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Sn = 2Sn-1 + 4 and Qn = 4Qn-1 + 8 for all n > 1. If S5 = Q4

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Sn = 2Sn-1 + 4 and Qn = 4Qn-1 + 8 for all n > 1. If S5 = Q4 [#permalink] New post 12 Jan 2012, 02:28
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Question Stats:

51% (03:10) correct 49% (02:17) wrong based on 127 sessions
Sn = 2Sn-1 + 4 and Qn = 4Qn-1 + 8 for all n > 1. If S5 = Q4 and S7 = 316, what is the first value of n for which Qn is an integer?

(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
[Reveal] Spoiler: OA

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Re: Sn = 2Sn-1 + 4 and Qn = 4Qn-1 + 8 for all n > 1. If S5 = Q4 [#permalink] New post 12 Jan 2012, 03:00
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enigma123 wrote:
Sn = 2Sn-1 + 4 and Qn = 4Qn-1 + 8 for all n > 1. If S5 = Q4 and S7 = 316, what is the first value of n for which Qn is an integer?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5

Any idea how to solve these guys? I have given up after scratching my head for a while.


Assuming I have understood the symbols used correctly answer is C- 3

S7 = 2S6 +4 = 316

S6 = 312/2 = 156 = 2S5 + 4

S5 = 152/2 = 76 = Q4

Q4 = 4Q3 + 8 = 76

Q3 = 68/4 = 17

Q3 = 4Q2 + 8 = 17

Q2 = 9/4 = 2.25

Q2 = 4Q1 + 8

Q1 will not be integer
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Status: Finally Done. Admitted in Kellogg for 2015 intake
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Re: Sn = 2Sn-1 + 4 and Qn = 4Qn-1 + 8 for all n > 1. If S5 = Q4 [#permalink] New post 12 Jan 2012, 21:11
Many thanks kp1811. Really appreciate your help.
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Re: Sn = 2Sn-1 + 4 and Qn = 4Qn-1 + 8 for all n > 1. If S5 = Q4 [#permalink] New post 26 Oct 2014, 03:46
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Re: Sn = 2Sn-1 + 4 and Qn = 4Qn-1 + 8 for all n > 1. If S5 = Q4 [#permalink] New post 05 Nov 2014, 20:11
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Re: Sn = 2Sn-1 + 4 and Qn = 4Qn-1 + 8 for all n > 1. If S5 = Q4 [#permalink] New post 06 Nov 2014, 05:43
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Re: Sn = 2Sn-1 + 4 and Qn = 4Qn-1 + 8 for all n > 1. If S5 = Q4 [#permalink] New post 17 Nov 2015, 09:39
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Re: Sn = 2Sn-1 + 4 and Qn = 4Qn-1 + 8 for all n > 1. If S5 = Q4 [#permalink] New post 28 Jan 2016, 01:56
Is there any shortcut for this question? It took me 4 mins to solve this question.
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Re: Sn = 2Sn-1 + 4 and Qn = 4Qn-1 + 8 for all n > 1. If S5 = Q4   [#permalink] 28 Jan 2016, 01:56
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Sn = 2Sn-1 + 4 and Qn = 4Qn-1 + 8 for all n > 1. If S5 = Q4

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