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A certain club has exactly 5 new members at the end of its [#permalink]
08 Dec 2012, 20:12

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Question Stats:

57% (03:10) correct
43% (02:40) wrong based on 72 sessions

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?

Re: A certain club has exactly 5 new members at the end [#permalink]
08 Dec 2012, 21:42

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This post received KUDOS

Expert's post

At the end of 2nd week, the number of new members are 5x. At the end of third week, the number of new members are (5x)*x. Therefore at the end of 12 th week, the number of new members are 5x^11.

Now here lies the trick. Consider the number of new members added each week be 15. Therefore x=15. Put this in above relation. It will come out to be 5*(15)^11 or 5*(3*5)^11 or 5^12 * 3^11.

Re: A certain club has exactly 5 new members at the end of its [#permalink]
09 Dec 2012, 05:53

1

This post received KUDOS

Expert's post

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?

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.

Re: A certain club has exactly 5 new members at the end of its [#permalink]
12 Dec 2012, 14:04

Bunuel wrote:

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?

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.

Re: A certain club has exactly 5 new members at the end of its [#permalink]
17 Jan 2014, 09:00

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?

I found it difficult and tricky. Started with previous week= m, first week= m+5, second week = m+5+5x, then got stuck.

Shouldn't the question read that 'y' is the number of members brought into the club at the beginning of the twelfth week instead of during? Cause during the week is not the 'stock' it is the new members brought in.

Re: A certain club has exactly 5 new members at the end of its [#permalink]
04 Jul 2014, 07:15

Bunuel wrote:

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?

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.

But how does 5x^11 = 3^11 x 5^12, 3^11 and 5^12 have unlike bases.

Re: A certain club has exactly 5 new members at the end of its [#permalink]
04 Jul 2014, 08:04

Expert's post

sagnik242 wrote:

Bunuel wrote:

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?

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.

But how does 5x^11 = 3^11 x 5^12, 3^11 and 5^12 have unlike bases.