If x and y are positive integers, each of the following could be the greatest common divisor of 30x and 15y except30x. 15y. 15(x + y). 15(x - y). 15,000.

The required option is D) 15(x-y).

Step-by-step explanation:

Consider the provided information.

If x and y are positive integers, each of the following could be the greatest common divisor of 30x and 15y

That means GCD must divide 30x and 15y

must be an integer.

Now consider the provided option.

Option A) 30x

Let x = 1 and y = 2 Then the numbers are 30x = 30, 15y = 30 and 30x = 30

GCD(30,30) = 30 thus the option A can be greatest common divisor.

Option B) 15y

Let x = 1 and y = 1 Then the numbers are 30x = 30,  15y = 15 and 15y = 15

GCD(30,15) = 15 thus the option B can be greatest common divisor.

Option C) 15(x+y)

Let x = 1 and y = 1 Then the numbers are 30x = 30, 15y = 15 and 15(x+y) = 30

GCD(30,15) = 15 ≠ 30 Thus, the option C cannot be greatest common divisor because 15(x+y) > 15y for any positive integer.

Option D) 15(x-y)

Let x = 2 and y = 1 Then the numbers are 30x = 60,  15y = 15 and 15(x-y) = 15

GCD(60,15) = 15 thus the option D can be greatest common divisor.

Option E) 15000

Let x = 500 and y = 1000 Then the numbers are 30x = 15000, 15y = 15000 and 15000

GCD(15000,15000) = 15000 thus the option D can be greatest common divisor.

Hence, the required option is D) 15(x-y).

7200

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