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# Sn = 2Sn-1 + 4 and Qn = 4Qn-1 + 8 for all n > 1. If S5 = Q4 and S7

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Senior Manager
Status: Finally Done. Admitted in Kellogg for 2015 intake
Joined: 25 Jun 2011
Posts: 472
Location: United Kingdom
GMAT 1: 730 Q49 V45
GPA: 2.9
WE: Information Technology (Consulting)
Sn = 2Sn-1 + 4 and Qn = 4Qn-1 + 8 for all n > 1. If S5 = Q4 and S7  [#permalink]

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Updated on: 11 Feb 2018, 00:33
7
00:00

Difficulty:

65% (hard)

Question Stats:

66% (02:35) correct 34% (03:01) wrong based on 268 sessions

### HideShow timer Statistics

$$S_n = 2S_{n-1} + 4$$ and $$Q_n = 4Q_{n-1} + 8$$ for all n > 1. If $$S_5 = Q_4$$ and $$S_7 = 316$$, what is the first value of n for which $$Q_n$$ is an integer?

(A) 1
(B) 2
(C) 3
(D) 4
(E) 5

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Best Regards,
E.

MGMAT 1 --> 530
MGMAT 2--> 640
MGMAT 3 ---> 610
GMAT ==> 730

Originally posted by enigma123 on 12 Jan 2012, 02:28.
Last edited by Bunuel on 11 Feb 2018, 00:33, edited 1 time in total.
Renamed the topic and edited the question.
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Re: Sn = 2Sn-1 + 4 and Qn = 4Qn-1 + 8 for all n > 1. If S5 = Q4 and S7  [#permalink]

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12 Jan 2012, 03:00
2
1
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
Senior Manager
Status: Finally Done. Admitted in Kellogg for 2015 intake
Joined: 25 Jun 2011
Posts: 472
Location: United Kingdom
GMAT 1: 730 Q49 V45
GPA: 2.9
WE: Information Technology (Consulting)
Re: Sn = 2Sn-1 + 4 and Qn = 4Qn-1 + 8 for all n > 1. If S5 = Q4 and S7  [#permalink]

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12 Jan 2012, 21:11
Many thanks kp1811. Really appreciate your help.
_________________

Best Regards,
E.

MGMAT 1 --> 530
MGMAT 2--> 640
MGMAT 3 ---> 610
GMAT ==> 730

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Location: Viet Nam
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Re: Sn = 2Sn-1 + 4 and Qn = 4Qn-1 + 8 for all n > 1. If S5 = Q4 and S7  [#permalink]

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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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Never forget what you are fighting for...
and when your mind and your body tell you to quit. Your heart will tell you to fight.

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Joined: 30 Apr 2015
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Re: Sn = 2Sn-1 + 4 and Qn = 4Qn-1 + 8 for all n > 1. If S5 = Q4 and S7  [#permalink]

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16 Feb 2016, 22:14
I wonder,why is it 700 level que?
It is quite simple
it is given
$$2S_4=4Q_3+4$$
$$S_4=2[Q_3+1]$$....i

we have been given that S_7=316
from this we can calculate S_6 and then ultimately S_4
$$S_4=36$$
putting this in equ i
$$Q_3=17$$ ...ans
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Joined: 11 Nov 2015
Posts: 20
Re: Sn = 2Sn-1 + 4 and Qn = 4Qn-1 + 8 for all n > 1. If S5 = Q4 and S7  [#permalink]

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18 Feb 2016, 06:18
mahakmalik wrote:
I wonder,why is it 700 level que?
It is quite simple
it is given
$$2S_4=4Q_3+4$$
$$S_4=2[Q_3+1]$$....i

we have been given that S_7=316
from this we can calculate S_6 and then ultimately S_4
$$S_4=36$$
putting this in equ i
$$Q_3=17$$ ...ans

I think it's because it is long to solve and you have a big chance to make mistakes while calculating given that we deal with big numbers
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Re: Sn = 2Sn-1 + 4 and Qn = 4Qn-1 + 8 for all n > 1. If S5 = Q4 and S7  [#permalink]

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11 Feb 2018, 00:28
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Re: Sn = 2Sn-1 + 4 and Qn = 4Qn-1 + 8 for all n > 1. If S5 = Q4 and S7 &nbs [#permalink] 11 Feb 2018, 00:28
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