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DS: is the product of x and s even? Help

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DS: is the product of x and s even? Help

by mahesh.aradhya » Thu Aug 18, 2011 7:43 am
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.

A. Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not.
B. Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not.
C. Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient.
D. Either statement BY ITSELF is sufficient to answer the question.
E. Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, meaning that further information would be needed to answer the question


On solving I got answer as C.

Is this correct?.Correct me if m wrong.
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by kmittal82 » Thu Aug 18, 2011 7:50 am
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
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by bblast » Thu Aug 18, 2011 8:36 am
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.
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by killer1387 » Thu Aug 18, 2011 8:42 am
A +1
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by mahesh.aradhya » Thu Aug 18, 2011 9:33 am
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).
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by kmittal82 » Thu Aug 18, 2011 2:01 pm
Ah, thanks for correcting me :)

A + 1
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by czarczar » Fri Aug 19, 2011 6:05 am
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.
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by GmatKiss » Fri Aug 19, 2011 9:16 am
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
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