Strongt wrote: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?


1
2
4
6
9

Answer is c

is there a simple/effecient way to solve this question in less than 10 minutes

Calculate just enough to see the pattern.

The UNITS digit of p will be determined by the sum of 30 2's: 30*2 = 60.
The TENS digit of p will be determined by whatever is carried over from the units place and the sum of 29 2's: 29*2 = 58.
The HUNDREDS digit of p will be determined by whatever is carried over from the tens place and the sum of 28 2's: 28*2 = 56.

The results are DECREASING CONSECUTIVE EVEN INTEGERS.

So the sums that will determine the digits of p, from left to right, are:
40-42-44-46-48-50-52-54-56-58-60.

Now work from right to left to see what gets carried over from one sum to the next.
In the list below, each integer in red represents a digits of p; the other value gets carried over to the next sum.
60 is in the units place, so the units digit is 0.
Carry the 6.
58+6 = 64.
Carry the 6.
56+6 = 62.
Carry the 6.
54+6 = 60.
Carry the 6.
52+6 = 58.
Carry the 5.
50+5 = 55.
Carry the 5.
48+5 = 53.
Carry the 5.
46+5 = 51.
Carry the 5.
44+5 = 49.
Carry the 4.
42+4 = 46.
Carry the 4.
40+4 = 44.
The 11th digit from the right = 4.

The correct answer is C.

Thanks GMATGuruNY

Appreciate you taking the time to answer this but i've been trying to figure it out for 20 minutes!

I got the 1st part where you identified the consecutive even integers.

But I'm confused regarding the numbers carried over to the next sum!

Thank you

without carry sum of the 2's for the 11th digit=20*2=40
4 gets carried from the 10th positio.

40+4=44

so resulting digit=4

Strongt wrote:Thanks GMATGuruNY

Appreciate you taking the time to answer this but i've been trying to figure it out for 20 minutes!

I got the 1st part where you identified the consecutive even integers.

But I'm confused regarding the numbers carried over to the next sum!

Thank you

Please see the following illustration:


Units place:
The sum of the 30 2's is 60.
60 units = 6 TENS and 0 units.
Thus, the units digit is 0, and the 6 TENS are carried over to the TENS place.

Tens place:
When we add the 6 tens carried over from the units place to the sum of the 29 2's, we get 6+58 = 64.
64 tens = 6 HUNDREDS and 4 TENS.
Thus, the tens digit is 4, and the 6 HUNDREDS are carried over to the HUNDREDS place.

Hundreds place:
When we add the 6 hundreds carried over from the tens place to the sum of the 28 2's, we get 6+56 = 62.
62 hundreds = 6 THOUSANDS + 2 HUNDREDS.
Thus, the hundreds digit is 2, and the 6 THOUSANDS are carried over to the THOUSANDS place.

And so on.
The rest of the calculations are illustrated here:


The 11th digit from the right is 4.