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[hareesh860]

If x and y are distinct integers, is x + y a prime number?
(1) x and y are prime numbers.
(2) x × y is odd.

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Statement 1:
x & y are prime so x+y can't be prime except when either x or y is 2.For every other prime number x+y=even.
So not sufficient

Statement 2:
x*y is odd, so x & y can both be odd and it doesn't gurantee x & y to be prime.
x=9,y=7
x=9,y=15
x=5,y=3
So Not sufficient.

Taking both Statement 1 & 2:

From statement 1 we know that either x or y could be equal to 2. But statement 2 tell us neither of them can be 2 as their product is odd.

Hence x+y can't be prime.

So answer is C

[Anurag@Gurome]

If x and y are distinct integers, is x + y a prime number?
(1) x and y are prime numbers.
(2) x × y is odd.

(1) If x = 2, y = 3, then x + y = 2 + 3 = 5, a prime number.
If x = 3, y = 5, then x + y = 3 + 5 = 8, not a prime number.
No definite answer; NOT sufficient.

(2) x × y is odd implies that x and y both should be odd integers.
If x = 1, y = 3, then x + y = 4, not a prime number.
If x = -1, y = 3, then x + y = 2, a prime number.
No definite answer; NOT sufficient.

Combining (1) and (2), x and y are prime numbers, where x and y cannot be equal to 2 (as they are odd integers). So, x and y will be positive odd integers, as a prime number is a natural number greater than 1. Hence, x and y will be positive odd integers, so x + y will always be even integer greater than 2, which will not result in a prime number. So, x + y will not be a prime number; SUFFICIENT.

The correct answer is C.

[mj78ind]

If x and y are distinct integers, is x + y a prime number?
(1) x and y are prime numbers.
(2) x × y is odd.

Stmt 1 - 5, 3. Thus 5+3 not prime. 2,3 2+3 prime. Thus INSUFFICIENT.

Stmt 2 - x*y can be odd ONLY if x AND y are odd. And we know that odd + odd = even. If x and y are positive then x+y can never be prime, however if x = 9, y = -7 then x+y = prime. Thus INSUFFICIENT.

Stmt 1 and 2: Now from 1 we know x and y are prime (thus non - negative) and from 2 we know they are both odd. Thus x+y has to be non prime. Hence sufficient.

Hence C

[dadu]

If x and y are distinct integers, is x + y a prime number?
(1) x and y are prime numbers.
(2) x × y is odd.

(1) If x = 2, y = 3, then x + y = 2 + 3 = 5, a prime number.
If x = 3, y = 5, then x + y = 3 + 5 = 8, not a prime number.
No definite answer; NOT sufficient.

(2) x × y is odd implies that x and y both should be odd integers.
If x = 1, y = 3, then x + y = 4, not a prime number.
If x = -1, y = 3, then x + y = 2, a prime number.
No definite answer; NOT sufficient.

Combining (1) and (2), x and y are prime numbers, where x and y cannot be equal to 2 (as they are odd integers). So, x and y will be positive odd integers, as a prime number is a natural number greater than 1. Hence, x and y will be positive odd integers, so x + y will always be even integer greater than 2, which will not result in a prime number. So, x + y will not be a prime number; SUFFICIENT.

The correct answer is C.

Can you please explain this a bit more. Is (2) alone not sufficient? With (2), we know that both x and y are odd (and distinct). And since the sum of two odds is always even, we know that x+y cannot be prime.