Number system

parallel_chase wrote:

nikhilagrawal wrote:35. If y ? 3 and 2x/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.

CASE III if x and y both are prime integers. Lets plug in values to find out.

if x=13, y=2 then 2x/y= 13
if x=5 , y=7 then 2x/y is not even an integer.

You've done this backwards, logically (and so has another post above). We know that 2x/y is a prime. That's a fact, provided in the question. It's absolutely impossible for x to be 5, and y to be 7, because then 2x/y is not a prime. You can't just assume x and y are any primes; you can only assume they are primes that make 2x/y an integer. Still, if we want to know whether III) must be true, we want to see if it's possible that it's false: that is, we want to see if we can find examples for x and y which are *not* prime, that still make 2x/y a prime.

What do we know: 2x/y is an odd prime- let's call it p. So:

2x/y = p
2x = py

The primes that divide the left side must divide the right side. So y is divisible by 2, and x is divisible by p. That's all we know, though. It could be that p is 5, y is 10, and x is 25, for example. So III) does not need to be true. (I'm assuming x and y need to be positive integers- I'd guess this should have been mentioned in the question).