monir6000 wrote:

x and y are positive integers. If x is a prime factor of y^2 , which of the following MUST be true?

A. x is even

B. x=y^2

C. y/x is even

D. x/y <=1

E. x+1 is also the prime factor of y^2

Let’s go through each answer choice:

A. x is even

If we let x = 3 and y = 3, we can see that x is a prime factor of y^2. So x does not need to even. Choice A is not correct.

B. x = y^2

Using the same numbers for x and y as in choice A, we see that choice B is not correct also.

C. y/x is even

Using the same numbers for x and y as in choice A, we see that choice C is not correct also.

D. x/y <=1

Using the same numbers for x and y as in choice A, we see that choice D might be correct. Let’s examine choice E.

E. x+1 is also the prime factor of y^2

Using the same numbers for x and y as in choice A, we see that choice D can’t be correct since x + 1 = 4 is not a prime factor y^2 = 9.

Thus, the correct answer must be D.

Answer: D

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