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 Post subject: GRE Arithmetic (Select One)
PostPosted: Tue Sep 14, 2010 2:58 am 
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Joined: Sun May 30, 2010 3:15 am
Posts: 424
A prize of $600 is to be distributed among 20 winners, each of whom must be awarded at least $20. If 2/5 of the prize will be distributed to 3/5 of the winners, what is the greatest possible individual award?
A. $20
B. $25
C. $45
D. $220
E. $300

(D) We are told that 2/5 of the prize is distributed to 3/5 of the winners:
2/5 of the prize = 2/5 × $600 = $240.
3/5 of the winners = 3/5 × 20 = 12 winners.
Since $240/12 = $20, we know that each of these people received the minimum of $20.

The remaining $360 will be divided among the 8 remaining winners. For one of these winners to receive the greatest possible award, the other seven winners must receive the minimum $20. These seven winners receive a total of: 7 × $20 = $140.

The eighth winner would receive all the remaining prize money:$360 – $140 = $220.

The correct answer is choice (D).
-------------

In the above question, you calculate a minimum of $20 to be distributed among the "12" people to whom $240 would be distributed. Then you claim that that $20 is also a minimum for the remaining 8 winners. It seems that the minimum amount that each of the remaining 8 winners could receive is 360/8 = $45.

So for one of these 8 winners to receive the greatest possible award, the remaining 7 winners must receive 7 × $45 (not $20) = $315.

So the eighth winner would receive the remaining of the prize:
$360 – $315 = $45

($240 + $315 + $45 = $600)

Please explain if my logic is flawed.
Thank you.


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 Post subject: Re: math (test 4, question 5): arithmetic, logic.
PostPosted: Tue Sep 14, 2010 3:24 am 
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Joined: Sun May 30, 2010 2:23 am
Posts: 498
The weak statement in your logic reasoning is following:
Quote:
It seems that the minimum amount that each of the remaining 8 winners could receive is $360/8 = $45.


$360/8 = $45 is the AVERAGE prize that one of the 8 remaining winners gets, NOT the minimal one. The minimal prize is determined in question statement and it is $20.

It is possible that EACH one of the 8 remaining winners gets the same amount of money however in this case greatest award is just $45 but we've shown in explanation that greatest award can be as big as $220.

Each one gets the same:
$45 $45 $45 $45 $45 $45 $45 $45

7 pers. get minimal, 8th gets the rest:
$220 $20 $20 $20 $20 $20 $20 $20

Let us take a look at this situation once again. We have $360 to be distributed among 8 people, each one of whom must receive at least $20.

Can one person get all $360? No, because other 7 must get at least $20 or 7 × $20 = $140 overall. So the most money one person can get is $360 – $140 = $220. And it can not be any larger amount of money because if we give him just $1 more we'll have to take that $1 out of somebody's MINIMAL prize.


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