What is the sum of all digits which appear in all the integers from 10 to 100?
- A855
- B856Correct
- C910
- D911
Explanation
To find the sum of all digits from 10 to 100, we break the range into two parts: 10 to 99 and the number 100.
First, consider the numbers 10 to 99. These are 90 two-digit numbers. In the tens place, each digit from 1 to 9 appears 10 times. For example, 1 appears in 10 through 19, 2 appears in 20 through 29, and so on. The sum of tens digits is 10 multiplied by the sum of 1 through 9. Sum of 1 to 9 is 45. So, 10 multiplied by 45 equals 450.
In the units place, each digit from 0 to 9 appears 9 times. For example, 1 appears in 11, 21, 31, up to 91. The sum of units digits is 9 multiplied by the sum of 0 through 9. So, 9 multiplied by 45 equals 405.
The total sum for numbers 10 to 99 is 450 plus 405, which equals 855.
Finally, we add the digits of the number 100. The digits are 1, 0, and 0. Their sum is 1.
The grand total is 855 plus 1, which equals 856.
Therefore, the correct option is B.
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