FDP - Need Help with a QB question

[vsathya]

Hi,

Please help me with the following 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?

There are 2 ways to solve this question.

(1) Starting with the units digit column, all 30 of the terms have a 2 in that position so the sum of the units column would be 30 x 2 = 60. A zero would be written as the units digit of the sum and a six would be carried over to the tens column. and so on..

(2) We could also have seen that each column has one less 2 than the previous, so if we started out with 30 2’s in the first column, the 11th column must have 11 - 1 = 10 less 2’s, for a total of 20 2’s.

In (2), 11th column should have 11 2's right? how did 20 2's come here? Please explain.

Thanks,
Sathya.

[messi10]

Hi Sathya,

That's a tough question. I have no yet attempted this question bank. Is this a 700 level question?

You are taking the 11th digit from the left to the right whereas the question is asking for the 11 digit from the right to the left starting from the units digit. To elaborate:

Units digit - 1st digit
Tens digit - 2nd digit
Hundreds - 3rd digit
.....so on

As the explanation says, units digit will have 30 2's, tens digit will have 29, hundreds will have 28 and so on.

1st digit - 30
2nd digit - 29
3rd digit - 28
4th digit - 27
5th digit - 26
6th digit - 25
7th digit - 24
8th digit - 23
9th digit - 22
10th digit - 21
11th digit - 20

I think the key on this question is to understand that the 11th digit will sum to 40 (20 x 2), but the carry over from the previous digit will be 4 (21 x 2 = 42 + carry over from previous digit). 40 + 4 = 44

Is the answer 4?

Regards

Sunil

[jnelson0612]

Check out this link: fdp-question-bank-14-t2258.html