It is currently Tue Sep 25, 2018 8:05 am

 All times are UTC - 5 hours [ DST ]

 Page 1 of 1 [ 2 posts ]
 Print view Previous topic | Next topic
Author Message
 Post subject: GRE Arithmetic (Select One)Posted: Tue Sep 14, 2010 2:58 am

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.

Top

 Post subject: Re: math (test 4, question 5): arithmetic, logic.Posted: Tue Sep 14, 2010 3:24 am

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.

Top

 Display posts from previous: All posts1 day7 days2 weeks1 month3 months6 months1 year Sort by AuthorPost timeSubject AscendingDescending
 Page 1 of 1 [ 2 posts ]

 All times are UTC - 5 hours [ DST ]

#### Who is online

Users browsing this forum: No registered users and 1 guest

 You cannot post new topics in this forumYou cannot reply to topics in this forumYou cannot edit your posts in this forumYou cannot delete your posts in this forumYou cannot post attachments in this forum

Search for:
 Jump to:  Select a forum ------------------ GMAT    GMAT: Quantitative Section (Math)    GMAT: Verbal Section    GMAT: Integrated Reasoning    GMAT: General Questions GRE    GRE: Quantitative Reasoning (Math)    GRE: Verbal Reasoning    GRE: General Questions General questions    Other questions