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Math Expert V
Joined: 02 Sep 2009
Posts: 58454
A jar of 264 marbles is divided equally among a group of marble-player  [#permalink]

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Difficulty:   55% (hard)

Question Stats: 67% (02:29) correct 33% (02:47) wrong based on 182 sessions

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A jar of 264 marbles is divided equally among a group of marble-players. If 2 people join the group, each one would receive 1 marble less. How many people are there in the group today?

A. 20.
B. 21.
C. 22.
D. 23.
E. 24.

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Re: A jar of 264 marbles is divided equally among a group of marble-player  [#permalink]

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1
Before solving it algebraically, let us prime factorize 264 = 2*2*2*2*11

Since number of marbles per person * total persons = 264, the answer should be a factor of 264. Only C is. And that's your answer.
Director  S
Joined: 21 Mar 2016
Posts: 505
Re: A jar of 264 marbles is divided equally among a group of marble-player  [#permalink]

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only 22 and 24 divide 264 perfectly,
assume initially, there are 22 people,, each will get 12 marbles
two people join, then 24 will get 11 marble each.
hence answer E == 24
Senior Manager  Joined: 02 Mar 2012
Posts: 272
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Re: A jar of 264 marbles is divided equally among a group of marble-player  [#permalink]

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FacelessMan wrote:
Before solving it algebraically, let us prime factorize 264 = 2*2*2*2*11

Since number of marbles per person * total persons = 264, the answer should be a factor of 264. Only C is. And that's your answer.

264 = 2*2*2*3*11 not 264 = 2*2*2*2*11 Current Student Joined: 18 Oct 2014
Posts: 803
Location: United States
GMAT 1: 660 Q49 V31 GPA: 3.98
Re: A jar of 264 marbles is divided equally among a group of marble-player  [#permalink]

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Bunuel wrote:
A jar of 264 marbles is divided equally among a group of marble-players. If 2 people join the group, each one would receive 1 marble less. How many people are there in the group today?

A. 20.
B. 21.
C. 22.
D. 23.
E. 24.

Back solving the question:-

Choice C says 22 people.

So marbles divided/person among 22 people = 264/22= 12 marbles

If people were 24 then marbles divided/person among 24 people= 264/24= 11 marbles

i.e. 1 marble less then when there were 2 people less. This is exactly we were looking for.

C is the answer
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Re: A jar of 264 marbles is divided equally among a group of marble-player  [#permalink]

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Or we can just use the 'Old School Approach':-

Solve 264/x - 1 = 264/(x+2) => x^2 + 2x - 528 = 0 satisfied only by option C.
Current Student G
Joined: 04 Jan 2016
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Re: A jar of 264 marbles is divided equally among a group of marble-player  [#permalink]

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FacelessMan wrote:
Before solving it algebraically, let us prime factorize 264 = 2*2*2*2*11

Since number of marbles per person * total persons = 264, the answer should be a factor of 264. Only C is. And that's your answer.

Though, your solution seems straight forward, but 24 is also a factor of 264 since its factors are included in the prime factorization of 264= 2*2*2*3*11
Intern  B
Joined: 14 Sep 2016
Posts: 10
Re: A jar of 264 marbles is divided equally among a group of marble-player  [#permalink]

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Bunuel wrote:
A jar of 264 marbles is divided equally among a group of marble-players. If 2 people join the group, each one would receive 1 marble less. How many people are there in the group today?

A. 20.
B. 21.
C. 22.
D. 23.
E. 24.

Hi Bunuel,
Good morning.

I am not able to solve this problem using following approach.

Lets say there are x players.
264 is divided equally among all players so, 264 = x * a
now 2 members are added so, x+2 and each one gets 1 less means, a -1
so, 264 = (x+2)(a-1)

How to proceed further? I am missing something here.

Thanks,
Math Expert V
Joined: 02 Sep 2009
Posts: 58454
Re: A jar of 264 marbles is divided equally among a group of marble-player  [#permalink]

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goal2016 wrote:
Bunuel wrote:
A jar of 264 marbles is divided equally among a group of marble-players. If 2 people join the group, each one would receive 1 marble less. How many people are there in the group today?

A. 20.
B. 21.
C. 22.
D. 23.
E. 24.

Hi Bunuel,
Good morning.

I am not able to solve this problem using following approach.

Lets say there are x players.
264 is divided equally among all players so, 264 = x * a
now 2 members are added so, x+2 and each one gets 1 less means, a -1
so, 264 = (x+2)(a-1)

How to proceed further? I am missing something here.

Thanks,

By solving system of equations: 264 = xa and 264 = (x+2)(a-1). Express x in terms of a (or vise-versa) substitute into the another equation and solve quadratics you get. But much easier approaches are presented above.
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Re: A jar of 264 marbles is divided equally among a group of marble-player  [#permalink]

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mohshu wrote:
only 22 and 24 divide 264 perfectly,
assume initially, there are 22 people,, each will get 12 marbles
two people join, then 24 will get 11 marble each.
hence answer E == 24

Hey,

I made the same mistake of assuming that E is the answe. But more than the calculation, the tricky part of the question is figuring out what is meant by 'how many people are in the group today' which means how many people are there BEFORE adding those two people.

Therefore, answer to that question would be 22. Hence (C) is the correct answer here.
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Intern  B
Joined: 23 Mar 2013
Posts: 4
Re: A jar of 264 marbles is divided equally among a group of marble-player  [#permalink]

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Another quick approach could be, 264 must be divisible by x (num of people) and x+2 (when 2 are added),
option c & e are factor of 264 but 24 + 2 = 26 is not a factor of 264, hence C satisfies Re: A jar of 264 marbles is divided equally among a group of marble-player   [#permalink] 14 Apr 2019, 07:36
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