Question

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.

Answer 1

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

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

`(30x)/(GCD)\ \text{and}\ (15y)/(GCD)` 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).