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A burger eating contest had 25 contestants and 450 burgers were consum 03 Jun 2022, 03:15
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88% (01:56) correct 12% (01:53) wrong based on 59 sessions

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A burger eating contest had 25 contestants and 450 burgers were consumed. The bottom 3/5 of the contestants ate at least 15 burgers each but not more than 20. And the next 9 contestants ate at least 20 burgers each. What is the maximum number of burgers that the winner has consumed to win the contest.

A. 44
B. 45
C. 46
D. 47
E. 48
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B
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A burger eating contest had 25 contestants and 450 burgers were consum 03 Jun 2022, 03:20
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What is meant by bottom 3535 contestant

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A burger eating contest had 25 contestants and 450 burgers were consum 03 Jun 2022, 04:08
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dassunil
What is meant by bottom 3535 contestant

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Typo. It's "bottom 3/5 of the contestants ". Fixed. Thank you.
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A burger eating contest had 25 contestants and 450 burgers were consum 03 Jun 2022, 07:44
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Bunuel
A burger eating contest had 25 contestants and 450 burgers were consumed. The bottom 3/5 of the contestants ate at least 15 burgers each but not more than 20. And the next 9 contestants ate at least 20 burgers each. What is the maximum number of burgers that the winner has consumed to win the contest.

A. 44
B. 45
C. 46
D. 47
E. 48

In order to maximize the burgers for the top contestant, we have to minimize the burgers for others

For 11 to 25 contestants, we'll give them 15 burgers each as they have to eat at least that much, totaling 225
For 2 to 10 contestants, we'll give them 20 burgers each as they have to eat at least that much, totaling 180
Total burgers hence equal 405
Hence contestant 1 gets 450-405 = 45 burgers if we maximize the burgers for this contestant.

Option B
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A burger eating contest had 25 contestants and 450 burgers were consum 03 Jun 2022, 09:01
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The contest had a total of 25 contestants; a total of 450 burgers were consumed.

Bottom 3/5 of the contestants = \(\frac{3}{5}\) * 25 = 15 contestants
Each of the above 15 contestants at a minimum of 15 burgers.
Therefore, minimum total number of burgers eaten by these contestants = 15 * 15 = 225

The next 9 contestants ate a minimum of 20 burgers.
Therefore, minimum total number of burgers eaten by these contestants = 9 * 20 = 180

Note that we have considered the minimum number of burgers per person for each of the 24 contestants, since we wish to maximise the number of burgers eaten by the winner.

Therefore, maximum total number of burgers eaten by winner = 450 – (225 + 180) = 450 – 405 = 45.

The correct answer option is B.
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