aditi2013 wrote:

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) 5^1/12

(B) 3^11 * 5^11

(C) 3^12 * 5^12

(D) 3^11 * 5^12

(E) 60^12

I found it difficult and tricky.

Started with previous week= m,

first week= m+5,

second week = m+5+5x, then got stuck.

Soon

At the end of the first week, there are 5 new members;

At the end of the second week, there are 5x new members (since each 5 new members from the previous week brings x new members);

At the end of the third week, there are 5x^2 new members (since each 5x new members from the previous week brings x new members);

...

At the end of the twelfth week, there are 5x^11 new members (since each 5x^10 new members from the previous week brings x new members).

We are given that 5x^11=y. Out of the answers only D yields integer value for x: 5x^11=3^11 * 5^12 --> x=3*5=15.

Answer: D.

P.S Please post OA's for the questions you post.Hello Bunuel. This is geometric progression with a formula b12=b1*q^11, which is y=5*x^11 for our example. However I couldn't figure out the answer, thank you for the explanation.