Author 
Message 
TAGS:

Hide Tags

Current Student
Joined: 12 Oct 2012
Posts: 118
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, 06:41
Question Stats:
54% (01:50) correct 46% (02:25) wrong based on 306 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.
Official Answer and Stats are available only to registered users. Register/ Login.
Originally posted by Mbawarrior01 on 08 Dec 2012, 21:12.
Last edited by Bunuel on 09 Dec 2012, 06:41, edited 1 time in total.
Renamed the topic, edited the question and added OA.




Math Expert
Joined: 02 Sep 2009
Posts: 48119

A certain club has exactly 5 new members at the end of its
[#permalink]
Show Tags
09 Dec 2012, 06:53
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.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics




VP
Status: Been a long time guys...
Joined: 03 Feb 2011
Posts: 1251
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, 22:42
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. D is the answer.
_________________
Prepositional Phrases ClarifiedElimination of BEING Absolute Phrases Clarified Rules For Posting www.UnivScholarships.com



Intern
Joined: 21 Oct 2012
Posts: 25
GMAT Date: 01192013

Re: A certain club has exactly 5 new members at the end of its
[#permalink]
Show Tags
12 Dec 2012, 15:04
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?
(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.
_________________
MGMAT1  610 MGMAT2  670 MGMAT3  640
OMG



SVP
Joined: 06 Sep 2013
Posts: 1848
Concentration: Finance

Re: A certain club has exactly 5 new members at the end of its
[#permalink]
Show Tags
17 Jan 2014, 10:00
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?
(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, 08:15
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?
(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.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: 48119

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: 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.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!
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Manager
Joined: 22 Aug 2014
Posts: 174

Re: A certain club has exactly 5 new members at the end of its
[#permalink]
Show Tags
09 May 2015, 00:03
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. in 2nd week=(5x).x in 12th week:(5 x^11)=y now value of 5 will be 1 power more than 3. D answer.



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, 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.
D is the answer. 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, 09:19
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?
(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. please explain 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: 48119

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: 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. please explain 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.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



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, 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.
D is the answer. 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, 06:51
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: 48119

Re: A certain club has exactly 5 new members at the end of its
[#permalink]
Show Tags
27 Jun 2017, 06:59



Director
Joined: 17 Dec 2012
Posts: 637
Location: India

A certain club has exactly 5 new members at the end of its
[#permalink]
Show Tags
Updated on: 27 Jun 2017, 23:57
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



Director
Joined: 13 Mar 2017
Posts: 616
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, 23:38
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 Answer D
_________________
CAT 99th percentiler : VA 97.27  DILR 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
GPA: 3.23

Re: A certain club has exactly 5 new members at the end of its
[#permalink]
Show Tags
28 Jun 2017, 13:12
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



NonHuman User
Joined: 09 Sep 2013
Posts: 7781

Re: A certain club has exactly 5 new members at the end of its
[#permalink]
Show Tags
19 Jul 2018, 11:41
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.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources




Re: A certain club has exactly 5 new members at the end of its &nbs
[#permalink]
19 Jul 2018, 11:41






