Is it a prime number?

[pepeprepa]

If x is a positive integer, is x! + (x+1) a prime number?
1) x<10
2) x is even

[saeed]

I guess the answer is E.

[sudhir3127]

If x is a positive integer, is x! + (x+1) a prime number?
1) x<10
2) x is even

IMO B

[parallel_chase]

B for me as well.

[saeed]

Say x=8, then X!+(X+1)= 40329, which is both divisible by 3& 9. So insufficient.

[pepeprepa]

The thing is to do this question in 2' time.

1) x<10
x=2 --> 2!+(2+1)=5 is prime
x=3 --> 3!+(3+1)=10 is not prime
We cannot state anything.

2) x is even
x=2 --> 2!+(2+1)=5 is prime
x=4 --> 4!+(4+1)=29 is prime
x=6 --> 6!+(6+1)=727 is prime
Ok it seems pretty cool with x even, and at this moment I stopped and took B which seems logic. What I would like to know is what can give you a clue that you have to go on? This trap is hard to forecast...
Because x=8 --> 8!+(8+1)=8*7*6*5*4*3*2 + 9
Both terms are multiple of 3 so the result is a multiple of 3 so the result is not a prime.
Insufficient

1)and2)
Now it's ok we have example/counter-example for x=2 and x=8 for example.
OA:E

[parallel_chase]

Yeah thats right made a calculation mistake took 40329 as 41129.

Answer is indeed E.

[pepeprepa]

Chase, till which number did you go ?
Indeed, with the statement 1) x<10, I think I should have been till 12 to see what happens above it. But it's already a lot of calculation for one question...

[parallel_chase]

Chase, till which number did you go ?
Indeed, with the statement 1) x<10, I think I should have been till 12 to see what happens above it. But it's already a lot of calculation for one question...

Yeah went till 12 but miscalculated 8! which landed B as an answer.

This was a huge blunder. Thanks for these wonderful questions, keeps us on our feet.

[Ian Stewart]

This is only for interest, and won't be much help on the GMAT:

There is no formula for generating prime numbers, which should make you a bit suspicious that the information in the above question is insufficient. Some formulas appear to always generate primes for small values of x, as when you plug even values of x into the above problem, but no formula generates primes for all x. Fermat (incorrectly) thought the following:

2^(2^x) + 1

would generate primes for all x, and if you plug in x = 1, 2, 3 and 4 you do get a prime each time (5, 17, 257 and 65,537 are all prime). These numbers are called Fermat primes. However, for x = 5, you do not get a prime (you do get a very large number, in the billions, so don't try to prove it isn't a prime!). In fact, to date, the only values of x for which the above formula is known to generate primes are exactly the values above: 1, 2, 3 and 4. This illustrates that it is sometimes dangerous to guess that a pattern will continue only because it holds true for a small number of values.