Check GMAT Club Decision Tracker for the Latest School Decision Releases https://gmatclub.com/AppTrack

 It is currently 23 May 2017, 13:30

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

A certain club has exactly 5 new members at the end of its

Author Message
TAGS:

Hide Tags

Manager
Joined: 12 Oct 2012
Posts: 129
WE: General Management (Other)
Followers: 1

Kudos [?]: 54 [3] , given: 198

A certain club has exactly 5 new members at the end of its [#permalink]

Show Tags

08 Dec 2012, 21:12
3
KUDOS
20
This post was
BOOKMARKED
00:00

Difficulty:

85% (hard)

Question Stats:

56% (02:55) correct 44% (02:27) wrong based on 212 sessions

HideShow timer Statistics

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.
[Reveal] Spoiler: OA

Last edited by Bunuel on 09 Dec 2012, 06:41, edited 1 time in total.
Renamed the topic, edited the question and added OA.
VP
Status: Been a long time guys...
Joined: 03 Feb 2011
Posts: 1382
Location: United States (NY)
Concentration: Finance, Marketing
GPA: 3.75
Followers: 178

Kudos [?]: 1462 [1] , given: 62

Re: A certain club has exactly 5 new members at the end [#permalink]

Show Tags

08 Dec 2012, 22:42
1
KUDOS
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.

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 38835
Followers: 7718

Kudos [?]: 105915 [2] , given: 11593

A certain club has exactly 5 new members at the end of its [#permalink]

Show Tags

09 Dec 2012, 06:53
2
KUDOS
Expert's post
3
This post was
BOOKMARKED
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.

_________________
Intern
Joined: 21 Oct 2012
Posts: 25
GMAT Date: 01-19-2013
Followers: 1

Kudos [?]: 9 [0], given: 15

Re: A certain club has exactly 5 new members at the end of its [#permalink]

Show Tags

12 Dec 2012, 15:04
Bunuel 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.

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.
_________________

MGMAT1 - 610
MGMAT2 - 670
MGMAT3 - 640

OMG

Current Student
Joined: 06 Sep 2013
Posts: 2005
Concentration: Finance
Followers: 68

Kudos [?]: 643 [0], given: 355

Re: A certain club has exactly 5 new members at the end of its [#permalink]

Show Tags

17 Jan 2014, 10:00
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.

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.
Manager
Joined: 28 Dec 2013
Posts: 80
Followers: 0

Kudos [?]: 2 [0], given: 3

Re: A certain club has exactly 5 new members at the end of its [#permalink]

Show Tags

04 Jul 2014, 08:15
Bunuel 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.

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.
Math Expert
Joined: 02 Sep 2009
Posts: 38835
Followers: 7718

Kudos [?]: 105915 [0], given: 11593

Re: A certain club has exactly 5 new members at the end of its [#permalink]

Show Tags

04 Jul 2014, 09:04
sagnik242 wrote:
Bunuel 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.

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.

$$5x^{11}=3^{11} * 5^{12}$$ --> reduce by 5: $$x^{11}=3^{11} * 5^{11}=(3*5)^{11}$$ --> $$x=3*5=15$$.

Hope it's clear now!
_________________
Manager
Joined: 22 Aug 2014
Posts: 193
Followers: 0

Kudos [?]: 10 [0], given: 49

Re: A certain club has exactly 5 new members at the end of its [#permalink]

Show Tags

09 May 2015, 00:03
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.

in 2nd week=(5x).x
in 12th week:(5 x^11)=y
now value of 5 will be 1 power more than 3.
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15406
Followers: 648

Kudos [?]: 205 [0], given: 0

Re: A certain club has exactly 5 new members at the end of its [#permalink]

Show Tags

22 Jul 2016, 03:36
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Intern
Joined: 23 Jun 2016
Posts: 1
Followers: 0

Kudos [?]: 0 [0], given: 0

Re: A certain club has exactly 5 new members at the end of its [#permalink]

Show Tags

12 Sep 2016, 23:37
Marcab wrote:
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.

How you consider that the number of new memebers added each week is 15
Intern
Joined: 10 Jun 2014
Posts: 21
Followers: 0

Kudos [?]: 10 [0], given: 88

Re: A certain club has exactly 5 new members at the end of its [#permalink]

Show Tags

13 Sep 2016, 09:19
Bunuel 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.

where 15 comes from?

lets say each week new member brings 1 new member.
can u calculate it for me please?
Math Expert
Joined: 02 Sep 2009
Posts: 38835
Followers: 7718

Kudos [?]: 105915 [0], given: 11593

Re: A certain club has exactly 5 new members at the end of its [#permalink]

Show Tags

13 Sep 2016, 09:24
azamaka wrote:
Bunuel 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.

where 15 comes from?

lets say each week new member brings 1 new member.
can u calculate it for me please?

$$5x^{11}=3^{11} * 5^{12}$$;

$$x^{11}=3^{11} * 5^{11}$$;

$$x^{11}=15^{11}$$;

x=15.
_________________
Intern
Joined: 10 Jun 2014
Posts: 21
Followers: 0

Kudos [?]: 10 [0], given: 88

Re: A certain club has exactly 5 new members at the end of its [#permalink]

Show Tags

13 Sep 2016, 11:51
Marcab wrote:
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.

I have 3 questions
1) why we have to consider 15 new member?
2) can we consider that each member brigs 1 new member?
3) this kind of quastion are common on gmat?
Re: A certain club has exactly 5 new members at the end of its   [#permalink] 13 Sep 2016, 11:51
Similar topics Replies Last post
Similar
Topics:
10 A club collected exactly \$599 from its members. If each 5 21 Jun 2016, 10:34
4 A certain club has 10 members, including Harry. One of the 8 25 Jul 2012, 21:13
140 A certain club has 10 members, including Harry. One of the 32 09 Feb 2017, 03:36
18 A certain club has 20 members. What is the ratio of the memb 20 09 Aug 2016, 07:25
31 A certain established organization has exactly 4096 members. 17 30 May 2016, 01:07
Display posts from previous: Sort by