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

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Director
Status: Finally Done. Admitted in Kellogg for 2015 intake
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GMAT 1: 730 Q49 V45
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WE: Information Technology (Consulting)
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Kudos [?]: 3379 [0], given: 217

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

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12 Jan 2012, 03:28
4
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Difficulty:

75% (hard)

Question Stats:

59% (03:03) correct 41% (02:07) wrong based on 183 sessions

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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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Best Regards,
E.

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

Senior Manager
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Kudos [?]: 171 [1] , given: 5

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

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12 Jan 2012, 04:00
1
KUDOS
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
Director
Status: Finally Done. Admitted in Kellogg for 2015 intake
Joined: 25 Jun 2011
Posts: 537
Location: United Kingdom
GMAT 1: 730 Q49 V45
GPA: 2.9
WE: Information Technology (Consulting)
Followers: 77

Kudos [?]: 3379 [0], given: 217

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

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12 Jan 2012, 22:11
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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Joined: 09 Sep 2013
Posts: 15445
Followers: 649

Kudos [?]: 209 [0], given: 0

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

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26 Oct 2014, 04:46
Hello from the GMAT Club BumpBot!

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Kudos [?]: 650 [1] , given: 57

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

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05 Nov 2014, 21:11
1
KUDOS
Math Expert
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Kudos [?]: 106131 [0], given: 11607

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

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06 Nov 2014, 06:43
nktdotgupta wrote:
Please change the OA to C

_______________
Done. Thank you.
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Kudos [?]: 209 [0], given: 0

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

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17 Nov 2015, 10:39
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).

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Kudos [?]: 11 [0], given: 58

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

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28 Jan 2016, 02:56
Is there any shortcut for this question? It took me 4 mins to solve this question.
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Schools: BYU-Marriott'18
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Kudos [?]: 23 [0], given: 30

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

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16 Feb 2016, 23:14
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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Kudos [?]: 8 [0], given: 57

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

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18 Feb 2016, 07:18
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
Re: Sn = 2Sn-1 + 4 and Qn = 4Qn-1 + 8 for all n > 1. If S5 = Q4   [#permalink] 18 Feb 2016, 07:18
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