rsarashi wrote:If a, b, and c are three positive integers, each greater than 1, what is the remainder when the product abc is divided by 2?
(1) If each of a, b, and c is divided by 2, the product of all three remainders is 0.
(2) If each of a, b, and c is divided by 2, the sum of all three remainders is 2.
Dividing an EVEN NUMBER by 2 yields a remainder of 0.
Dividing an ODD NUMBER by 2 yields a remainder of 1.
Thus, to determine the remainder when abc is divided by 2, we need to know whether abc is even or odd.
abc = odd only if a, b, and c are all odd.
Question stem, rephrased:
Are a, b and c all odd?
Statement 1:
For the product of the three remainders to be 0, at least one of the three remainders must be 0.
Since only an even integer will yield a remainder of 0 when divided by 2, at least one of the three integers must be EVEN.
Thus, a, b, and c are NOT all odd, and the answer to the rephrased question stem is NO.
SUFFICIENT.
Statement 2:
If a, b and c are all odd, then each will yield a remainder of 1 when divided by 2, with the result that the sum of the three remainders = 1+1+1 = 3.
Since the sum of the three remainder is not 3, it is not possible that a, b and c are all odd.
Thus, the answer to the rephrased question stem is NO.
SUFFICIENT.
The correct answer is
D.
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