An art auction house makes a commission of 5 percent on the first $10,

Question

An art auction house makes a commission of 5 percent on the first $10,000 of the selling price of a painting, 3 percent on the next $8,000, and a certain percent on any amount thereafter. If the auction house made a commission of $800 on a painting that sold for $22,000, what was the percent of the commission on the amount in excess of $18,000 ?

A. 0.5%
B. 1.0%
C. 1.5%
D. 2.0%
E. 2.5%

Source: Skills Insight

A. 0.5%
B. 1.0%
C. 1.5%
D. 2.0%
E. 2.5%

Source: Skills Insight

Abhishekgmat87 · Accepted Answer

Commission on the first $10,000 = 5 % of 10000 = 500
Commission on next $8,000 = 3 % of 8000 = 240

Commission made = 800

Commission made on $ 4000 (amount in excess of $18,000) = 800 - 740 = 60 
Let the required percentage be x %
x % of 4000 = 60
x = 1.5%

yazadsarkari · Answer

How to overcome these questions easily ?

Dbrunik · Answer

These questions can appear to be difficult to solve without a calculator unless you know a great percentage trick.

the 5% of the 10000 is easy, since 10000 is a round number. this is simply going to be 500.

the 8000 is a little bit more tricky because its not a "10" and you are asked for a less straightforward percent of 3%. thats okay, just remember that you can breakdown 8000. 10% of 8000 is 800, 5% of 8000 would then be 400... hmmm but we need to take out another 2% from our 5% to get to 3%. what number, multiplied by 5 would give us 400? 80!

now. you can just take 3*80 and get that 240. (in the explanation above mine, somebody else seemed to solve this without much pain, but this tactic ive presented makes it a little more digestable)

one last step. we now know we have earned 740 up to this point of 18,000. but we still have 4000 more to account for, and we now know that we need to get 60$ more in commission to bring us to our given 800.

so what is 60/4000? again this might not be that straightforward to solve for without a calculator, but break it down.

4000 at 10% is 400. 5% would be 200, 2.5% would be 100.... okay we are getting very close.... 1.25 would then be 50... but thats too low? estimate 10 more to get to 60, and round to the closest answer, C 1.5%

Dbrunik · Answer

nice but how were able to quickly solve that 3% of 8000 is 240?

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An art auction house makes a commission of 5 percent on the first $10,

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