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

Question

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.

FacelessMan · Accepted Answer

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.

mohshu · Answer

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

hsbinfy · Answer

264 = 2*2*2*3*11 not 264 = 2*2*2*2*11

Divyadisha · Answer

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

ligeraks · Answer

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.

Heseraj · 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

goal2016 · Answer

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,

Bunuel · Answer

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.

ashikaverma13 · Answer

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.

vijay282001 · Answer

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

Raunak1x · Answer

Let x equal the number of marble players.

Then each player must have received 264/x.

If two more were to join, then each of them would be receiving 264/(x+2) marbles, which is 1 marble less than what they were receiving.

So, this equation can be stated as

(264/x) - (264/x+2) = 1

528/(x(x+2)=1

x^2+2x-528=0

x^2+24x-22x-528=0

x(x+24)-22(x+24)=0

Hence, x must be 22 and we discard the negative 24 value.

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

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

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