Problem Solving

If y ≠ 3 and 3x/y is a prime integer greater than 2, which of the following
must be true?
I. x = y
II. y = 1
III. x and y are prime integers.
(A) None
(B) I only
(C) II only
(D) III only
(E) I and III

This is very tricky so I might go wrong here but:

We can go with either x or y here. When we take a quick look at the different statements we see that y is represented in every single one of them so this should be easier.

3x/y=(ANY GIVEN PRIME > 2)
y=3x/(ANY GIVEN PRIME > 2)

I. x=y
You can easily solve for y to equal x (ANY GIVEN PRIME > 2) must equal 3, however things don't end there. It can just as easily be 5,11,17 and it will solve for 3x/y=(ANY GIVEN PRIME). In short X=Y does solve for 3x/y=(ANY GIVEN PRIME > 2), however it doesn't cover everything so it doesn't NEED to be true. //doesn't need to be true

II. y=1
Only by looking at y=3x/(ANY GIVEN PRIME > 2) and not having any restrictions for x and y you can conclude that it's solvable for any y not just 1 //doesn't need to be true

III. As II you can conclude it's solvable for any y not just primes. //doesn't need to be true

So in my opinion it should be A.
However it took me more than 2 minutes to solve(If it's a correct solution of course) so if anyone knows some tips or tricks we can use here please share them.

let x=25, y=15

3x/y = 3*25/15 = 5

which is a prime > 2..........and y is not equal to 3

now we go with choices

I: x (25) is not equal to y(15): False

II: again y is not equal to 1: False

III: 25 and 15 are not primes

I will go with NONE, as this is a must be true question.

B) I only
I am not sure though...
what is the OA ?

If y ≠ 3 and 3x/y is a prime integer greater than 2, which of the following
must be true?
I. x = y
II. y = 1
III. x and y are prime integers.
(A) None
(B) I only
(C) II only
(D) III only
(E) I and III

None a)



I) 3*35/21

3 * 6/6


II) y=1

x=2 y=2 x/y*3 is still a prime 3 > 2

Need not be true

III) x and y are prime integers.

x=4 y=4 x=2 y=2

Need not be true

Another vote for None

none