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Bill has d animals, 12 of which were sold at a profit of 10%

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Bill has d animals, 12 of which were sold at a profit of 10% [#permalink] New post 01 Nov 2012, 21:59
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Question Stats:

73% (02:56) correct 27% (02:10) wrong based on 64 sessions
Bill has d animals, 12 of which were sold at a profit of 10% each while the rest were sold at a loss of 20% each. Overall, Bill made neither a profit nor a loss. Which of the following is equal to d?

(A) 6
(B) 12
(C) 18
(D) 24
(E) 36
[Reveal] Spoiler: OA
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Re: Bill has d animals, 12 of which were sold at a profit of 10% [#permalink] New post 01 Nov 2012, 22:15
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total d animals, suppose each has price of x - total price = dx

now 12 were sold at profit of 10%, making equation - - 12*1.1x
now d-12 were sold at loss of 20%, making eqn --- (d-12)*0.8x

Now he made no profit or loss so,

dx = 12*1.1x + (d-12)*0.8x

solving for d, we get d=18

Ans C
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Re: Bill has d animals, 12 of which were sold at a profit of 10% [#permalink] New post 01 Nov 2012, 22:21
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Again if we go by eliminating the option method,

ans A and B are out as they are value less then or eul to 12.
Ans d = 12 sold at 10% profit while 12 sold at 20% loss , so here Loss will come which is contradicted to question stem..
Ans e = 12 sold at 10% profit while 24 sold at 20% los, so here also Loss will come which is contradicted to question stem..

only option C = 18 balances eqn ---> 12 at Profit and 6 at loss.
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Re: Bill has d animals, 12 of which were sold at a profit of 10% [#permalink] New post 02 Nov 2012, 11:33
bhavinshah5685 wrote:
Again if we go by eliminating the option method,

ans A and B are out as they are value less then or eul to 12.
Ans d = 12 sold at 10% profit while 12 sold at 20% loss , so here Loss will come which is contradicted to question stem..
Ans e = 12 sold at 10% profit while 24 sold at 20% los, so here also Loss will come which is contradicted to question stem..

only option C = 18 balances eqn ---> 12 at Profit and 6 at loss.


nice elimination technique, it's realy worth Kudos
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Re: Bill has d animals, 12 of which were sold at a profit of 10% [#permalink] New post 13 Feb 2015, 11:27
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Re: Bill has d animals, 12 of which were sold at a profit of 10% [#permalink] New post 13 Feb 2015, 12:12
Expert's post
Hi All,

Since this question asks for the TOTAL number of animals, and the answers are numbers, this is a perfect opportunity to TEST THE ANSWERS.

We're told a few Facts about a group of animals:
1) There are D total animals
2) 12 of them are sold at a 10% profit
3) The rest are sold at a 20% loss
4) The profits and losses "cancel out"

We're asked to solve for D.

Since 12 animals were sold for a profit, while the rest were sold for a loss, the total number of animals MUST be MORE than 12. Eliminate A and B.

Since we need the profits and losses to cancel out, we're likely looking for a situation in which there were FEWER animals sold for a loss than were sold for a profit (since each individual 'loss' is so much bigger than each individual 'profit').

Let's TEST Answer C....
IF there were 18 animals, 12 were sold for a profit and 6 were sold for a loss.

IF....each animal costs $100
The 12 that were sold for a 10% profit --> $110 each ---> 12($10 profit each) = $120 profit
The 6 that were sold for a 20% loss ---> $80 each --->6($20 loss each) = $120 loss

Here, the profits and losses cancel out, so C MUST be the answer.

Final Answer:
[Reveal] Spoiler:
C


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Re: Bill has d animals, 12 of which were sold at a profit of 10%   [#permalink] 13 Feb 2015, 12:12
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