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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 prize of $600 is to be distributed among 20 winners, each of whom mu [#permalink]

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09 Jul 2015, 04:43

Bunuel wrote:

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. $200 B. $220 C. $280 D. $300 E. $360

Kudos for a correct solution.

Total value of the prize =$600 Number of people = 20

2/5 of 600 (=$240) should be distributed among 3/5 of 20 (=12 people ) with each getting $20 each. Remaining money = 600-240 = $360. Now in order to 'maximize' 1 prize, we need to minimise the others and we have been given that each should get $20. Thus, minimising the remaining 7 people (=20-12-1. '-1' to exclude 1 that needs to be maximised) = 7*20=140.

Thus the maximum award can be = 360-140 = $220, hence B is the correct answer.

Re: A prize of $600 is to be distributed among 20 winners, each of whom mu [#permalink]

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09 Jul 2015, 05:11

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This post received KUDOS

Bunuel wrote:

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. $200 B. $220 C. $280 D. $300 E. $360

Kudos for a correct solution.

Solution -

Given that, 2/5th of prize $240 distribute to 3/5th of winners i.e.,12

Remaining 8 winners will share $360. ---------1

Minimum award shared among 7 winners = 7*20 = $140 -------------2

1 - 2 --> Total remaining amount shared to 8th winner = $360 - $140 = $220. ANS B
_________________

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. $200 B. $220 C. $280 D. $300 E. $360

Kudos for a correct solution.

Total Prize = $600 (2/5) of Prize = (2/5)*600 = 240

No. of Winners = 20 (3/5) of No. of Winners = (3/5)*20 = 12

i.e. $240 to be given to 12 Winners and 600-240 = $360 to be given to remaining 8 Winners

Minimum award to be given to each = $20 i.e. Prize money distributed among 8 winners = 20*8 = 160 Remaining money = 360-160 = $200

i.e. Maximum Prize anyone can get = $200+$20 = $220

Answer: Option B
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Re: A prize of $600 is to be distributed among 20 winners, each of whom mu [#permalink]

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09 Jul 2015, 10:52

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Bunuel wrote:

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. $200 B. $220 C. $280 D. $300 E. $360

Kudos for a correct solution.

Without the conditions, we can give 20*19=380 to 19 winners and 600-380=220 as the greatest possible award to 1 winner. But we have conditions

2/5 of prize is 600*2/5=240 3/5 of winners is 20*3/5=12

Notice that this satisfies the condition of giving the minimum prize money of $20 to all the winners other than 1 that we discussed before (240/12=20).

Lets suppose that the same is true for the rest of the 7 winners. Here we can apply out above calculation and conclude that the greatest possible award to 1 winner can be $220.

Re: A prize of $600 is to be distributed among 20 winners, each of whom mu [#permalink]

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09 Jul 2015, 11:04

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option B- $220. 3\5*600 = 360 divided among remaining 8 people( 2\5*20). Least for 7 people= $140. Hence, greatest possible individual award is remaining $220.

Re: A prize of $600 is to be distributed among 20 winners, each of whom mu [#permalink]

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11 Jul 2015, 11:08

Bunuel wrote:

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. $200 B. $220 C. $280 D. $300 E. $360

Kudos for a correct solution.

2/5th of the prize=$240 which is distributed to 12 people, each of whom will get $20 3/5th of the prize=$360 which is distributed to 8 people. If 7 out of get $20(minimize 7 to maximize for the 8th person), 8th person will get $220 Answer B

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. $200 B. $220 C. $280 D. $300 E. $360

Kudos for a correct solution.

800score Official Solution:

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 (B). _________________

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. $200 B. $220 C. $280 D. $300 E. $360

3/5 of the winners is 3/5 x 20 = 12 people.

So, 2/5 x 600 = 240 dollars is distributed to those 12 people and 600 - 240 = 360 dollars is left for the remaining 8 people.

We do not need to find the greatest amount that could be awarded among the group of 12 because in this group, less money is distributed to a greater number of people; there is no hope of finding a greater prize money than the other group.

If we minimize the amount received by 7 of those 8 remaining people, then the most one person can receive is 360 - 7 x 20 = 360 - 140 = 220 dollars.

Answer: B
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