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A group of five friends have $87 dollars between them. Each one only has bills, that is, whole dollar amounts, no coins.

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A group of five friends have $87 dollars between them. Each one only has bills, that is, whole dollar amounts, no coins.

by BTGmoderatorDC » Tue May 03, 2022 7:49 pm

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A group of five friends have $87 dollars between them. Each one only has bills, that is, whole dollar amounts, no coins. Dolores has $29: does she have the most money of the five of them?

(1) Three of the friends are tied for the median value, and one has two dollars less.
(2) Two of the friends, Andie and Betty, have $30 between them, and each has more than $5 herself.


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Re: A group of five friends have $87 dollars between them. Each one only has bills, that is, whole dollar amounts, no co

by coursetakers » Fri May 06, 2022 3:00 am

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Statement #1: three people share the same median value. Suppose Dolores were one of those three friends. Then, each would have $29, and together the three of them would have 3*29 = $87. A fourth would have $27, and we are already way over the amount of the whole group. It’s not possible for Dolores to have the median value or to be less than the median, so the only other possibility would be for Dolores to have the value greater than the median – i.e. the maximum value. The answer to the prompt question is a clear “yes.” This statement allows us to determine a definitive answer to the prompt question. This statement, alone and by itself, is sufficient.
Statement #2: First of all, neither Andie nor Betty could have as much as Dolores has. If Andie has just $6, then Betty could be as high as $24, but Betty can’t go any higher, because Andie must be above $5 and their sum must be $30. So, Andie & Betty each must be lower than Dolores. Now, between the three of them, Andie & Betty & Dolores, they must have $30 + $29 = $59, leaving only $87 – $59 = $28 for the other two people. If the other two people have $28 together, neither one can have as much as Dolores. Thus, Dolores has to have the most. This statement allows us to determine a definitive answer to the prompt question. This statement, alone and by itself, is sufficient.
Answer = (D)
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