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Math Expert V
Joined: 02 Sep 2009
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A local club has between 24 and 57 members. The members of the club ca  [#permalink]

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Difficulty:   55% (hard)

Question Stats: 66% (02:14) correct 34% (02:24) wrong based on 118 sessions

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A local club has between 24 and 57 members. The members of the club can be separated into groups of which all but the final group, which will have 3 members, will have 4 members. The members can also be separated into groups so that all groups but final group, which will have 3 members, will have 5 members. If the members are separated into as many pairs as possible, how many members will be in the final group?

A. 1
B. 2
C. 3
D. 5
E. 6

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Math Expert V
Joined: 02 Aug 2009
Posts: 7756
Re: A local club has between 24 and 57 members. The members of the club ca  [#permalink]

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Bunuel wrote:
A local club has between 24 and 57 members. The members of the club can be separated into groups of which all but the final group, which will have 3 members, will have 4 members. The members can also be separated into groups so that all groups but final group, which will have 3 members, will have 5 members. If the members are separated into as many pairs as possible, how many members will be in the final group?

A. 1
B. 2
C. 3
D. 5
E. 6

Responding to a PM..

since we are looking for number of people left when pairs are made..
so we have 2 in each group except the last which can have 1 or 2..
now 1 or 2 will depend on the total number - If total is ODD, only one will be in the last group an dif number is even, 2 will be left over..

How do we check TOTAL..
the line - The members of the club can be separated into groups of which all but the final group, which will have 3 members, will have 4 members. - is enough to get to an answer, nothing else is required.
Now, if we put all in groups of 4, the last one has 3. Thus we have ODD number of people and we will have 1 in the last group.

A
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Senior Manager  B
Joined: 13 Oct 2016
Posts: 364
GPA: 3.98
Re: A local club has between 24 and 57 members. The members of the club ca  [#permalink]

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1
4
$$N = 4x + 3$$
$$N = 5y +3$$

Hence: $$N = LCM (4,5)*n + 3 = 20n + 3$$

Our AP: $$3, 23, 43, 63$$

$$24 < N < 57$$ -----> $$N=43$$

Now we need to find remainder upon division by 2 (division into pairs)

43 is odd and our remainder is 1.

Another fast approach: N=20n + 3 = even + odd = odd will always produce odd number. Hence remainder upon division by 2 will be 1.
General Discussion
Senior Manager  G
Joined: 21 Aug 2016
Posts: 259
Location: India
GPA: 3.9
WE: Information Technology (Computer Software)
A local club has between 24 and 57 members. The members of the club ca  [#permalink]

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2
1
We have to find the number of members in the final group when the groups are formed by 2 members max(pair).
So final group will either have 2 members or 1 member (leaving us with choice A and choice B).

For the first condition, assume that there is x number of the members in each group except final one. Total members= x*4+3
For the second condition, assume that there is y number of the members in each group except final one. Total members= y*5+3
x*4+3=y*5+3
4x=5y

the possibe integer values that can satisfy above equation are x=5, y=4 or x=10, y=8 or x=15, y=12

We are given that the number of the members should be between 24 and 57

the only value that satisfy above condition is x=10, y=8

total number of the members 10*4+3=43=> odd number, the number of members in the last group will certainly be 1

+1 Kudos if you like the post Manager  S
Joined: 27 Aug 2014
Posts: 54
Concentration: Strategy, Technology
GMAT 1: 660 Q45 V35 GPA: 3.66
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Re: A local club has between 24 and 57 members. The members of the club ca  [#permalink]

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The members of the club can be separated into groups of which all but the final group, which will have 3 members, will have 4 members -

This means the number will be a multiple of 4+3 so the number could be 24+3, 28+3, 32+3, 36+3,40+3 etc. Right here is enough to prove that when this number is divided by 2 (pairs) we will get a remaining group of 1 but just to be sure we go to second statement. Here we can say that the number of members is a multiple of 5 and then a+3 so 25+3, 30+3, 35+3 or 40+3

43 is common, 43/2 will give a remainder of 1.

This could be a great DS question too.
VP  P
Joined: 07 Dec 2014
Posts: 1196
A local club has between 24 and 57 members. The members of the club ca  [#permalink]

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Bunuel wrote:
A local club has between 24 and 57 members. The members of the club can be separated into groups of which all but the final group, which will have 3 members, will have 4 members. The members can also be separated into groups so that all groups but final group, which will have 3 members, will have 5 members. If the members are separated into as many pairs as possible, how many members will be in the final group?

A. 1
B. 2
C. 3
D. 5
E. 6

lowest possible membership=4*5+3=23
23/5=Q4+R3
23/4=Q5+R3
23/11=Q2+R1
next lowest membership=23+4*5=43
43/21=Q2+R1
1
A
Manager  G
Joined: 14 Jun 2018
Posts: 223
Re: A local club has between 24 and 57 members. The members of the club ca  [#permalink]

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Since 2 leaves a remainder of 0 or 1 , ans is A
Intern  Joined: 02 Jan 2019
Posts: 2
Re: A local club has between 24 and 57 members. The members of the club ca  [#permalink]

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pandeyashwin wrote:
Since 2 leaves a remainder of 0 or 1 , ans is A

Came to say this. Easiest 2sec approach.
Intern  B
Joined: 29 Mar 2019
Posts: 7
Anand: Jain
GPA: 3.13
A local club has between 24 and 57 members. The members of the club ca  [#permalink]

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I am not sure whether this is the correct way to look at the problem but it does get the answer:

It says maximum groups possible: minimum number of people required in a group i.e 2
Therefore any odd number will leave 1 as a remainder. No need to look at the pairing mentioned in the question.

Thanks. A local club has between 24 and 57 members. The members of the club ca   [#permalink] 08 Apr 2019, 09:59
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