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

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Manager
Joined: 30 Jul 2007
Posts: 130
S is the infinite sequence S1 = 2, S2 = 22, S3 = 222,...Sk =  [#permalink]

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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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Joined: 29 Aug 2007
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18 Aug 2008, 11:12
1
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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Manager
Joined: 30 Jul 2007
Posts: 130

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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!
Manager
Joined: 04 Jun 2008
Posts: 141

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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.
SVP
Joined: 29 Aug 2007
Posts: 2420

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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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Senior Manager
Joined: 16 Jul 2008
Posts: 279

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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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SVP
Joined: 29 Aug 2007
Posts: 2420

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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.

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