To find the number greater than 19 and less than 34 that is divisible by both 6 and 10, let’s first identify the divisibility conditions.
A number is divisible by:
- 10 if it ends in 0.
- 6 if it is divisible by both 2 and 3.
Since we are looking for a number that ends in 0 (to be divisible by 10), we narrow down our candidates in the specified range. The numbers between 19 and 34 that end in 0 are:
- 20
- 30
Next, we need to check which of these numbers is also divisible by 6.
Checking 20:
- Ends in 0 (divisible by 10).
To check if 20 is divisible by 6:
- Divisibility by 2: Yes, because 20 is even.
- Divisibility by 3: The sum of digits is \(2 + 0 = 2\), which is not divisible by 3.
Thus, 20 is not divisible by 6.
Checking 30:
- Ends in 0 (divisible by 10).
To check if 30 is divisible by 6:
- Divisibility by 2: Yes, because 30 is even.
- Divisibility by 3: The sum of digits is \(3 + 0 = 3\), which is divisible by 3.
Thus, 30 is divisible by 6.
Since 30 meets all the criteria (greater than 19, less than 34, divisible by 6 and 10), the answer is:
D. 30