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

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Math Expert
Joined: 02 Sep 2009
Posts: 60515
A local club has between 24 and 57 members. The members of the club ca  [#permalink]

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14 Dec 2016, 06:00
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Difficulty:

55% (hard)

Question Stats:

65% (02:43) correct 35% (02:31) wrong based on 47 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 4 members, will have 5 members. If the members are separated into as many groups of 11 as possible, how many members will be in the final group?

A. 7
B. 6
C. 3
D. 2
E. 1

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Joined: 18 Oct 2016
Posts: 128
Location: India
WE: Engineering (Energy and Utilities)
Re: A local club has between 24 and 57 members. The members of the club ca  [#permalink]

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14 Dec 2016, 11:45
2
Option B

X: Total number of members

Given: 24<X<57

X = 4m + 3 - I
X = 5n + 4 - II

LCM (4,5) = 20
Possible X values adhering to I & II: 19, 39, 59

24<X<57 : X = 39

Remainder ($$\frac{X}{11}$$) = 6
Re: A local club has between 24 and 57 members. The members of the club ca   [#permalink] 14 Dec 2016, 11:45
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