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

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A certain club has exactly 5 new members at the end of its [#permalink] New post 08 Dec 2012, 20:12
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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, 05:41, edited 1 time in total.
Renamed the topic, edited the question and added OA.
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Re: A certain club has exactly 5 new members at the end [#permalink] New post 08 Dec 2012, 21:42
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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.
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A certain club has exactly 5 new members at the end of its [#permalink] New post 09 Dec 2012, 05:53
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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.
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Re: A certain club has exactly 5 new members at the end of its [#permalink] New post 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?

(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.
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Re: A certain club has exactly 5 new members at the end of its [#permalink] New post 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?

(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.
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Re: A certain club has exactly 5 new members at the end of its [#permalink] New post 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?

(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.
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Re: A certain club has exactly 5 new members at the end of its [#permalink] New post 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?

(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!
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NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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?
25 extra-hard Quant Tests

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