and only these members

sanju09 wrote:A certain club has exactly 5 new members at the end of its first week. Every subsequent week, each of the revious 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. (5)^(1/12)
B. (3^11)*(5^11)
C. (3^12)*(5^12)
D. (3^11)*(5^12)
E. 60^12

New members at the end of the first week = 5

New members at the end of the second week = 5x

New members at the end of the third week = 5x^2 (remember only the new members of the last week bring new members into the group)

So new members at the end of the 12th week = 5x^11.

It is clear that now our option should be such that if it is divided by 5, the remaining number must be in the form of x^11. Only option satisfying this condition is 3^11 * 5^12.

So choice D