A group of five friends have $87 dollars between them. Each one only

Question

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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ManifestDreamMBA · Answer

T = 87
D = 29

Is D max?

Statement 2
A+B = 30 and both have atleast 5, which makes the max possible with anyone as 24 (=30-6)
Remaining amount = 87-30-29 = 28
The other 2 friends have 28 together, even if 1 person has all the 28, they are still less than D
Seems like D is max
Sufficient

This eliminates A,C,E

Statment 1
let median be m
Distribution looks like m-2,m,m,m, _
If we take m = 29, then the sum will be more than 87, so the fifth entry is 29
4m-2+29=87
4m = 60
m = 15
The distribution is 13,15,15,15,29
Dis max
Sufficient

Answer D

Dereno · Answer

Let the group of five friends be denoted as a, b, c, d, e.

Given d has $29. And a + b + c+ d+ e = $87.

Putting d in the eqn, we get  a+b+c+e = $58

Statement 1:

(1) Three of the friends are tied for the median value, and one has two dollars less.

a+b+c+e = $58

three tied to median value m. And one is m-2 and it has to be an only.

m-2+m+m+m =58

4m =60

m= 15.

There fore the values are : a= 13, b=c=e= 15, d = 29.

Hence,  SUFFICIENT  to answer D has the largest amount.

Statement 2:

(2) Two of the friends, Andie and Betty, have $30 between them, and each has more than $5 herself.

Given two friends a+b has a total of 30 with them.

a+b+c+e = $58

c + e = $28.

moreover, it’s mentioned  each has more than $5 herself.

C or e can take a minimum value of 6. And the other can take value of 22.

Among a and b, one cannot take values 29 or 30.  Because, each has to have value greater than 5.

Hence , with the constraints we can be sure that d has the maximum.

SUFFICIENT.

OPTION D

Bunuel · Answer

MAGOOSH OFFICIAL SOLUTION:

A crucial numerical fact to recognize is that 87 = 3*29. In other words, Dolores’ share is 1/3 of the entire pot.

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)

bumpbot · Answer

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A group of five friends have $87 dollars between them. Each one only

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A group of five friends have $87 dollars between them. Each one only

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