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If x is a positive integer, is x! + (x + 1) a prime number?

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Re: If x is a positive integer, is x! + (x + 1) a prime number? [#permalink]

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New post 08 Feb 2016, 18:05
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

If x is a positive integer, is x! + (x + 1) a prime number?

(1) x < 10

(2) x is even


In the original condition, there is 1 variable(x), which should match with the number of equations. So you need 1 equation. For 1) 1 equation, for 2) 1 equation, which is likely to make D the answer.
For 1), x=2 -> yes, x=8 -> no, which is not sufficient.
For 2), x=2 -> yes, x=8 -> no, which is not sufficient.
When 1) & 2), x=2 -> yes, x=8 -> no, which is not sufficient.
Therefore, the answer is E.


-> For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.
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Re: If x is a positive integer, is x! + (x + 1) a prime number? [#permalink]

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New post 11 Aug 2016, 11:27
see 1 an 2 statements and then try to 2, 3 an 4 as examples. E

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Re: If x is a positive integer, is x! + (x + 1) a prime number? [#permalink]

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New post 29 Aug 2017, 21:52
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Re: If x is a positive integer, is x! + (x + 1) a prime number?   [#permalink] 29 Aug 2017, 21:52

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