GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 15 Nov 2018, 22:12

### 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 November
PrevNext
SuMoTuWeThFrSa
28293031123
45678910
11121314151617
18192021222324
2526272829301
Open Detailed Calendar
• ### Free GMAT Strategy Webinar

November 17, 2018

November 17, 2018

07:00 AM PST

09:00 AM PST

Nov. 17, 7 AM PST. Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT.
• ### GMATbuster's Weekly GMAT Quant Quiz # 9

November 17, 2018

November 17, 2018

09:00 AM PST

11:00 AM PST

Join the Quiz Saturday November 17th, 9 AM PST. The Quiz will last approximately 2 hours. Make sure you are on time or you will be at a disadvantage.

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

Author Message
TAGS:

### Hide Tags

Current Student
Joined: 12 Oct 2012
Posts: 114
WE: General Management (Other)
A certain club has exactly 5 new members at the end of its  [#permalink]

### Show Tags

Updated on: 09 Dec 2012, 05:41
5
26
00:00

Difficulty:

95% (hard)

Question Stats:

49% (02:44) correct 51% (02:58) wrong based on 308 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.

Originally posted by Mbawarrior01 on 08 Dec 2012, 20:12.
Last edited by Bunuel on 09 Dec 2012, 05:41, edited 1 time in total.
Renamed the topic, edited the question and added OA.
Math Expert
Joined: 02 Sep 2009
Posts: 50613
A certain club has exactly 5 new members at the end of its  [#permalink]

### Show Tags

09 Dec 2012, 05:53
4
4
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.

_________________
##### General Discussion
VP
Status: Been a long time guys...
Joined: 03 Feb 2011
Posts: 1159
Location: United States (NY)
Concentration: Finance, Marketing
GPA: 3.75
Re: A certain club has exactly 5 new members at the end  [#permalink]

### Show Tags

08 Dec 2012, 21:42
2
2
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.

_________________
Intern
Joined: 21 Oct 2012
Posts: 24
GMAT Date: 01-19-2013
Re: A certain club has exactly 5 new members at the end of its  [#permalink]

### Show Tags

12 Dec 2012, 14:04
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

SVP
Joined: 06 Sep 2013
Posts: 1745
Concentration: Finance
Re: A certain club has exactly 5 new members at the end of its  [#permalink]

### Show Tags

17 Jan 2014, 09:00
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: 68
Re: A certain club has exactly 5 new members at the end of its  [#permalink]

### Show Tags

04 Jul 2014, 07:15
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: 50613
Re: A certain club has exactly 5 new members at the end of its  [#permalink]

### Show Tags

04 Jul 2014, 08:04
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: 163
Re: A certain club has exactly 5 new members at the end of its  [#permalink]

### Show Tags

08 May 2015, 23:03
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.
Intern
Joined: 23 Jun 2016
Posts: 1
Re: A certain club has exactly 5 new members at the end of its  [#permalink]

### Show Tags

12 Sep 2016, 22:37
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: 19
Re: A certain club has exactly 5 new members at the end of its  [#permalink]

### Show Tags

13 Sep 2016, 08:19
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: 50613
Re: A certain club has exactly 5 new members at the end of its  [#permalink]

### Show Tags

13 Sep 2016, 08:24
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: 19
Re: A certain club has exactly 5 new members at the end of its  [#permalink]

### Show Tags

13 Sep 2016, 10:51
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?
Intern
Joined: 21 May 2016
Posts: 8
Re: A certain club has exactly 5 new members at the end of its  [#permalink]

### Show Tags

27 Jun 2017, 05:51
Hello All,

Need some quick help.When I read the question,my approach was

1st week end : 5 members
2nd week end : 5+x members
3rd week end : 5 + x + x members (x members have bought x new members).
.
.
12 th week end : 5 + 11 x = y.

Can anyone please explain where I am missing ? In the heat of the exam I might end up with the same approach.
Math Expert
Joined: 02 Sep 2009
Posts: 50613
Re: A certain club has exactly 5 new members at the end of its  [#permalink]

### Show Tags

27 Jun 2017, 05:59
1
GouthamNandu wrote:
Hello All,

Need some quick help.When I read the question,my approach was

1st week end : 5 members
2nd week end : 5+x members
3rd week end : 5 + x + x members (x members have bought x new members).
.
.
12 th week end : 5 + 11 x = y.

Can anyone please explain where I am missing ? In the heat of the exam I might end up with the same approach.

Let me ask you a question: if a club has 5 members and EACH member will bring 2 new members, how many NEW members you'll have 5 + 2 = 7 or 5*2 = 10?
_________________
Director
Joined: 17 Dec 2012
Posts: 629
Location: India
A certain club has exactly 5 new members at the end of its  [#permalink]

### Show Tags

Updated on: 27 Jun 2017, 22:57
Mbawarrior01 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.

1. Number of new members in the second week is 5*(x) and in the third week 5*(x^2) and so on and in the 12th week 5*(x^11)
2. So we see in the choices that 5 has to be raised at least to the power of 11 and so is 3 which means x should be a multiple of 5 and 3 i.e, a multiple of 15.
3. We can eliminate choice A and rewrite choice E as 60* (60 ^11) or 5* (12 *(60^11) ). We can eliminate this also as this does not fit the format of x^11
4. We get only D with x =15.
_________________

Srinivasan Vaidyaraman
Sravna Holistic Solutions
http://www.sravnatestprep.com

Holistic and Systematic Approach

Originally posted by SravnaTestPrep on 27 Jun 2017, 22:14.
Last edited by SravnaTestPrep on 27 Jun 2017, 22:57, edited 2 times in total.
Director
Joined: 13 Mar 2017
Posts: 630
Location: India
Concentration: General Management, Entrepreneurship
GPA: 3.8
WE: Engineering (Energy and Utilities)
Re: A certain club has exactly 5 new members at the end of its  [#permalink]

### Show Tags

27 Jun 2017, 22:38
Mbawarrior01 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.

It is a very tricky question. Though it seems easy in the first instance but when we start solving it, the question gets tougher because of the unknown x. The questions asks which of the options could be y. That means we will have to somehow eliminate the options apart from correct one.

So. Lets start solving
The number of members added at the end of 1st week = 5
Total members = m+5 ( Let me be the members during the start of 1st week)
New members = 5

There on after at the end of each week, no. of members added = x times the new members last week.
2nd week : total members = m + 5 + 5x ; New members = 5x

3rd week : total members = m+ 5+5x + 5x^2 ; New members = 5X^2

..
..

12th week : Total members = m + 5+ 5x+ 5x^2 +..... +5x^11 ; New members = 5x^11.

Now as explained above we will have to check option for integral value of x (As x is an integer.)

Option 1 : 5^1/12 = 5 X^11 => x^11 = 5^(1/12 -1)= 5^(-11/12) (x is not an integer)
Option 2 : 3^11 * 5^11 = 5 X^11 => 3^11 *5^10 = x^11 (x is not an integer)
Option 3 : 3^12 * 5^12 = 5 X^11 => 3^12 * 5^11 = x^11 (x is not an integer)
Option 4 : 3^11 * 5^12 = 5 x^11 => 3^11 * 5^11 = x^11 => x = 15 (x is an integer)
Option 5 : 60^12 = 5 X^11 => 12 * 60^12 = x^11 (x is not an integer)

So Option D gives us an integral value of X

_________________

CAT 2017 99th percentiler : VA 97.27 | DI-LR 96.84 | QA 98.04 | OA 98.95
UPSC Aspirants : Get my app UPSC Important News Reader from Play store.

MBA Social Network : WebMaggu

Appreciate by Clicking +1 Kudos ( Lets be more generous friends.)

What I believe is : "Nothing is Impossible, Even Impossible says I'm Possible" : "Stay Hungry, Stay Foolish".

Manager
Joined: 30 May 2017
Posts: 66
Concentration: Finance, General Management
GMAT 1: 690 Q47 V38
GPA: 3.23
Re: A certain club has exactly 5 new members at the end of its  [#permalink]

### Show Tags

28 Jun 2017, 12:12
Quote:
$$5x^{11}=3^{11} * 5^{12}$$;

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

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

x=15.

I am still not getting this step.

I got 5x^11 and don't see how we know where to go from here.
_________________

Veritas Prep 6/18/17 600 Q:38 V:35 IR:5
Veritas Prep 6/29/17 620 Q:43 V:33 IR:4
Manhattan 7/12/17 640 Q:42 V:35 IR:2.4
Veritas Prep 7/27/17 640 Q:41 V:37 IR:4
Manhattan 8/9/17 670 Q:44 V:37 IR:3
Veritas Prep 8/21/17 660 Q:45 V:36 IR:7
GMAT Prep 8/23/17 700 Q:47 V:38 IR:8
GMAT Prep 8/27/17 730 Q:49 V:40 IR:8
Veritas Prep 8/30/17 690 Q:47 V:37 IR:8

Non-Human User
Joined: 09 Sep 2013
Posts: 8778
Re: A certain club has exactly 5 new members at the end of its  [#permalink]

### Show Tags

19 Jul 2018, 10:41
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.
_________________
Re: A certain club has exactly 5 new members at the end of its &nbs [#permalink] 19 Jul 2018, 10:41
Display posts from previous: Sort by