May 24 10:00 PM PDT  11:00 PM PDT Join a FREE 1day workshop and learn how to ace the GMAT while keeping your fulltime job. Limited for the first 99 registrants. May 25 07:00 AM PDT  09:00 AM PDT Attend this webinar and master GMAT SC in 10 days by learning how meaning and logic can help you tackle 700+ level SC questions with ease. May 27 01:00 AM PDT  11:59 PM PDT All GMAT Club Tests are free and open on May 27th for Memorial Day! May 27 10:00 PM PDT  11:00 PM PDT Special savings are here for Magoosh GMAT Prep! Even better  save 20% on the plan of your choice, now through midnight on Tuesday, 5/27
Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 55228

A group of five friends have $87 dollars between them. Each one only
[#permalink]
Show Tags
23 Feb 2015, 03:16
Question Stats:
65% (02:18) correct 35% (02:37) wrong based on 107 sessions
HideShow timer Statistics
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.
Official Answer and Stats are available only to registered users. Register/ Login.
_________________



Intern
Joined: 18 Apr 2014
Posts: 15
Concentration: Strategy, Finance
GMAT Date: 03302015
WE: Web Development (Computer Software)

Re: A group of five friends have $87 dollars between them. Each one only
[#permalink]
Show Tags
23 Feb 2015, 05:07
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)



Intern
Joined: 30 Mar 2013
Posts: 10
Location: India

Re: A group of five friends have $87 dollars between them. Each one only
[#permalink]
Show Tags
23 Feb 2015, 04:46
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 Correct Answer: D



Intern
Joined: 29 Dec 2014
Posts: 24
Concentration: Operations, Strategy
GMAT 1: 690 Q48 V35 GMAT 2: 710 Q48 V39

Re: A group of five friends have $87 dollars between them. Each one only
[#permalink]
Show Tags
23 Feb 2015, 07:12
Ans: D Stmnt 1: by definition of median and the fact that of the 5 friends, 3 are at median value implies, of the remaining two one has to be below the median and the other above..Dolores cannot be the one below the median as per stmnt 1 which states that the 5th pal has an amount lesser than the median. hence logical conclusion..dolores is the one above the median. ( mathematically 13,15,15,15,29) sufficient Stmnt 2: since andy and betty have a combined sum of 30$ 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: 7684

Re: A group of five friends have $87 dollars between them. Each one only
[#permalink]
Show Tags
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 x2.... 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 5729=28... so none can have more than dolores... sufficient
_________________



Math Expert
Joined: 02 Sep 2009
Posts: 55228

Re: A group of five friends have $87 dollars between them. Each one only
[#permalink]
Show Tags
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. Answer = (D)
_________________



Intern
Joined: 29 Dec 2018
Posts: 31

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






