yellowho wrote:If x and y are positive integers, what is
the value of y ?
(1) x is an even multiple of y.
(2) x-y=2
Hi there!
[I´ve slightly modified the question stem, because the fraction mentioned in the original problem has no contribution/restriction involved.]
(1) Insufficient
Take x = 2 and y = 1
Take x = 4 and y = 2
Important: please note that from sttm (1) we may say that
x = My, where M is necessarily even whenever y is odd. (When y is even, we just know that M is an integer, but it can be odd or even.)
(2) Insufficient
Take x = 4 and y = 2
Take x = 6 and y = 4
(1+2) Sufficient (This one is the hard one to justify, isn´t it?)
Please note that My = x = y+2 implies (*) y(M-1) = 2, where y and M-1 are integers. That means both are DIVISORS of 2, therefore we should look at -2, 2, -1 and 1 only as candidates for them!
From the fact that y>0, there are only two possibilities for y: 1 and 2.
If y =1 , from the sentence in bold we would have M-1 also odd, therefore y(M-1) could not be even (nor equal to 2, for sure).
The only possible solution for y is therefore 2, and we are done.
POST-MORTEM: take y = 2 in (*) to realize that x = My = 2*2 = 4, therefore (x,y) = (4,2) is the only pair that satisfies the question stem and both statements taken together.
Regards,
Fabio.
