Kaczet wrote:
There are 108 integers. 50% of the integers have 5 as unit digit and 50% have 0 as unit digit. 1/3 of integers have 2 as tenth digit, 1/3 of integers have 6 as tenth digit and 1/3 of integers have 8 as tenth digit.
What is the tenth digit of the sum of those 108 integers?
(A) 8
(B) 3
(C) 6
(D) 2
(E) 0
Hi,
In general, we can write two-digit numbers as follows:
\(n_i = a_i + 10b_i\) .
In the above question \(a_i \in \{0,5\}\) and \(b_i \in \{2,6,8\}\).
From question we have the following information:
54 numbers with 5 as unit digit
54 numbers with 0 as unit digit
36 numbers with 2 as the tens digit
36 numbers with 6 as the tens digit
36 numbers with 8 as the tens digit
Sum of all the numbers = 36*10 (2 + 6 + 8) + 54*1*(5 + 0) = 6030.
Hence, at tens digit of the sum of 108 integers = 3. Answer (B).
Note: In the question prompt "tenth" should be replaced by "tens".
Thanks.