Data Sufficiency

Is x+1 a factor of 12?

1. x+1 is even
2. x+1 is a factor of 2 and 3

Please explain your answer

(1) x+1 is even --> clearly insufficient, x+1 could be 2 or 30.

(2) x+1 is a factor of 2 and 3

My query is even though A is not sufficent for ans, still it should holds true for solution, I mean X+1 must be even though it cant solely give ans, " which solution contradicts" given below
[spoiler]--> 2 and 3 are consecutive integers, consecutive integers are co-prime, which means that they do not share ANY common factor but 1 (for example 5 and 6, two consecutive integers share only one common factor: 1). So as x+1 is a factor of BOTH 2 and 3 then x+1=1 and 1 is a factor of 12. Sufficient.

Answer: B[/spoiler]

The problem can be rephrases as follows:

vipulgoyal wrote:Is x+1 a factor of 12?

1. x+1 is even
2. x+1 is a factor of 2 and 3

Statement 1: x+1 is even
If x+1=2, then x+1 is a factor of 12.
If x+1=100, then x+1 is not a factor of 12.
INSUFFICIENT.

Statement 2: x is a factor of 2 and 3
Only one positive integer divides evenly into both 2 and 3:
1.
Since x+1 = 1, x+1 is a factor of 12.
SUFFICIENT.

The correct answer is B.

vipulgoyal wrote:Is x+1 a factor of 12?

1. x+1 is even
2. x+1 is a factor of 2 and 3

[/spoiler]

Question : Is x+1 a factor of 12?

Factors of 12 = 1, 2, 3, 4, 6, 12

Question Rephrased : Is X+1 any one of the numbers {1, 2, 3, 4, 6, 12}?
To be Answered in the form of YES/NO

Statement 1) x+1 is even
i.e. X+1 can be 2, 4, 6, 8, 10 ... etc.
i.e. X can be 1 or 3 YES or 7 NO
INSUFFICIENT

Statement 2) x+1 is a factor of 2 and 3
Factors of 2 = 1, 2
Factors of 3 = 1, 3
i.e. X+1 is definitely part of the set {1, 2, 3, 4, 6, 12} YES
SUFFICIENT

Answer: Option B