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Updated on: 12 Jan 2014, 07:25
Originally posted by goodyear2013 on 12 Jan 2014, 06:58.
Last edited by goodyear2013 on 12 Jan 2014, 07:25, edited 1 time in total.
Last edited by goodyear2013 on 12 Jan 2014, 07:25, edited 1 time in total.
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
53% (02:12) correct
47%
(02:05)
wrong
based on 219
sessions
History
Date
Time
Result
Not Attempted Yet
If x is a positive integer and z = x! + (x + 2), is z prime?
(1) x is odd.
(2) 2 < x < 12
OE
(1) x is odd.
(2) 2 < x < 12
OE
(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 → z = 11 = prime
If x = 4 → z = 4! + (4 + 2) → z = (4 x 3 x 2 x 1) + 6 → z = 24 + 6 → z = 30 → z = not prime
Insufficient
Combined: x = {3, 5, 7, 9, or 11}
If x = 3, z = 11
If x = 5, z = 5! + (5 + 2), z = (5 x 4 x 3 x 2 x 1) + 7 = prime
If x = 7, z = 7! + (7 + 2), z = (7 x 6 x 5 x 4 x 3 x 2 x 1) + 9, z = (7!) + (3 x 3), z = 3 x [(7!) + 3] = not prime
Insufficient
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 → z = 11 = prime
If x = 4 → z = 4! + (4 + 2) → z = (4 x 3 x 2 x 1) + 6 → z = 24 + 6 → z = 30 → z = not prime
Insufficient
Combined: x = {3, 5, 7, 9, or 11}
If x = 3, z = 11
If x = 5, z = 5! + (5 + 2), z = (5 x 4 x 3 x 2 x 1) + 7 = prime
If x = 7, z = 7! + (7 + 2), z = (7 x 6 x 5 x 4 x 3 x 2 x 1) + 9, z = (7!) + (3 x 3), z = 3 x [(7!) + 3] = not prime
Insufficient
12 Jan 2014, 07:03
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goodyear2013
Number-plugging can give us the answer in less than 30 seconds.
If x = 3, then x! + (x + 2) = 11 = prime.
If x = 7, then x! + (x + 2) = 7! + 9 = {a multiple of 3} + {a multiple of 3} = {a multiple of 3}, which is not a prime.
Two different answers. Not sufficient.
Answer: E.
14 Feb 2021, 03:56
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