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prime number

by umaa » Thu Dec 03, 2009 9:36 pm
If x is a positive integer, is x! + (x + 1) a prime number?

(1) x < 10

(2) x is even
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Source: — Data Sufficiency |
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by papgust » Thu Dec 03, 2009 11:15 pm
It should be E

1) We know that x < 10 and x is a positive integer. Therefore, x ranges from 1 to 9. Substitute values of x until you get 2 different answers,

x=1, 1+2=3 (YES)
x=2, 2+3=5 (YES)
x=3, 6+4=10 (NO). Stop right there!

Insufficient.

2) x is even
we know that when x=2, x! + (x+1) will be a prime.
Take x as 8, then x! + (x+1) will NOT be a prime.

Insufficient.

Combined, Insufficient again. Prime for x values 2,4,6 but not for 8.

Hence, E
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