Source : - Manhattan GMAT ( www.manhattangmat.com )
A certain club has exactly 5 new members at the end of its first week. Every subsequent week, each of the previous week's new members (and only these members) brings exactly x new members into the club. If y is the number of new members brought into the club during the twelfth week, which of the following could be y?
A)Root 12 (5)
(B)3^11*5^11
(C)3^12*5^12
(D)3^11*5^12
(E)60^12
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given :
Num of new members at the end of 1st week = 5
each new member brings exactly x new members , so
num of NEW members at the end of 2nd week = 5x
proceeding so...
num of NEW members at the end of 3rd week = 5x * x =5x^2
.
.
.
num of NEW members at the end of 12th week = 5 * x^11
So y = 5 x^11
among given choices 3^11*5^12 can be written as 5*( 3^11*5^11) = 5* 15^11
So, D is the answer
Num of new members at the end of 1st week = 5
each new member brings exactly x new members , so
num of NEW members at the end of 2nd week = 5x
proceeding so...
num of NEW members at the end of 3rd week = 5x * x =5x^2
.
.
.
num of NEW members at the end of 12th week = 5 * x^11
So y = 5 x^11
among given choices 3^11*5^12 can be written as 5*( 3^11*5^11) = 5* 15^11
So, D is the answer
