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# A jar of 264 marbles is divided equally among a group of marble-player

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

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19 Jun 2016, 11:15
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Difficulty:

55% (hard)

Question Stats:

67% (02:27) correct 33% (02:45) wrong based on 169 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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19 Jun 2016, 12:34
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.
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Re: A jar of 264 marbles is divided equally among a group of marble-player  [#permalink]

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21 Jun 2016, 05:35
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.
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Re: A jar of 264 marbles is divided equally among a group of marble-player  [#permalink]

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21 Jun 2016, 07:48
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

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

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21 Jun 2016, 08:28
1
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.

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

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04 Jul 2016, 01:57
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.
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Re: A jar of 264 marbles is divided equally among a group of marble-player  [#permalink]

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11 Jun 2017, 16:40
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
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Re: A jar of 264 marbles is divided equally among a group of marble-player  [#permalink]

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20 Jun 2017, 12:46
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,
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Posts: 54376
Re: A jar of 264 marbles is divided equally among a group of marble-player  [#permalink]

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20 Jun 2017, 13:29
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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23 Sep 2017, 03:02
1
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.

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

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14 Apr 2019, 07:36
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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