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08 Jul 2014, 07:07
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
67% (01:53) correct
33%
(01:45)
wrong
based on 794
sessions
History
Date
Time
Result
Not Attempted Yet
If x is a positive integer greater than 1, is x! + x + 1 a prime number?
(1) x < 10
(2) x is odd
OE
(1) x < 10
(2) x is odd
OE
(1) INSUFFICIENT
If x = 2: 2! + (2 + 1) = 5, which is prime.
If x = 3: 3! + (3 + 1) = 6 + (3 + 1) = 10, which is not prime.
(2) SUFFICIENT:
If x = 3: 3! + (3 + 1) = 10, which is not prime.
If x = 5: 5! + (5 + 1) = (5 × 4 × 3 × 2 × 1) + 6.
This expression must be divisible by 3, since both of its terms are divisible by 3.
Furthermore it must be even, because both terms are even.
Therefore, it is not a prime number.
If x = 2: 2! + (2 + 1) = 5, which is prime.
If x = 3: 3! + (3 + 1) = 6 + (3 + 1) = 10, which is not prime.
(2) SUFFICIENT:
If x = 3: 3! + (3 + 1) = 10, which is not prime.
If x = 5: 5! + (5 + 1) = (5 × 4 × 3 × 2 × 1) + 6.
This expression must be divisible by 3, since both of its terms are divisible by 3.
Furthermore it must be even, because both terms are even.
Therefore, it is not a prime number.
08 Jul 2014, 07:55
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goodyear2013
If x is a positive integer greater than 1, is x! + x + 1 a prime number?
(1) x < 10.
If x=2, then x! + x + 1 = 5 = prime.
If x=3, then x! + x + 1 = 10, not a prime.
Not sufficient.
(2) x is odd. So, x is an odd integer greater than 1: 3, 5, 7, ... In this case x! + x + 1 = even + odd + odd = even > 2, not a prime. Sufficient.
Answer: B.
General Discussion
09 Jul 2014, 01:19
Kudos
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Let X<10, then
for the x=2
x! + x + 1 = 5 = prime number
& for the x=3
x! + x + 1 = 10, not a prime number
So it is not possible if x is a positive integer greater than 1, is x! + x + 1 a prime number..
for the x=2
x! + x + 1 = 5 = prime number
& for the x=3
x! + x + 1 = 10, not a prime number
So it is not possible if x is a positive integer greater than 1, is x! + x + 1 a prime number..
