Karen was the winner of a hot dog eating competition. There was a tota

There are 13 people and the median is 7.

So we have a group of the first 6 people, Median, and a group of the next 6 people.

Average is 13 and total is 13 so the sum is 13 * 13 = 169

The first 6 people may eat any number of hotdogs but not more than 7. So, let us say all of them have eaten 7 each.

=> 7 * 7 = 49.

Remaining hot dogs are: 169 - 49 = 120

These 120 hot dogs will be eaten by the remaining group of 6 people so precisely each of them can eat 20 as 20 * 6 = 120.

But there is only 1 winner who ate the most number of hot dogs and that should be the least she should eat.

If Karen eats say 22, we need 98 more to be distributed among 5 people which can be done as = 19 + 19 +19 + 20 + 21.

But if Karen eats 21, we can still distribute 99 among 5 people as 20 + 20 + 20 + 20 + 19.

Answer B

Thank you for clearing this up. While I easily arrived at the part that the top 6 ate 120 hot dogs, I was wondering if we have used some straight-up calculation/algebra going forward. I am still struggling with understanding where to stop using maths and start employing common sense to solve some questions.

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