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

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Math Expert
Joined: 02 Sep 2009
Posts: 59586
A group of five friends have \$87 dollars between them. Each one only  [#permalink]

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23 Feb 2015, 03:16
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Difficulty:

45% (medium)

Question Stats:

66% (02:19) correct 34% (02:39) wrong based on 116 sessions

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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.

Kudos for a correct solution.

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Re: A group of five friends have \$87 dollars between them. Each one only  [#permalink]

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23 Feb 2015, 04:46
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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.

Statement 1 says "Three of the friends are tied for the median value, and one has two dollars less."
Let us say that the three friends have 'x' and the fourth one has 'x - 2'
Dolores has 29\$ and hence cannot be the median or the one below the median because then total amount of money would go above 87\$

If Dolores is not one of the above 4, then:
3x + x - 2 + 29 = 87
=> 4x = 60
=> x = 15
=> The five friends have 13, 15, 15, 15, 29
=> Dolores has the most amount of money

From Statement 1, we can answer YES Dolores has the most amount of money.
=> Statement 1 is sufficient

Statement 2 says, Two of the friends, Andie and Betty, have \$30 between them, and each has more than \$5 herself.
=> Both Andie & Betty have less than Dolores
=> Total amount Andie, Betty, and Dolores have = 30 + 29 = 59
=> Amount of money left = 87 - 59 = 28\$
=> The other two friends also have less than 29\$
=> Dolores has the most amount of money.

From Statement 2, we can answer YES Dolores has the most amount of money.
=> Statement 2 is sufficient

We can answer the question from both statements individually
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GMAT Date: 03-30-2015
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Re: A group of five friends have \$87 dollars between them. Each one only  [#permalink]

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23 Feb 2015, 05:07
2
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.
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Joined: 29 Dec 2014
Posts: 23
Concentration: Operations, Strategy
GMAT 1: 690 Q48 V35
GMAT 2: 710 Q48 V39
Re: A group of five friends have \$87 dollars between them. Each one only  [#permalink]

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23 Feb 2015, 07:12
1
Ans: D
Stmnt 1: by definition of median and the fact that of the 5 friends, 3 are at median value implies, of the remaining two one has to be below the median and the other above..Dolores cannot be the one below the median as per stmnt 1 which states that the 5th pal has an amount lesser than the median. hence logical conclusion..dolores is the one above the median. ( mathematically 13,15,15,15,29)
sufficient
Stmnt 2: since andy and betty have a combined sum of 30\$ and dolores has 29\$..thus the other 2 pals can together have 87-(29 +30) =28\$ at max. an amount lesser than what dolores has with her.
sufficient
Math Expert
Joined: 02 Aug 2009
Posts: 8281
Re: A group of five friends have \$87 dollars between them. Each one only  [#permalink]

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23 Feb 2015, 07:35
Bunuel wrote:
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.

Kudos for a correct solution.

in these we should give highest possible values to any other value to test for max..
1) statement one gives us four values.. 3 have say x and fourth x-2.... if we take dolores is having median value.. total median value =3*29=87... but one is given 2 dollars less... not possible so median value has to be less than 29... hence dolores has max money...sufficient

2)two friends have 30 in total but each has more than 5.. so max one of them can have is 24 .. so rest three have remaining 57 but dolores has 29 so remaining two will have 57-29=28... so none can have more than dolores... sufficient
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Posts: 59586
Re: A group of five friends have \$87 dollars between them. Each one only  [#permalink]

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02 Mar 2015, 07:03
Bunuel wrote:
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.

Kudos for a correct solution.

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.

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A group of five friends have \$87 dollars between them. Each one only  [#permalink]

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24 Mar 2019, 04:37
I am not a native speaker, and I don't know what "tied for" means. I have checked the two most common used dictionaries, Oxford and Cambridge, in my country, but still couldn't find its meaning. I thought the sentence means that the sum of three amount is the median.
A group of five friends have \$87 dollars between them. Each one only   [#permalink] 24 Mar 2019, 04:37
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