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S is the infinite sequence S1 = 2, S2 = 22, S3 = 222,...Sk =

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S is the infinite sequence S1 = 2, S2 = 22, S3 = 222,...Sk =  [#permalink]

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New post 18 Aug 2008, 10:29
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S is the infinite sequence S1 = 2, S2 = 22, S3 = 222,...Sk = Sk–1 + 2(10^(k–1)). If p is the sum of the first 30 terms of S, what is the eleventh digit of p, counting right to left from the units digit?

A) 1
B) 2
C) 4
D) 6
E) 9

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Re: PS - sequence  [#permalink]

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New post 18 Aug 2008, 11:12
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sarzan wrote:
S is the infinite sequence S1 = 2, S2 = 22, S3 = 222,...Sk = Sk–1 + 2(10^(k–1)). If p is the sum of the first 30 terms of S, what is the eleventh digit of p, counting right to left from the units digit?

A) 1
B) 2
C) 4
D) 6
E) 9


P = S1 + S2 + S3 + ................ + S30
SO THE LAST DIGIT ISD THE SUM OF THIRTY 2'S.

the 6th digits from the right to left is 1 (25x2 + 5)/
so the 11th digits from the right to left is 4 (20x2 + 4)/

So C. 4.
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Re: PS - sequence  [#permalink]

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New post 18 Aug 2008, 12:07
GMAT TIGER wrote:
sarzan wrote:
S is the infinite sequence S1 = 2, S2 = 22, S3 = 222,...Sk = Sk–1 + 2(10^(k–1)). If p is the sum of the first 30 terms of S, what is the eleventh digit of p, counting right to left from the units digit?

A) 1
B) 2
C) 4
D) 6
E) 9


P = S1 + S2 + S3 + ................ + S30
SO THE LAST DIGIT ISD THE SUM OF THIRTY 2'S.

the 6th digits from the right to left is 1 (25x2 + 5)/
so the 11th digits from the right to left is 4 (20x2 + 4)/

So C. 4.


You're a ninja! +1

I understood the question, I just had no idea how to approach it, but I guessed it right!
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Re: PS - sequence  [#permalink]

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New post 18 Aug 2008, 13:18
GMAT TIGER wrote:
sarzan wrote:
S is the infinite sequence S1 = 2, S2 = 22, S3 = 222,...Sk = Sk–1 + 2(10^(k–1)). If p is the sum of the first 30 terms of S, what is the eleventh digit of p, counting right to left from the units digit?

A) 1
B) 2
C) 4
D) 6
E) 9


P = S1 + S2 + S3 + ................ + S30
SO THE LAST DIGIT ISD THE SUM OF THIRTY 2'S.

the 6th digits from the right to left is 1 (25x2 + 5)/
so the 11th digits from the right to left is 4 (20x2 + 4)/

So C. 4.


hey how did you get 25*2 + 5 for the 6th digit.. how does this carry over(5) works here.
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Re: PS - sequence  [#permalink]

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New post 18 Aug 2008, 22:20
chan4312 wrote:
GMAT TIGER wrote:
sarzan wrote:
S is the infinite sequence S1 = 2, S2 = 22, S3 = 222,...Sk = Sk–1 + 2(10^(k–1)). If p is the sum of the first 30 terms of S, what is the eleventh digit of p, counting right to left from the units digit?

A) 1
B) 2
C) 4
D) 6
E) 9


P = S1 + S2 + S3 + ................ + S30
SO THE LAST DIGIT ISD THE SUM OF THIRTY 2'S.

the 6th digits from the right to left is 1 (25x2 + 5)/
so the 11th digits from the right to left is 4 (20x2 + 4)/

So C. 4.


hey how did you get 25*2 + 5 for the 6th digit.. how does this carry over(5) works here.


first, there was a typo. the 6th digits from the right to left is 5 (25x2 + 5) not 1. i was doing for 27th digit but forgot to edit it.
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Re: PS - sequence  [#permalink]

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New post 18 Aug 2008, 23:53
I understand the 11th digit is 20x2 plus something, but how do you determine it is 4 without actually brute forcing the problem from the first digit? Something to do with the 6th digit? I feel dumb.
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Re: PS - sequence  [#permalink]

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New post 19 Aug 2008, 09:05
Nerdboy wrote:
I understand the 11th digit is 20x2 plus something, but how do you determine it is 4 without actually brute forcing the problem from the first digit? Something to do with the 6th digit? I feel dumb.


for 10th digit there are twnenty-one 2s i.e. 21x2 = 42 plus 4 [from 46 (21x2 + 4) or 47 (21x2 + 5) but doesnot matter because the carry over is 4] is 6. so 4 is to be added to 40 (20x2). so it is 4 of 44.


when there are thirty 2's, the carry over is 6.
when there are at least twenty-seven 2's, the carry over is still 6.

but when there are twenty-six 2's, the carry over is 5.
when there are twenty-four 2's, the carry over is 5.
when there are twenty-three 2's, the carry over is still 5.
when there are twenty-two 2's, the carry over is 4.
when there are eighteen 2's, the carry over is still 4.
but when there are seventeen 2's, the carry over is 3.

so follow the pattern........

--== Message from GMAT Club Team ==--

This is not a quality discussion. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.

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Gmat: http://gmatclub.com/forum/everything-you-need-to-prepare-for-the-gmat-revised-77983.html


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Re: PS - sequence &nbs [#permalink] 19 Aug 2008, 09:05
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