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The majority owner of a business received 25% of the profit,

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The majority owner of a business received 25% of the profit,  [#permalink]

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New post Updated on: 26 Feb 2013, 01:49
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The majority owner of a business received 25% of the profit, with each of 4 partners receiving 25% of the remaining profit. If the majority owner and two of the owners combined to receive $62,500, how much profit did the business make?

A. $100,000
B. $125,000
C. $150,000
D. $200,000
E. $250,000

Originally posted by thinktank on 25 Feb 2013, 10:11.
Last edited by Bunuel on 26 Feb 2013, 01:49, edited 1 time in total.
Edited the question.
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Re: The majority owner of a business received 25% of the profit,  [#permalink]

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New post 25 Feb 2013, 14:21
thinktank wrote:
The majority owner of a business received 25% of the profit, with each of 4 partners receiving 25% of the remaining profit. If the majority owner and two of the owners combined to receive $62,500, how much profit did the business make?
(A) $100,000
(B) $125,000
(C) $150,000
(D) $200,000
(E) $250,000

Call profits P. The majority owner took 0.25*P = P/4 for himself, leaving 0.75*P = 3P/4 for the partners. Each of the four partners took a quarter of this ----- (0.25)*(0.75)*P = 3P/16. (It's a toss up whether it's easier to do this math with fractions or with decimals ---- I'll use decimals.)

Majority owner + two partners = 0.25*P + 2*(0.25)*(0.75)*P = 0.25*P + (0.5)*(0.75)*P = 0.25*P + (0.375)*P = (0.625)*P

This equals $62,500.

(0.625)*P = 62,500 ----- divide both sides by 625

(0.001)*P = 100 ------ multiply by 1000

P = 100,000

Answer = A

I like that it looked like the math was going to be a nightmare, but then because of some fortuitous arrangements, the arithmetic wound up being very easy.

Mike :-)
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Re: The majority owner of a business received 25% of the profit,  [#permalink]

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New post 03 Dec 2015, 23:22
Hi All,

Based on the answer choices to this question, you can solve this prompt with a bit of logic and very little math.

We're told that the profits are split among the majority owner (25%) and 4 partners (1/4 of the remaining 75% each = 18 3/4% each). Next, we're told that the majority owner and 2 of the partners received a total of $62,500. We're asked for the TOTAL profit of the business.

Since the majority owner + 2 partners =
25% + 2(18 3/4%) =
25% + 37 1/2% =
62 1/2%

We know that $62,500 is MORE THAN HALF of the profits (if you're really paying attention, you'll notice that 62 1/2% = $62,500, which makes the logic even easier to deal with). There's ONLY 1 answer that would make $62,500 MORE than 1/2 of the total.

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Re: The majority owner of a business received 25% of the profit,   [#permalink] 03 Dec 2015, 23:22

The majority owner of a business received 25% of the profit,

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