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# A local club has between 24 and 57 members. The members of the club ca

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Manager
Joined: 02 Jun 2015
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Location: Ghana
A local club has between 24 and 57 members. The members of the club ca  [#permalink]

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21 Oct 2016, 08:54
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Difficulty:

45% (medium)

Question Stats:

69% (02:24) correct 31% (02:53) wrong based on 164 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 the final group, which will have 3 members, will have 5 members. If the members are separated into as many groups of 6 as possible, how many members will be in the final group? (Source: Bell Curves)

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

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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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21 Oct 2016, 09:13
Case 1: Final group = 3; Rest of the group = 4A; Number of members = 4A + 3
Case 2: Final group = 3; Rest of the group = 5B; Number of members = 5B + 3

4A + 3 = 5B + 3
4A = 5B --> Possible values = 20, 40, 60, ........ --> But only 40 satisfies the given conditions

Number of members = 40 + 3 = 43
When divided into groups of 6, final group will have 1 member (6*7 + 1).

Manager
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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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21 Oct 2016, 09:23
1
On Dividing in groups of 4 final group is left with 3 members = 4x + 3

On Dividing in groups of 5 final group is left with 3 members = 5y + 3

So, the first number which satisfies the above equation will be 23. But we are given that number of ppl are between 24 and 57.

So the general formula to satisfy the above 2 equations would be 20x + 23 which gives the next possible number as 43.

On dividing by 6 in a group we are left with 1 member in the last group.

So option E.
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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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21 Oct 2016, 10:00
duahsolo 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 the final group, which will have 3 members, will have 5 members. If the members are separated into as many groups of 6 as possible, how many members will be in the final group? (Source: Bell Curves)

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

No of members = 24 to 57

No of members = x/4 + 3 = x/5 + 3

Or, x/4 = x/5

From here try to find the values of x

x can be { 20, 40 }

Since x > 20 , value of x must be 40

So, total no of members is 43

When members are grouped in pairs of 6 remainder will be 1

Hence answer will be (E) 1

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Joined: 05 Nov 2016
Posts: 3
Re: A local club has between 24 and 57 members. The members of the club ca  [#permalink]

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22 Nov 2016, 08:35
Is this a real GMAT question?
Intern
Joined: 22 Feb 2017
Posts: 19
Location: India
GPA: 3.6
WE: Engineering (Manufacturing)
Re: A local club has between 24 and 57 members. The members of the club ca  [#permalink]

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28 Apr 2017, 06:30
duahsolo 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 the final group, which will have 3 members, will have 5 members. If the members are separated into as many groups of 6 as possible, how many members will be in the final group? (Source: Bell Curves)

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

the question is unclear..what the hell does the above highlighted line means? rather it should be "which will have 3 member left, when it have 4 members.." I don't think such an ambiguous question is likely to appear in GMAT..rest is ok
Intern
Joined: 23 Aug 2016
Posts: 48
Re: A local club has between 24 and 57 members. The members of the club ca  [#permalink]

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01 May 2017, 13:25
I'm not following how the users above me concluded that 4x=5x must mean that x=40..

I solved this by testing numbers starting with 55. This does not result in a remainder of 3 when divided by 5, so I incrementally moved down by factors of 4 until I reached 43. Divide by 6, we get remainder = 1.
Manager
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Posts: 51
Re: A local club has between 24 and 57 members. The members of the club ca  [#permalink]

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01 May 2017, 14:19
all but the final group, which will have 3 members, will have 4 members.
all group=4 members (divisor)
final group=3 members (remainder)
N(total member)=4a+3

all groups but the final group, which will have 3 members, will have 5 members
all group=5 members (divisor)
final group=3 members (remainder)
N(total member)=5b+3

N=N
4a+3=5b+3
4a=5b
so, 4a=5b=20 [lcm of 4,5]
N=20+3=23

so, first (total number of member) satisfying 2 conditions= 23
but [A local club has between 24 and 57 members]. so, we need to find a general number that will satisfy all condition.

Finding next pool
lcm of 4,5=20
The general number=20c+23 [will satisfy all condition] [where c>0]

Question asked: If the members are separated into many groups of 6 (dividend) then how many members will be in the final group (remainder)?

(20c+23)/6
[(18c+18)+(2c+5)]/6

(18c+18)/6 = remainder 0
(2c+5)]/6= remainder 1 [c=1]

(rem 0 + rem 1)/6
= remainder 1

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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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01 May 2017, 17:36
duahsolo 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 the final group, which will have 3 members, will have 5 members. If the members are separated into as many groups of 6 as possible, how many members will be in the final group? (Source: Bell Curves)

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

(n-3)/4-1=(n-3)/5
n=23
23+4*5=43
43/6 gives a remainder of 1
E
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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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10 May 2017, 11:39
1
duahsolo 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 the final group, which will have 3 members, will have 5 members. If the members are separated into as many groups of 6 as possible, how many members will be in the final group? (Source: Bell Curves)

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

Let’s let x = the number of initial groups. The number of members in these x groups will be 4x. The final group has 3 members. Thus, the total number of members is 4x + 3.

Similarly, the number of initial 5-member groups can be represented as y, and the final group has 3 members. Thus, the total number of members is equal to 5y + 3.

From the information above, we deduce that three less than the number of members must be a multiple of both 4 and 5; therefore, the number of members must be 3 more than a multiple of 20. The total membership can’t be 23 members because 23 is below the lower bound provided for the members. Similarly, the number of members can’t be 63, which is higher than the upper bound provided for the number of members. The only possible number left is 43, and it is consistent with the provided information about the number of members.

Now, since 43 divided by 6 produces a remainder of 1, when the 43 members are separated into groups of 6, there will be one person left for the final group.

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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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31 May 2018, 07:37
duahsolo 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 the final group, which will have 3 members, will have 5 members. If the members are separated into as many groups of 6 as possible, how many members will be in the final group? (Source: Bell Curves)

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

There are 2 givens:
1) We can separate the members into number of groups, all groups are 4 members, only 1 group is 3.
2) We can separate the members into number of groups, all groups are 5 members, only 1 group is 3.

Now subtract 3 (last group members) from the possible members,
Therefore the remaining members are from 21 to 54.

The number has to be divisible by both 5 & 4 (Note the above givens),
The only number in the range (21 to 54) that satisfies this condition is 40.
Therefore the total number of members are 43.

Now, we need to separate 43 members into groups, where the number of groups that contains 6 members are maximized.
Then we can divide 42 members into 7 groups leaving only 1 member in the last group.

So the answer is 1 (E)
Re: A local club has between 24 and 57 members. The members of the club ca &nbs [#permalink] 31 May 2018, 07:37
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