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Sequence of Twos (DIGITS)

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Sequence of Twos (DIGITS)

by tomada » Sun Dec 26, 2010 1:49 pm
This one comes from a "Fractions, Decimals, & Percents" Question Bank of the Manhattan GMAT website. According to the site, this is a 700-800 question, and it's a dandy. I eventually solved it correctly, although it took me too long for my liking.


Question

S is the infinite sequence S1 = 2, S2 = 22, S3 = 222,...Sk = Sk-1 + 2(10k-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?

Choices

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

OA: C
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by anshumishra » Sun Dec 26, 2010 2:10 pm
tomada wrote:This one comes from a "Fractions, Decimals, & Percents" Question Bank of the Manhattan GMAT website. According to the site, this is a 700-800 question, and it's a dandy. I eventually solved it correctly, although it took me too long for my liking.


Question

S is the infinite sequence S1 = 2, S2 = 22, S3 = 222,...Sk = Sk-1 + 2(10k-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?

Choices

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

OA: C
Sum------------------------------ Remainder-----------Last digit
30*2 (60)----------------------- 6----------------------- ---0
29*2 (58+6 = 64)------------- 6-------------------------- 4
28*2 (56+6 = 62)--------------6---------------------------2
27*2 (54+6 = 60)--------------6---------------------------0
26*2 (52+6 = 58)--------------5---------------------------8
25*2 (50+5 = 55)--------------5---------------------------5
24*2 (48+5 = 53)--------------5---------------------------3
23*2 (46+5 = 51)--------------5---------------------------1
22*2 (44+5 = 49)--------------4---------------------------9
21*2 (42+4 = 46)--------------4---------------------------6
20*2 (40+4 = 44)--------------4---------------------------4
Last edited by anshumishra on Mon Dec 27, 2010 9:19 am, edited 1 time in total.
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by tomada » Sun Dec 26, 2010 2:38 pm
Nicely done! I think I was initially too intimidated by picturing the sum of 30 terms, and it took me a while to finally set it up like you did.
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by fskilnik@GMATH » Mon Dec 27, 2010 9:10 am
Hi there!

Just two small corrections:
Sk = Sk-1 + 2(10k-1).
Should be S_{k} = S_{k-1} + 2*10^{k-1}
anshumishra wrote:24*2 (48+5 = 53)--------------3---------------------------5
23*2 (46+3 = 49)--------------4---------------------------9 should be 46+5=51

(And the following lines should be corrected accordingly.)
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Fabio.
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by anshumishra » Mon Dec 27, 2010 9:23 am
fskilnik wrote:Hi there!
anshumishra wrote:24*2 (48+5 = 53)--------------3---------------------------5
23*2 (46+3 = 49)--------------4---------------------------9 should be 46+5=51

(And the following lines should be corrected accordingly.)
Regards,
Fabio.
Edited ! Thanks Fabio for pointing that out !
(I wish to save my luck for exam rather than making mistakes here and still getting right answer :)
Thanks
Anshu

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by fskilnik@GMATH » Mon Dec 27, 2010 9:38 am
anshumishra wrote:Edited ! Thanks Fabio for pointing that out !
(I wish to save my luck for exam rather than making mistakes here and still getting right answer :)
My pleasure, Anshu! LoL :)
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