Bunuel wrote:
If x is an integer, is 3x + 7 even?
(1) (x – 5)(x + 1) = 0
(2) x is a factor of 105.
Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.
The first step of the VA (Variable Approach) method is to modify the original condition and the question, and then recheck the numbers of variables and equations.
The question that \(3x + 7\) is even is equivalent to the statement that \(x\) is odd, because if \(x\) is odd, \(3x + 7\) is even and if \(x\) is even, \(3x + 7\) is odd.
Condition 1)
\((x-5)(x+1)=0\) is equivalent to \(x = 5\) or \(x = -1\).
Both of them are odd.
Thus this is sufficient.
Condition 2)
The condition 2) that \(x\) is a factor of \(105\) means all factors are odd since \(105\) doesn't have a factor \(2\).
Thus \(x\) must be odd.
Thus this is sufficient, too.
Therefore, the answer is D.
If the original condition includes “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations” etc., one more equation is required to answer the question. If each of conditions 1) and 2) provide an additional equation, there is a 59 % chance that D is the answer, a 38% chance that A or B is the answer, and a 3% chance that the answer is C or E. Thus, answer D (conditions 1) and 2), when applied separately, are sufficient to answer the question) is most likely, but there may be cases where the answer is A,B,C or E.