Hi All,
This question can be solved by TESTing VALUES, although you'll have to do a little bit of extra work at the end to prove that your answer is correct.
We're told that X is a POSITIVE INTEGER. We're asked if (X-1)(X+1) is divisible by 24. This is a YES/NO question.
Fact 1: X is NOT divisible by 3.
IF...
X = 1
(0)(2) = 0 and the answer to the question is YES.
X = 2
(1)(3) = 3 and the answer to the question is NO.
Fact 1 is INSUFFICIENT
Fact 2: X-1 is divisible by 2
This means that X MUST be ODD.
IF...
X = 1, then the answer to the question is YES (we did the work in Fact 1 already).
X = 3
(2)(4) = 8 and the answer to the question is NO
Fact 2 is INSUFFICIENT
Combined, we know...
X MUST be odd
X is NOT divisible by 3
IF....
X = 1, then the answer to the question is YES
X = 5
(4)(6) = 24 and the answer to the question is YES
X = 7
(6)(8) = 48 and the answer to the question is YES
X = 11
(10)(12) = 120 and the answer to the question is YES
We have a consistent result.
Combined, SUFFICIENT
Final Answer:
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Rich
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