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

Question

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

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

shanmugamgsn · Accepted Answer

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

Bunuel · Answer

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.

Carcass · Answer

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

avohden · Answer

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.

mejia401 · Answer

Back solving to arrive at $24,000. The variable is amount greater than $50,000 because 15% of 50,000 is $7,500 and therefore what brings the calculation to $16,500.

A. $115,000  - 50,000 = 65,000 * 10% = $6,500. Not correct.  
B. $160,000  - 50,000 = 110,000 * 10% = $11,000. Not correct. 
C. $215,000  - 50,000 = 165,000 * 10% = 16,500. Correct. 
D. $240,000  Going to be too high. Not correct. 
E. $365,000  Going to be too high. Not correct.

Thanks,
A

EMPOWERgmatRichC · Answer

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:  C

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

ScottTargetTestPrep · Answer

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

Abhishek009 · Answer

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)

CrushTheQuant · Answer

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

oyasumipp · Answer

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?

EMPOWERgmatRichC · Answer

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: [email protected]

proddnav · Answer

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!

AnishPassi · Answer

I’ll share how I solved this question.

As a practice, one thing I do while reading the question is scan the answer choices. I do this even before I start any mental calculations.

1:

When I scanned the answer choices, I noticed (D) $240,000. It immediately stood out. Why? Because I realized that 10% of 240,000 is 24,000 (the total commission amount).

If the commission were 10% on the entire $240,000, that alone gives $24,000. 
 But in reality, the first $50,000 is charged at the higher 15%, which means the total commission would exceed $24,000 if I consider the sale price of 240,000. 
 So (D). $240,000 cannot be correct.

This was a quick way to eliminate one extreme option without much calculation.

2:

Now, notice something important: since 10% of $240,000 already equals $24,000, what we actually need is a value less than $240,000 so that:

part of the price is charged at the higher 15%, and 
 the rest at 10%,

... giving exactly $24,000 as the total commission.

That means any value higher than $240,000 would only push the commission further up, so we can also rule out Option E ($365,000) straight away.

So now we’re left with only A, B, and C to consider.

3:

Out of A, B, and C, I picked $160,000 (Option B) next. Why? Because it neatly splits the three remaining options. With one check, I can figure out if the correct answer is exactly 160,000, below it or above it.

Now, this is where my fast mental maths helped me. I know 15x15 is 225. So, 15 x 16 would be 225 + 15 =240.

So, if the entire $160,000 were charged at 15%, the commission would be exactly $24,000. 
 But in reality, part of the price is charged at the lower 10%. 
 That means if the price were 160,000 the total commission would be less than $24,000. So $160,000 is too low.

So the actual price must be greater than $160,000.

4:

At this stage:

$160,000 was too low. 
 $240,000 and $365,000 were too high.

I can reject answers <= 160,000 and answers >= 240,000.

That leaves $215,000 as the only possibility.

5:

(Not required. But, if you can afford the time a good idea to double-check.)

First $50,000 @ 15%  → 10% of 50,000 + half of 10% of 50,000   → 5,000 + 5,000/2 = 5,000 + 2,500 =7,500.  
 Remaining: 215,000 - 50,000 = $165,000 @ 10% = $16,500 
 Total commission = $7,500 + $16,500 = $24,000

Fits!

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

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