If a, b, and c are integers. Is abc+ab+c an odd?
1) ac=odd
2) ab=odd
Source : Math Revolution
Official Answer : D
1) ac=odd
2) ab=odd
Source : Math Revolution
Official Answer : D
Hi ziyuenlau,
This DS question can be solved with Number Properties, although you should be careful to write everything on your pad so that you don't miss any of the details.
We're told that A, B and C are all INTEGERS. We're asked if (A)(B)(C) + (A)(B) + C is an ODD number. This is a YES/NO question.
1) (A)(C) = ODD
This Fact tells us that BOTH A and C are ODD integers. If we 'plug' that information into the question, we get...
Is.... (B)(Odd) + (B)(Odd) + (Odd) = Odd?
IF....
B is Odd, then....
(Odd)(Odd) + (Odd)(Odd) + (Odd) = the sum of 3 Odd numbers, which IS Odd - and the answer to the question is YES.
B is Even, then....
(Even)(Odd) + (Even)(Odd) + (Odd) =
(Even) + (Even) + (Odd) = Odd - and the answer to the question is YES.
The answer is ALWAYS YES.
Fact 1 is SUFFICIENT
2) (A)(B) = ODD
This Fact tells us that BOTH A and B are ODD integers. If we 'plug' that information into the question, we get...
Is.... (C)(Odd) + (Odd) + (C) = Odd?
IF....
C is Odd, then....
(Odd)(Odd) + (Odd) + (Odd) = the sum of 3 Odd numbers, which IS Odd - and the answer to the question is YES.
C is Even, then....
(Even)(Odd) + (Odd) + (Even) =
(Even) + (Odd) + (Even) = Odd - and the answer to the question is YES.
The answer is ALWAYS YES.
Fact 2 is SUFFICIENT
Final Answer: D
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