 = 24,000

0.1p + 2,500 = 24,000

0.1p = 21,500

p = 21,500/0.1 = 215,000

Answer: C

15% of 50000 + 10% of x = 24000

Or, 7500 + x/10 = 24000

Or, x = 165000

So, Price of a painting for which the house charged is 165000 + 50000 = 215,000 . Answer must be (C)

This question is pretty easy to answer if you draw a quick diagram like the one used in this explanation on YouTube:

https://www.youtube.com/watch?v=y2Fehjw ... PA9GX6g4I4

I think I was on the right track of solving this question but then English is not my first language and I do not really understand the term 'in excess' lol.
Can anyone help elaborate?

Hi oyasumipp,

If you do not understand every word that appears in a prompt, then there's still ways to get to the correct answer (although you have to think critically about all of the other information that you DO understand - and you might have to do a little extra work to determine that one way of interpreting the prompt is not correct). This issue comes up a bit more often in the Verbal section (you will probably see an RC and/or CR with some challenging language on Test Day), but the basic idea can still be applied with this Quant prompt:

The question begins by telling us that there's a commission of 15% on the FIRST $50,000.... so immediately, I have to ask "what if something costs MORE than $50,000....?" There must be a 'change' in the commission at that point (otherwise, the prompt would not specifically mention $50,000 as some type of threshold).

The next part of the prompt tells us "PLUS 10% of the....." so once we pass the first $50,000, there's really only two ways to interpret the change the would occur:

Either the rate is going to change to 10% or the rate is going to change to (15% + 10% = 25%) for a more expensive item - and notice the word "plus" - so we're ADDING to that initial commission (re: 15% of $50,000 = $7,500 commission). If you assume that it's 10% of anything over the initial $50,000, then you get the correct answer. If you assume that it's 25% of anything over the initial $50,000, then you end up with an answer that is NOT among the 5 choices (so you would know that this interpretation was NOT correct).

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

Contact Rich at: Rich.C@empowergmat.com

The Base Commission is 15% on the first $50,000
The Commission is 10% after the amount exceeds $50,000
Total Commission earned is $24,000

To find total sale amount of painting:

Lets take the total sale amount of the painting as "X"

With this we can create the expression:

50,000*(15/100) +(10/100)*(X-50,000)= 24,000 (Since 10% commission is charged after the base of 50,000, hence it is (X- 50,000)

500*15 + (1/10)(X-50,000)= 24,000

500*15(10)+X-50,000=24,000*10

75000+X-50,000=240,000

X=240,000-25,000

X=215,000

Therefore the value of the painting is $215,000

Hope this helps!

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.