DS- NUmber properties Manhattan CATs

[sandeep1306]

If x and y are positive integers and 3x + 5 < x + 11, is x a prime number?

(1) The sum of x and y is even.

(2) The product of x and y is odd.

OA is B

[Frankenstein]

Hi,
3x+5 < x+11
So, 2x < 6 => x<3
As x and y are positive integers, x=1 or 2
From(1):
sum of x and y is even.
if y is odd, x=1
if y is even, x=2
Not sufficient
From(2):
product of x and y is odd. So, x and y are both odd.
So, x=1 which is not prime
Sufficient

Hence, B

[amit2k9]

x<3 means x can be either 1 or 2.

a y can be 3,5 or 4,6 with x 1,2. not sufficient.

b x cannot be 2. thus B it is.