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All the people in a small county belong either to club A or club B but

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Retired Moderator
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All the people in a small county belong either to club A or club B but  [#permalink]

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New post 21 Mar 2019, 22:30
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

78% (02:37) correct 22% (03:10) wrong based on 27 sessions

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All the people in a small county belong either to club A or club B but not both. On a particular day, both the clubs held their respective meets and it was noted that all the members in each of the two clubs were present. Members of club A could be evenly divided into groups of 4 each, with no member left over. Members of club B could be arranged into groups of 5 each, with just 1 member left over. If total number of members in both clubs are equal, then which of the following could be the sum of members in the two clubs?

I) 112
II) 84
III) 72
IV) 32

A. I only
B. I and II only
C. II, III and IV only
D. I, II and IV only
E. I, III and IV only
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Re: All the people in a small county belong either to club A or club B but  [#permalink]

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New post 22 Mar 2019, 00:14
Given- members in both clubs are equal.
Club A - Multiple of 4.
Club B - 1 left when divided by 5.

a) 112. 56+56. Possible.
b) 84. 42+42. Not possible. As 42/5 gives remainder of 2.
c) 72. 36+36. Possible.
d) 32. 16+16. Possible.

E is the answer.
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Re: All the people in a small county belong either to club A or club B but  [#permalink]

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New post 29 Mar 2019, 09:18
amanvermagmat wrote:
All the people in a small county belong either to club A or club B but not both. On a particular day, both the clubs held their respective meets and it was noted that all the members in each of the two clubs were present. Members of club A could be evenly divided into groups of 4 each, with no member left over. Members of club B could be arranged into groups of 5 each, with just 1 member left over. If total number of members in both clubs are equal, then which of the following could be the sum of members in the two clubs?

I) 112
II) 84
III) 72
IV) 32

A. I only
B. I and II only
C. II, III and IV only
D. I, II and IV only
E. I, III and IV only


divide each given option by 2 ; and then check validity of group a & group b

I) 112-- 56 ; OK remainder 1 for group b
II) 84-- 42; not ok ; remainder 2 for group b
III) 72-- 36; ok ; remainder 1 for group b
IV) 32-- 16 ; ok remainder 1 for group b
IMO E
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Re: All the people in a small county belong either to club A or club B but   [#permalink] 29 Mar 2019, 09:18
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