lheiannie07 wrote:If integer n is greater than 1, Does n have more than two distinct factors?
(1) 11! + 2 < n < 11! + 11
(2) n is not a prime number.
If n is prime, it will have exactly 2 distinct factors (1 and itself).
If n is NOT prime, then it will have more than 2 distinct factors.
Thus, the question stem can be rephrased as follows:
Is n prime?
Statement 1: 11! + 2 < n < 11! + 11
11! + 2 and 11! + 11 are huge numbers, implying that n must be very large.
If a DS problem asks whether a very large integer is prime, the answer must be NO.
The reason:
While there are straightforward ways to prove that a very large integer is NOT prime -- if the integer is even, if the units digit is 5, and so on -- there is no straightforward way to prove that a very large integer IS prime.
Thus, no work is needed here.
Since we cannot be expected to prove in Statement 1 that n IS prime, Statement 1 must provide sufficient information to determine that n is NOT prime.
SUFFICIENT.
Statement 2: n is not a prime number
SUFFICIENT.
The correct answer is
D.
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