if p is a multiple of 3 and q is a multiple of 5 which of the following is true?
I think both of them are wrong.
If p is a multiple of 3, it means that p can be expressed as the product of 3 and an integer. Similarly, if q is a multiple of 5, it means that q can be expressed as the product of 5 and an integer.
Now, let's analyze the given options to determine which one is true:
Option 1: p + q is a multiple of 8
To check if p + q is a multiple of 8, we need to see if the sum of two multiples of 3 and 5 will always be divisible by 8.
Let's consider an example. Suppose p = 6 and q = 10, both multiples of 3 and 5, respectively. In this case, p + q = 16, which is not divisible by 8. Hence, Option 1 is not necessarily true.
Option 2: p * q is a multiple of 15
To check if p * q is a multiple of 15, we need to see if the product of two multiples of 3 and 5 will always be divisible by 15.
Let's consider the same example where p = 6 and q = 10. In this case, p * q = 60, which is divisible by 15 because 60/15 = 4. Hence, Option 2 is true.
Option 3: p - q is a multiple of 2
To check if p - q is a multiple of 2, we need to see if the difference between two multiples of 3 and 5 will always be divisible by 2.
Again, let's consider p = 6 and q = 10. In this case, p - q = -4, which is not divisible by 2. Hence, Option 3 is not true.
Therefore, the correct answer is Option 2: p * q is a multiple of 15.