Bunuel wrote:
GMAT CLUB'S FRESH QUESTION
If x and y are positive integers, is x odd?
(1) x - 2y is a prime number
(2) x + 2y is a prime number
The point to remember in this question is that x and y are given as positive integers, therefore x and y can take values such as 1, 2, 3...
Now, we need to check if x can be expressed as 2n+1
1) Given x-2y is prime
Here, 2y will be at least 2 (since lowest value y can take is 1)
This shows that x can take values such as 4 or 5:
If x is 4, then x-2y=4-2=2 (which is a prime number).
Thus, x is evenand
If x is 5, then x-2y=5-2=3 (which is a prime number).
Thus, x is oddSince, we cannot conclusive check if x will be even or odd, this is insufficient.
2) Given x+2y is prime
Here, again 2y will be at least 2 (since lowest value y can take is 1)
Now, we need to check
only for values 2 and 3 because all prime numbers that are greater than 2 are odd.If x+2y=2, x can only take value 0 which is not possible since x has to a positive integer. In fact, x can never take 2 as a value in order to satisfy this equation.
If x+2y=3, then x=1 (which is odd). Thus, we have safely concluded that no even value of x can make x+2y result in a prime number.
Hence, this is sufficientAnswer is B