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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]
I picked E.

1.) Not Sufficient
2! + (2+1) =2*1 + 3 = 5 (prime number)
3! + (3+1) = 3*2*1 + 4 = 10 (not a prime number)

2.) Not Sufficient
2! + (2+1) =2*1 + 3 = 5 (prime number)
4! + (4+1) = 4*3*2*1 + 5 = 29 (prime number)
6! + (6+1) = 6*5*4*3*2*1 + 7 = 727 (prime number)
8! + (8+1) = 8*7*6*5*4*3*2*1 + 9 = 40329 (not a prime number)

Combined Statements 1 and 2..not sufficient because when x<10 and x is even you get prime and non-prime numbers

Is there any way to resolve this problem faster???
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Re: If x is a positive integer, is x! + (x + 1) a prime number? [#permalink]
1
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1: insuffcieint
2 - 2!+3 = 5 - prime
3 - 3!+4 = 10 - not prime
8 = 8!+9 - not prime

2: insuffcient
x= 0, x! + (x + 1) = 1 - Not prime.
x= 2, x! + (x + 1) = 5 - prime.

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

(1) x < 10

(2) x is even

Similar question to practice: if-x-is-a-positive-integer-greater-than-1-is-x-x-1-a-p-173982.html
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Re: If x is a positive integer, is x! + (x + 1) a prime number? [#permalink]
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.

-> 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]
If x is a positive integer, is $$x! + (x + 1)$$ a prime number?

(1) $$x < 10$$

if $$x = 1$$
$$1 + 1 + 1$$= prime
$$if x = 2$$
$$3! + 3 + 1$$ = not prime

INSUFFICIENT.

(2) $$x is even$$

if $$x = 2$$
$$2! + 2 + 1$$ = prime
$$8! + 8 + 1$$ = not prime

INSUFFICIENT

(1&2) $$x < 10, x is even$$

Two scenarios we used in statement 2 still work. INSUFFICIENT.
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Re: If x is a positive integer, is x! + (x + 1) a prime number? [#permalink]
Step 1: Analyse Question Stem

x is a positive integer.
We have to find if x! + (x+1) is a prime number.

Step 2: Analyse Statements Independently (And eliminate options) – AD / BCE

Statement 1: x < 10

If x = 2, the expression yields a prime number.
If x = 3, the expression yields a composite number.

The data in statement 1 is insufficient to answer the question with a definite Yes or No..
Statement 1 alone is insufficient. Answer options A and D can be eliminated.

Statement 2: x is even.

If x = 2, the expression yields a prime number.
If x = 8, the expression yields a composite number since both 8! and (8 + 1) are divisible by 3.

The data in statement 1 is insufficient to answer the question with a definite Yes or No..
Statement 2 alone is insufficient. Answer option B can be eliminated.

Step 3: Analyse Statements by combining

From statement 1: x < 10

From statement 2: x is even.

Even after combining the statements, the same values of x = 2 and x = 8 satisfy both the constraints.

The combination of statements is insufficient to answer the question with a definite Yes or No.
Statements 1 and 2 together are insufficient. Answer option C can be eliminated.

The correct answer option is E.
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Re: If x is a positive integer, is x! + (x + 1) a prime number? [#permalink]
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Re: If x is a positive integer, is x! + (x + 1) a prime number? [#permalink]
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