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Sequences

by surajgarg » Wed Jul 28, 2010 2:06 am
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

OA D

I started to attempt this problem and got lost midway :(
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by outreach » Wed Jul 28, 2010 2:12 am
week1 5
week2 5x
week3 5x^2

so new members in the end of nth week 5^(n)*x^(n-1)

B
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by surajgarg » Wed Jul 28, 2010 2:29 am
outreach wrote:week1 5
week2 5x
week3 5x^2

so new members in the end of nth week 5^(n)*x^(n-1)

B
Thats exactly the approach I was taking, but if you notice the exponent of 5 remains constant whereas that of x is increasing.

But the answer says otherwise.
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by kvcpk » Wed Jul 28, 2010 2:55 am
surajgarg 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

OA D

I started to attempt this problem and got lost midway :(
New members at the end of
First week 5
Second Week 5x
Third week 5x^2
Fourth week 5x^3
..
12th week 5x^11

Question is asking which of the following could be y ?

Let us see each option :
5x^11 = 5^(1/12)
x^11 = 5^(-11/12)
x comes to be a fraction.. OUT

5x^11 = 3^11*5^11
x^11 = 3^11 * 5^10
x= 3 * 5^(10/11)
not integer... OUT

5x^11 = 3^12*5^12
x^11 = 3^12 * 5^11
x = 3^12/11 * 5
Not Integer.. OUT

5x^11 = 3^11*5^12
x^11 = 3^11 * 5^11
x= 15.. PERFECT

5x^11 =60^12
5x^11 =12^12 * 5^12
x^11 = 12^12 * 5^11
x = 12^12/11 * 5
Not Integer.. OUT

pick D
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