Hi All,
These types of questions will almost always involve some type of pattern in the numbers (or in this case, the digits of the numbers). Here's one way to solve this problem (based on the patterns in the digits):
We're asked to deal with the numbers 1 to 110, inclusive. I'm going to break this into two groups: 1 - 99 and 100 - 110
The numbers from 1 to 99 follow an interesting pattern: each digit appears 10 times in the "tens spot" and 10 times in the "units spot"
For example, the digit 1:
10, 11, 12, …..19 ---> 10 times in the "tens spot"
1, 11, 21, 31….91 ---> 10 times in the "units spot"
So, we have to multiply each digit by 20 to get it's total sum. There's a faster way to do it though:
1+2+3+4+5+6+7+8+9 = 45
45 x 20 = 900
So the sum of the digits of the numbers from 1 to 99 is 900
Now, for the numbers from 100 to 110
We have 11 "ones" in the "hundreds spot" = 11
We have the digits 1 to 9 in the "ones spot" = 45
We have one more 1 in the "tens spot" = 1
11+ 45 + 1 + 900 = 957
Final Answer:
GMAT assassins aren't born, they're made,
Rich
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