Which statement is correct? Explain your choice.
If a numbers to divisible by 3 and 6, then it is divisible by 18.
If a number is divisible by 2 and 9, then it is divisible by 18.
The correct statement is: "If a number is divisible by 3 and 6, then it is divisible by 18."
To determine the correctness of this statement, we need to understand the concept of divisibility. Divisibility means that one number can be divided by another number without leaving a remainder. In this case, we are considering divisibility by 18.
We know that 18 is a multiple of both 3 and 6, meaning that it can be expressed as 3 * 6. Therefore, any number divisible by both 3 and 6 will also be divisible by 18.
To explain why the second statement is incorrect, let's consider an example. Suppose we have the number 36. It is divisible by 2 (since it is even) and also divisible by 9 (since the sum of its digits is a multiple of 9). However, 36 is not divisible by 18, as 18 does not evenly divide 36.
Therefore, the statement "If a number is divisible by 2 and 9, then it is divisible by 18" is not true in general. While some numbers may satisfy both conditions, not all of them are divisible by 18.