Official Solution: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.
Since we have 3 variables (x, y and z) and 0 equations, E is most likely to be the answer. So, we should consider conditions 1) and 2) together first.
Conditions 1) and 2):
There are two cases to consider.
Case 1: If x, y, and z are all even, then the answer is 'yes'
Case 2: If x, y, and z are all odd, then the answer is also 'yes'
Since no other cases are possible, both conditions are sufficient, when taken together.
Since this is an integer question (one of the key question areas), CMT
(Common Mistake Type) 4(A) of the VA (Variable Approach) method tells us that we should also check answers A and B.
Condition 1)
Since it tells us nothing about y, condition 1) is not sufficient.
Condition 2)
Since it tells us nothing about y, condition 2) is not sufficient.
Therefore, C is the answer.
Normally, in problems which require 2 equations, such as those in which the original conditions include 2 variables, or 3 variables and 1 equation, or 4 variables and 2 equations, each of conditions 1) and 2) provide an additional equation. In these problems, the two key possibilities are that C is the answer (with probability 70%), and E is the answer (with probability 25%). Thus, there is only a 5% chance that A, B or D is the answer. This occurs in common mistake types 3 and 4. Since C (both conditions together are sufficient) is the most likely answer, we save time by first checking whether conditions 1) and 2) are sufficient, when taken together. Obviously, there may be cases in which the answer is A, B, D or E, but if conditions 1) and 2) are NOT sufficient when taken together, the answer must be E.
Answer: C
_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spareThe one-and-only
World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $79 for 1 month Online Course""Free Resources-30 day online access & Diagnostic Test""Unlimited Access to over 120 free video lessons - try it yourself"