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A prize of $600 is to be distributed among 20 winners, each of whom mu

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

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

Kudos for a correct solution.
[Reveal] Spoiler: OA

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

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New post 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.

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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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New post 09 Jul 2015, 05:11
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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.


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
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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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New post 09 Jul 2015, 05:35
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 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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New post 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.

Answer: 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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New post 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.

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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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New post 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

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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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New post 13 Jul 2015, 02:56
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.


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).
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New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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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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New post 13 Oct 2017, 09:22
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


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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Re: A prize of $600 is to be distributed among 20 winners, each of whom mu   [#permalink] 13 Oct 2017, 09:22
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