If a, b & c are integers, is abc odd?

Hi All,

We're told that A, B and C are INTEGERS. We're asked if (A)(B)(C) is ODD. This is a YES/NO question and can be solved with Number Properties and TESTing VALUES.

1) (A)(B) is ODD

Since A and B are both integers, the only way the product of those two numbers to be odd is if BOTH A and B are ODD. However, we don't know whether C is odd or even.
IF...
A=1, B=1, C=1, then (A)(B)(C) = 1 and the answer to the question is YES
A=1, B=1, C=2, then (A)(B)(C) = 2 and the answer to the question is NO
Fact 1 is INSUFFICIENT

2) (B)(C) is ODD

Since B and C are both integers, the only way the product of those two numbers to be odd is if BOTH B and C are ODD. However, we don't know whether A is odd or even.
IF...
A=1, B=1, C=1, then (A)(B)(C) = 1 and the answer to the question is YES
A=2, B=1, C=1, then (A)(B)(C) = 2 and the answer to the question is NO
Fact 2 is INSUFFICIENT

Combined, we know...
A and B are ODD
B and C are ODD
Thus, (A)(B)(C) will ALWYS be ODD and the answer to the question is ALWAYS YES.
Combined, SUFFICIENT

Final Answer:

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