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.
My answer is none
I think most people here are assuming that x and y are integers. This is not a given.
1> x = y
Lets use some susbtitution:
If 3x/y = 3 then x = y [x=4, y=4]
If 3x/y = 5 then x = 5/3y [x=5/3, y=1]
This shows that x = y is not necessarily true.
2> y = 1
This will mean 3x/y = 3x. 3x cannot be a prime number. Hence this is not true either.
3> x and y prime
If 3x/y is prime and greater than 2 then it is not necessary for x and y to be prime. Try a few numbers:
x = 5/3, y = 1
x = 14/3, y = 2