Vincen 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
The OA is C.
Do I have to make the entire list? Is there another way to solve this PS question? Experts, I want to see you explanation for this exercise. Thanks.
First, let's determine the two-digit numbers in the range of 24 to 99, inclusive, that have a digital sum of a multiple of 7:
To get a digital sum of 7, it needs to be 70, 61, 25, 52, 34 or 43.
To get a digital sum of 14, it needs to be 77, 68, 86, 59, or 95.
Since no digital sum of a two-digit number can be 21 or more, we see that there are 11 2-digit numbers that meet the criteria.
Now, let's determine the three-digit numbers in the range of 100 to 125, inclusive, that have a digital sum of a multiple of 7:
To get a digital sum of 7, it needs to be 106, 115 or 124.
Since no digital sum of a three-digit number (no more than 125) can be 14 or more, we see that we have a total of three 3-digit numbers that fit the criteria..
Therefore, there are a total of 11 + 3 = 14 such numbers.
Answer: C
