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3 + 3 + 3 + 2 × 3^2 + 2 × 3^3 + 2 × 3^4 + 2 × 3^5 + 2 × 3^6

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gmattokyo
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3 + 3 + 3 + 2 × 3^2 + 2 × 3^3 + 2 × 3^4 + 2 × 3^5 + 2 × 3^6 [#permalink] New post   Updated on: 12 Nov 2013, 10:34
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Question Stats:

73% (02:20) correct 27% (02:30) wrong based on 111 sessions
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3 + 3 + 3 + 2 × 3^2 + 2 × 3^3 + 2 × 3^4 + 2 × 3^5 + 2 × 3^6 + 2 × 3^7 =

(A) 3^7
(B) 3^8
(C) 3^14
(D) 3^28
(E) 3^30

OPEN DISCUSSION OF THIS QUESTION IS HERE: 3-108690.html

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B

Originally posted by gmattokyo on 28 Oct 2009, 08:22.
Last edited by Bunuel on 12 Nov 2013, 10:34, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
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Re: 3 + 3 + 3 + 2 × 3^2 + 2 × 3^3 + 2 × 3^4 + 2 × 3^5 + 2 × 3^6 [#permalink] New post   28 Oct 2009, 08:50
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gmattokyo wrote:
Found this interesting, so sharing.

3 + 3 + 3 + 2 × 3^2 + 2 × 3^3 + 2 × 3^4 + 2 × 3^5 + 2 × 3^6 + 2 × 3^7 =



Not tough, but interesting.

3+3+3 becomes 3^2,
3^2+2*3^2 becomes 3*3^2, then works out to 3^3

3*3^6 is assumed right before 2*3^7

3^7 + 2*3^7 becomes 3*3^7 , then to 3^8

good for brain exercise
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Re: 3 + 3 + 3 + 2 × 3^2 + 2 × 3^3 + 2 × 3^4 + 2 × 3^5 + 2 × 3^6 [#permalink] New post   28 Oct 2009, 09:15
Right on!
Hope I'd have got it so easily too :)
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Re: 3 + 3 + 3 + 2 × 3^2 + 2 × 3^3 + 2 × 3^4 + 2 × 3^5 + 2 × 3^6 [#permalink] New post   28 Oct 2009, 12:11
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The answer choices make this too simple for me -
The last term 2*3^7>3^7
so Option 1 is ruled out.

Option 2 is possibly correct.

Option 3 - 3^14 - At least my common sense says that a sequence of Geometric progression with the largest term 2*3^7 could ever "Add" up to 3^14.

Other options are ruled out as they are larger than option 3.

So Option 2 is the only possibility. IMO there is no point solving questions with such answer choices, but good job solving the problem yuskay.
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Re: 3 + 3 + 3 + 2 × 3^2 + 2 × 3^3 + 2 × 3^4 + 2 × 3^5 + 2 × 3^6 [#permalink] New post   29 Oct 2009, 04:50
powers of 3 form a GP.solving using the formula we get 3^8

I will choose option B
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Re: 3 + 3 + 3 + 2 × 3^2 + 2 × 3^3 + 2 × 3^4 + 2 × 3^5 + 2 × 3^6 [#permalink] New post   12 Nov 2013, 10:15
gmattokyo wrote:
Found this interesting, so sharing.

3 + 3 + 3 + 2 × 3^2 + 2 × 3^3 + 2 × 3^4 + 2 × 3^5 + 2 × 3^6 + 2 × 3^7 =

(A) 3^7
(B) 3^8
(C) 3^14
(D) 3^28
(E) 3^30


Did somebody find any other elegant way to solve this? I didn't get the explanation provided by Mr. Yusjkay
Cheers!
J :)

Will provide some lovely Kudos
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Re: 3 + 3 + 3 + 2 × 3^2 + 2 × 3^3 + 2 × 3^4 + 2 × 3^5 + 2 × 3^6 [#permalink] New post   12 Nov 2013, 10:34
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jlgdr wrote:
gmattokyo wrote:
Found this interesting, so sharing.

3 + 3 + 3 + 2 × 3^2 + 2 × 3^3 + 2 × 3^4 + 2 × 3^5 + 2 × 3^6 + 2 × 3^7 =

(A) 3^7
(B) 3^8
(C) 3^14
(D) 3^28
(E) 3^30


Did somebody find any other elegant way to solve this? I didn't get the explanation provided by Mr. Yusjkay
Cheers!
J :)

Will provide some lovely Kudos


3 + 3 + 3 + 2 × 3^2 + 2 × 3^3 + 2 × 3^4 + 2 × 3^5 + 2 × 3^6 + 2 × 3^7 =

A. 3^7
B. 3^8
C. 3^14
D. 3^28
E. 3^30

We have the sum of 9 terms. Now, if all terms were equal to the largest term 2*3^7 we would have: sum=9*(2*3^7)=2*3^9=~3^10, so the actual sum is less than 3^10 and more than 3^7 (option A) as the last term is already more than that. So the answer is clearly B.

Answer: B.

Check similar questions to practice:
2-99058.html
tough-and-tricky-exponents-and-roots-questions-125956-40.html?hilit=geometric#p1029222
sequence-s-is-defined-as-follows-s1-2-s2-2-1-s3-2-2-sn-129435.html

OPEN DISCUSSION OF THIS QUESTION IS HERE: 3-108690.html

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Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
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Thank you for understanding, and happy exploring!
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Re: 3 + 3 + 3 + 2 × 3^2 + 2 × 3^3 + 2 × 3^4 + 2 × 3^5 + 2 × 3^6 [#permalink]
12 Nov 2013, 10:34
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