Question

Determine the number greater than 19 and less than 34 that is divisible by 6 and 10

Reminder, a number is divisible by 10 if the last digit ends in 0 and a number is divisible by 6 if its also divisible by 3 and 2, a number is divisible by 2 if the final digit ends in an even number and a number is divisible by 3 if the sum of all the digits is divisible by 3

A. 20

B. 24

C. 60

D. 30

Answer 1

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**