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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