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# If x and y are distinct integers, is x + y a prime number?

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Re: If x and y are distinct integers, is x + y a prime number? [#permalink]
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Statement 1 says both x and y are prime. This could mean 2+3 or any other two odd primes. 2+3 = 5 (prime) and any other two primes will always sum to an even number. Insufficient

Statement 2 says their product is odd. This just means x and y are two odd integers--we must forget what St1 says (that both are prime). So you can have 1+3=4 (not prime) or -1+3=2 (prime). Insufficient

Combining the statements, we see that the addition of any two distinct odd prime numbers will always be even and always be at least a multiple of 2 (not prime). Answer is C.
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Re: If x and y are distinct integers, is x + y a prime number? [#permalink]
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Ankur9 wrote:
Bunuel wrote:

Tough and Tricky questions: Number Properties.

If x and y are distinct integers, is x + y a prime number?

(1)
(2) xy is odd.

Kudos for a correct solution.

Source: Chili Hot GMAT

st1---> x and y are prime numbers.
x=2 ; y=3 then x+y= 5 prime
x=5 ; y=2 then x+y=7 prime
x=3 ; y=5 then x+y = 8 not prime

st2--> xy is odd. then both x and y has to be odd.
if x and y both odd then x+y = even and 2 is the only even prime number
x=-1 ; y=3 then x+y=2 prime
x=5; y=3 then x+y=8 not prime
NOt sufficient

combining statement 1 and 2 , we need two odd prime numbers
x=7 ; y=11 then x+y=18 not prime
since sum of two odd number will be even and 2 is the only even prime number thus combining both statements we can answer that x+y is not prime.
Thus [C].

Aaaaa, I am so stupid, didnt really think of the fact that sum of two odd will always even thus the sum can not be prime aaaaaaaaaa
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Re: If x and y are distinct integers, is x + y a prime number? [#permalink]
Bunuel wrote:

Tough and Tricky questions: Number Properties.

If x and y are distinct integers, is x + y a prime number?

(1) x and y are prime numbers.
(2) xy is odd.

Kudos for a correct solution.

Source: Chili Hot GMAT

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If x and y are distinct integers, is x + y a prime number? [#permalink]
I have a question about an edge case and that is when x + y = 2.

I think this can be done by, for example, x = 5 and y = -3. In this case, xy = odd, and x and y are both prime. This would make x + y = 2 which is prime.

If my reasoning is correct, the answer would be E not C.

Am I missing something?
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Re: If x and y are distinct integers, is x + y a prime number? [#permalink]
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DerrickWayne wrote:
I have a question about an edge case and that is when x + y = 2.

I think this can be done by, for example, x = 5 and y = -3. In this case, xy = odd, and x and y are both prime. This would make x + y = 2 which is prime.

If my reasoning is correct, the answer would be E not C.

Am I missing something?

Prime numbers are positive. So, y = -3 doesn't meet the given condition.
Re: If x and y are distinct integers, is x + y a prime number? [#permalink]
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