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In order to remain a member of a certain club, each member must sign

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In order to remain a member of a certain club, each member must sign  [#permalink]

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New post 18 Nov 2019, 09:01
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In order to remain a member of a certain club, each member must sign on exactly two more new members exactly one year after he joins, after which he can sign on no new members. If the original members of the club also followed these rules, and no member has left the club, how many original members must there have been if the club has 35 members in its third year?

A. 5
B. 7
C. 10
D. 13
E. 15
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In order to remain a member of a certain club, each member must sign  [#permalink]

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New post 18 Nov 2019, 10:00
gmat1393 wrote:
In order to remain a member of a certain club, each member must sign on exactly two more new members exactly one year after he joins, after which he can sign on no new members. If the original members of the club also followed these rules, and no member has left the club, how many original members must there have been if the club has 35 members in its third year?

A. 5
B. 7
C. 10
D. 13
E. 15


Ans. Checking by option
A. At the end of 1st Year, (initially is 5 as given)
5 member must join 2 members each, so total joined is 5 + 10 (5*2) = 15
at the end of 2nd year, Initially, 5 members has completed their target, Now last year joined member has to joins 2 members each,i.e. 20 new members will be added (10*2)
So total member in the 3rd year will be : 5 (joined initially) + 10 (joined in 2year) + 20 (joined in 3rd year) = 35
= 35
So, option A is right.

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Re: In order to remain a member of a certain club, each member must sign  [#permalink]

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New post 22 Nov 2019, 12:40
gmat1393 wrote:
In order to remain a member of a certain club, each member must sign on exactly two more new members exactly one year after he joins, after which he can sign on no new members. If the original members of the club also followed these rules, and no member has left the club, how many original members must there have been if the club has 35 members in its third year?

A. 5
B. 7
C. 10
D. 13
E. 15


We can let x = the number of members originally in the club. Therefore, 2x new members will join in the second year, and 4x new members will join in the third year. We can therefore create the equation:

x + 2x + 4x = 35

7x = 35

x = 5

Answer: A
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Re: In order to remain a member of a certain club, each member must sign   [#permalink] 22 Nov 2019, 12:40
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