GMAT Question of the Day - Data Sufficiency - Number Properties
If z and x are integers is (z^3 + x)(z^4 + x) even?
(1) x^3 + x^2 is even
(2) (z^2 + x^2)/2 is odd
GMAT Question of the Day Solution
Simplify GMAT DS questions. Break down what the question is asking. Take this seriously. It's your job on DS questions to figure out how to simplify the question. On this GMAT question of the day we're really being asked if z + x is even which further breaks down to: Do x and z have the same parity? What about the exponents? Provided that the numbers themselves are integers and that the exponents are positive integers the exponents do not change the oddness or evenness. Usually the GMAT puts in exponents to distract you from the real question.
Statement (1) only tells about x. Insufficient. Statement (2) tells us that z + x must be even. Why? When divided by 2 only an even number can result in an integer. In this case that even number only has one two as a factor and so when divided by two the result is an odd number. So the given expression must be even. The answer is yes. Sufficient.