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06 May 2016, 23:26
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
85%
(hard)
Question Stats:
38% (01:54) correct
62%
(02:05)
wrong
based on 89
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If x = n!+1, is x a prime number?
(1) x has no factor other than 1 common with any number less than or equal to n.
(2) x has no factor other than 1 common with any integer between n and n! , inclusive.
self made
(1) x has no factor other than 1 common with any number less than or equal to n.
(2) x has no factor other than 1 common with any integer between n and n! , inclusive.
self made
07 May 2016, 01:40
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stmt-1:
say n=3 then x=7, take any number less than 7 say 2. here X IS PRIME and has only 1 in common.
say n=4 then x=25,take any number less than 25 say 11. here X IS NOT PRIME and has only 1 in common.
INSUFF.
stmt-2:
say n=3 then x=7, take any number greater than 7 say 11. here X IS PRIME and has only 1 in common.
say n=4 then x=25,take any number greater than 25 say 31. here X IS NOT PRIME and has only 1 in common.
INSUFF.
combined:
even if we combine the results X can or cannot be prime. insuff.
Answer should be E.
say n=3 then x=7, take any number less than 7 say 2. here X IS PRIME and has only 1 in common.
say n=4 then x=25,take any number less than 25 say 11. here X IS NOT PRIME and has only 1 in common.
INSUFF.
stmt-2:
say n=3 then x=7, take any number greater than 7 say 11. here X IS PRIME and has only 1 in common.
say n=4 then x=25,take any number greater than 25 say 31. here X IS NOT PRIME and has only 1 in common.
INSUFF.
combined:
even if we combine the results X can or cannot be prime. insuff.
Answer should be E.
07 May 2016, 03:00
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chetan2u
Hi Chetan,
I am a bit skeptical about Statement 2.
St2: x has no factor other than 1 common with any integer greater than n:
n = 0 --> x = 2 but x cannot be 2 because x has a factor common with 2 which is > 0
n = 2 --> x = 3 but x cannot be 3 because x has a factor common with 3 which is > 2
n = 5 --> x = 121 but x cannot be 121 because x has a factor common with 11 which is > 5
Actually this statement states that x can be 0, 1 or any negative integer. However, according to the given expression, minimum value of x has to be 2.
Statement 2 appears to be flawed. Please correct me if I am wrong.
