Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 10163
GPA: 3.82
Re: Is y^2 + 7y + xy even?
[#permalink]
15 Sep 2015, 09:26
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem.
Remember equal number of variables and independent equations ensures a solution.
Is y^2 + 7y + xy even?
(1) (x + y)(x - y) is a multiple of 4
(2) (x + 2)(x - 2) is a multiple of 4
Transforming the original condition and the question we have y(y+7+x)=even? and thus there are 2 variables (x,y). In order to match the number of variables and equations we need 2 equations and since there is 1 each in 1) and 2), there is high probability that C is the answer.
Using both 1) & 2) together we have (This saves us time)
x=even=4, y=2 yes, x=2sqrt2, y=2 no(since there is no guarantee that x,y are integers) therefore the conditions are not sufficient. The answer is E.
Normally for cases where we need 2 more equations, such as original conditions with 2 variable, or 3 variables and 1 equation, or 4 variables and 2 equations, we have 1 equation each in both 1) and 2). Therefore C has a high chance of being the answer, which is why we attempt to solve the question using 1) and 2) together. Here, there is 70% chance that C is the answer, while E has 25% chance. These two are the key questions. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since C is most likely to be the answer according to DS definition, we solve the question assuming C would be our answer hence using ) and 2) together. (It saves us time). Obviously there may be cases where the answer is A, B, D or E.