Hi All,
We're told that X, Y and Z are INTEGERS and (X)(Y) + Z is an ODD integer. We're asked if X is an EVEN integer. This is a YES/NO question and can be solved by either TESTing VALUES or using Number Properties. While it certainly appears more complex than a typical DS prompt, the basic Number Property rules involved are just about multiplication and addition, so you might find it easiest to think in terms of those patterns (although this question is step-heavy and you do have to be thorough with your work and not miss any of the options).
To start, since (X)(Y) + Z is an ODD, we can 'map out' the limited number of possibilities for the 3 variables. We could have...
(X)(Y) = Even, Z = Odd
(X)(Y) = Odd, Z = Even
From here, we then need to sub-divide (X)(Y):
-IF (X)(Y) is Even, then either both are Even OR one is Odd and the other is Even (this includes the option in which one is 0 and the other could be any integer).
-IF (X)(Y) is Odd, then both MUST be Odd
This ultimately means that these are the only 4 options for the three variables:
X = Even, Y = Even, Z = Odd
X = Even, Y = Odd, Z = Odd
X = Odd, Y = Even, Z = Odd
X = Odd, Y = Odd, Z = Even
Having this list should make working through the two Facts a lot easier.
(1) (X)(Y) + (X)(Z) is an EVEN integer
Using the 4 options above, (X)(Y) + (X)(Z) would be....
(E)(E) + (E)(O) = Even... This IS a match
(E)(O) + (E)(O) = Even... This IS a match
(O)(E) + (O)(O) = Odd... This is NOT a match
(O)(O) + (O)(E) = Odd... This is NOT a match
Two of the options fit Fact 1 - and they BOTH require that X be EVEN, so the answer to the question is ALWAYS YES.
Fact 1 is SUFFICIENT
(2) Y + (X)(Z) is an ODD integer
Using the 4 options above, (Y) + (X)(Z) would be....
(E) + (E)(O) = Even... This is NOT a match
(O) + (E)(O) = Odd... This IS a match
(E) + (O)(O) = Odd... This IS a match
(O) + (O)(E) = Odd... This IS a match
In the three options that fit Fact 2, X is sometimes Even (a "Yes" answer) but sometimes Odd (a "No" Answer).
Fact 2 is INSUFFICIENT
Final Answer:
GMAT assassins aren't born, they're made,
Rich
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