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Prime number

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Source: — Data Sufficiency |
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by GMATGuruNY » Fri Aug 23, 2013 6:23 am
vinay1983 wrote:If X is a positive integer, is X!+(x+1) a prime number?

1. X is less than 10
2. X is even
Both statements are satisfies by x=2.
Here, x! + (x+1) = 2! + 3 = 5, which is prime.

Both statements are satisfied by x=8.
Here, x! + x+1 = 8! + 9 = (8*7*6*5*4*3*2*1) + (3*3) = 3(8*7*6*5*4*2*1 + 3).
In this case, x! + (x+1) has a factor of 3 and thus is NOT prime.

Thus, the two statements combined are INSUFFICIENT.

The correct answer is E.
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by Brent@GMATPrepNow » Fri Aug 23, 2013 6:34 am
vinay1983 wrote:If X is a positive integer, is X!+(x+1) a prime number?

1. X is less than 10
2. X is even

Target question: Is x! + (x+1) a prime number?

Statement 1: X is less than 10
To make things easy on ourselves, we'll try small values of x
x = 1: we get 1! + (1+1) = 3, which is prime
x = 3: we get 3! + (3+1) = 10, which is not prime
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: X is even
Start with small values of x
Try x = 2: we get 2! + (2+1) = 5, which is prime
Try x = 4: we get 4! + (4+1) = 29, which is prime
Try x = 6: we get 6! + (6+1) = 727, which is prime??? TOO HARD - SKIP IT
Try x = 8: we get 8! + (8+1) = 8! + 9. DO NOT EVALUATE! Since 8! and 9 are both divisible by 3, (8!+9) must be divisible by 3, which means it is not prime
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
When x = 2, x!+(x+1) is a prime number.
When x = 8, x!+(x+1) is not prime .
So, the combined statements are NOT SUFFICIENT

Answer = E

Cheers,
Brent
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by vinay1983 » Fri Aug 23, 2013 6:38 am
Brent@GMATPrepNow wrote:
vinay1983 wrote:If X is a positive integer, is X!+(x+1) a prime number?

1. X is less than 10
2. X is even

Target question: Is x! + (x+1) a prime number?

Statement 1: X is less than 10
To make things easy on ourselves, we'll try small values of x
x = 1: we get 1! + (1+1) = 3, which is prime
x = 3: we get 3! + (3+1) = 10, which is not prime
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: X is even
Start with small values of x
Try x = 2: we get 2! + (2+1) = 5, which is prime
Try x = 4: we get 4! + (4+1) = 29, which is prime
Try x = 6: we get 6! + (6+1) = 727, which is prime??? TOO HARD - SKIP IT
Try x = 8: we get 8! + (8+1) = 8! + 9. DO NOT EVALUATE! Since 8! and 9 are both divisible by 3, (8!+9) must be divisible by 3, which means it is not prime
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
When x = 2, x!+(x+1) is a prime number.
When x = 8, x!+(x+1) is not prime .
So, the combined statements are NOT SUFFICIENT

Answer = E

Cheers,
Brent
So does this mean that if a sequence of numbers have 3 in them, then that sequence is divisible/multiple by/of 3?
Can this be generalized?
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by Brent@GMATPrepNow » Fri Aug 23, 2013 6:42 am
vinay1983 wrote:
So does this mean that if a sequence of numbers have 3 in them, then that sequence is divisible/multiple by/of 3?
Can this be generalized?
You bet.
We can say that n! is divisible by n, n-1, n-2, n-3, . . . 3, 2 and (of course) 1
For example, 11! is divisible by 11, 10, 9, 8, . . . 3, 2 and 1

Aside: 11! is also divisible by numbers other than those mentioned.

Cheers,
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