honchos
The sum of the digits used to write the sum 10 + 11 + 12 + 13 is 10. What is the sum of the digits used to write the sum of the integers from 1 to 110, inclusive?
A. 900
B. 911
C. 955
D. 957
E. 1001
IMPORTANT: Always check the answer choices before beginning any solution. The answer choices may hint at an approach and/or suggest that you can skip tedious calculations. Here, the units digits in the answer choices are all different, which suggests that I may be able to avoid some "grunt" work.
First, let's examine the numbers from 00 to 99 inclusive (i.e., 00, 01, 02, .... 97, 98, 99)
[note: adding 00 to the mix doesn't change the final answer]Notice that there are 100 digits from 00 to 99 inclusive.
Also notice that the digits in the tens and units position are
equally distributedSo, in the
UNITS position, there will be ten 0's, ten 1's, ten 2's . . . ten 8's and ten 9's
In the
TENS position, there will be ten 0's, ten 1's, ten 2's . . . ten 8's and ten 9's
So, the sum of
ALL DIGITS from 00 to 99 will equal 20(1+2+3+...7+8+9)
IMPORTANT: We don't need to calculate 20(1+2+3+...7+8+9). We need only recognize that the units digit will equal 0. That is 20(1+2+3+...7+8+9) =
??0From here, we need to add the digits in 100 to 110 inclusive.
To do so, we can use Rich's approach, or we might even list the values and add them in our head, since there aren't many to add here.
When we add the digits in 100 to 110 inclusive, we get
57 So, the sum of the digits from 00 to 110 inclusive =
??0 +
57 = ??
7Since only D has a 7 in the units position, this is the correct answer.
Cheers,
Brent