Sequence of Twos (DIGITS)

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

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.

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.)

Regards,
Fabio.

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

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