If x is a positive integer and z = x! + (x + 2), is z prime?
(1) x is odd.
(2) 2 < x < 12
OE
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(1) x is odd.
(2) 2 < x < 12
OE
[Reveal] Spoiler:
(1):
If x = 1 → z = 1! + (1 + 2) → z = 1 + 3 → z = 4 → z = not prime
If x = 3 → z = 3! + (3 + 2) → z = (3 x 2 x 1) + 5 → z = 6 + 5 → z = 11 → z = prime
Insufficient
(2): Since some of the possible values for x are even, it’s possible that z could be a non-prime.
But x could also equal odd value that would yield a prime for z.
If x = 3 →
If x = 1 → z = 1! + (1 + 2) → z = 1 + 3 → z = 4 → z = not prime
If x = 3 → z = 3! + (3 + 2) → z = (3 x 2 x 1) + 5 → z = 6 + 5 → z = 11 → z = prime
Insufficient
(2): Since some of the possible values for x are even, it’s possible that z could be a non-prime.
But x could also equal odd value that would yield a prime for z.
If x = 3 →
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