mmelendez wrote:
The digital sum of a number is the sum of its digits. For how many of the positive integers 24-125 inclusive is the digital sum a multiple of 7?
A 7
B 8
C 14
D 16
E 20
Kudos if you like this question and the solution I will provide
No way but listing all numbers, but in better way.
First, we count the 2-digit numbers.
The largest 2-digit numbers is 99, and its digital sum is 18 > 14. Hence, we need to consider 2 cases:
Case 1: The digital sum is 7:
From 24, the next number which has digital sum 7 is 25. Now, we have the list:
25, 34, 43, ..., 61, 70 (there are 7 - 2 + 1 = 6 numbers)
Case 2: The digital sum is 14.
Not that the largest unit digit is 9, so the smallest ten digit is 5. Hence, we have the list:
59, 68, 77, ..., 95 (there are 9 - 5 + 1 = 5 numbers)
Second, we count the 3-digit numbers.
The largest possible number is 125, so the number that has largest digital sum is 119. It's digital sum is 11 < 14. Hence, we just need to consider only 1 case: The digital sum is 7:
From 100, the next number which has digital sum 5 is 106. Now we have the list:
106, 115, 124 (there are 2 - 0 + 1 = 3 numbers)
The total possible numbers are: 6 + 5 + 3 = 14 numbers.
The answer is C.
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