I'm getting (D). Lets start with a few observations:

- All prime numbers will end in a odd number (1,3,5,7,9)
- Even x Even = Even
- Even x Odd = Even

(1) x + 3 is prime, which means that x ends with an even digit, i.e. x is even.
Sufficient

(2) s + 1 is prime, which means that s ends with an even digit, i.e. s is even.
Sufficient

Hi,
the answer to this problem should be A.

stat 1 :
x+3 is prime-x can only be 2,4,6 etc. {x cannot be negative}
this is always even hence whatever we multiple with it will be even

note that if we were not given that x is a positive integer- then this would have been insufficient at x = -1.

stat 2:
s+1 is prime, s can be both 1 and 2. (odd or even). No info about X, thus insufficient

the correct answer is A.

A +1

bblast wrote:Hi,
the answer to this problem should be A.

stat 1 :
x+3 is prime-x can only be 2,4,6 etc. {x cannot be negative}
this is always even hence whatever we multiple with it will be even

note that if we were not given that x is a positive integer- then this would have been insufficient at x = -1.

stat 2:
s+1 is prime, s can be both 1 and 2. (odd or even). No info about X, thus insufficient

the correct answer is A.

(A) If at least one of x or s is even, the product xs will be even. This is because:
ODD × EVEN = EVEN and EVEN × EVEN = EVEN.

Statement (1) tells us that x + 3 is a prime number. Since x is at least 1 (from the question stem), the prime number (x + 3) must be at least 4. 4 is not prime, but all prime numbers greater than 4 are odd, so:
x + 3 = ODD
x = ODD - 3
An ODD number minus another ODD number is always EVEN. x = EVEN.

Since x is even, the product xs will be even and Statement (1) is sufficient.

Statement (2) allows for the possibility that the prime number is 2, where s = 1, which is an ODD. The prime number could also be 3, where s = 2, which is EVEN. The product xs can be odd or even, so Statement (2) is insufficient.

Since Statement (1) is sufficient, and Statement (2) is insufficient, the correct answer is choice (A).

Ah, thanks for correcting me

A + 1

A.

Incase of B s can be either 1 or 2.

1+1 =2 prime number.
2+1= 3 prime number.

So, incase s =1 product will depend on value of X.
Incase s=2 product will be even.

If x and s are both positive integers, is the product of x and s even?
(1) (x + 3) is a prime number.
(2) (s + 1) is a prime number.

1) a can be 2,4,6,8... ending with even numbers.
so x is an even number. Even*odd(s) or even*even(s) = even. sufficient

2) s can be 1,2 and so on.
1 is odd i.e odd(x)*odd = odd but, even(x)*odd = odd/even.
so we are not sure of the outcome. Insufficient

Answer should be A