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If -x is a prime number, what is the value of x?

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Bunuel
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If -x is a prime number, what is the value of x? [#permalink] New post   22 Jun 2017, 06:01
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If -x is a prime number, what is the value of x?

(1) x^2 + 5x + 6 = 0
(2) x^2 + 3x + 2 = 0
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B
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Re: If -x is a prime number, what is the value of x? [#permalink] New post   22 Jun 2017, 06:05
Given data => -x is a prime number.

Statement 1 => x^2 + 5x + 6 = 0
x => {-2,-3}
Both are possible as -x would be 2 and 3 which are both prime.

Not sufficient.

Statment 2 => x^2 + 3x + 2 = 0
x=>{-1,-2}
Here x cannot be -1 as 1 is not prime.

Hence x must be -2


Sufficient.

Hence B.
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Re: If -x is a prime number, what is the value of x? [#permalink] New post   22 Jun 2017, 06:08
Bunuel wrote:
If -x is a prime number, what is the value of x?

(1) x^2 + 5x + 6 = 0
(2) x^2 + 3x + 2 = 0


1) (x+3)(x+2)=0
Insufficient. 2 values of x.

2) (x+1)(x+2)=0
x = 2. Sufficient.

B.
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Re: If -x is a prime number, what is the value of x? [#permalink] New post   22 Jun 2017, 06:10
Bunuel wrote:
If -x is a prime number, what is the value of x?

(1) x^2 + 5x + 6 = 0
(2) x^2 + 3x + 2 = 0


(1) \(x^2 + 5x + 6 = 0\)
\(x^2+3x+2x+6 = 0\)
\(x(x+3)+2(x+3) = 0\)
\((x+3)(x+2) = 0\)
\(x = -2, -3\)
(1) has 2 values of x. I is Not Sufficient.

(2) \(x^2 + 3x + 2 = 0\)
\(x^2+2x+x+2 = 0\)
\(x(x+2)+1(x+2) = 0\)
\((x+1)(x+2) = 0\)
\(x = -2,-1.\)

Given, x is prime number. Therefore x could only be 2. (1 is not prime)

(2) has only 1 value of x. Hence II is Sufficient. Answer (B)...
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Re: If -x is a prime number, what is the value of x? [#permalink] New post   22 Jun 2017, 06:11
Bunuel wrote:
If -x is a prime number, what is the value of x?

(1) x^2 + 5x + 6 = 0
(2) x^2 + 3x + 2 = 0


We know x is a negative of prime number

(1) On solving x^2 + 5x + 6 = 0 we get x as -3 and -2 . Not sufficient

(2) On solving x^2 + 3x + 2 = 0 we get x as -2 and -1 .Sufficient as 1 is not a prime number

Hence B
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Re: If -x is a prime number, what is the value of x? [#permalink] New post   22 Jun 2017, 06:17
Bunuel wrote:
If -x is a prime number, what is the value of x?

(1) x^2 + 5x + 6 = 0
(2) x^2 + 3x + 2 = 0


Lets start checking the options 1 and 2
1. x^2 + 5x + 6 = 0
-> (x+3)(x+2) = 0
-> x = -3,-2

Prime numbers 3,2 NOT SUFFICIENT

2. x^2 + 3x + 2 = 0
-> (x+2)(x+1) = 0
-> x = -2, -1
Prime Number 2. SUFFICIENT

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Answer B.
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Re: If -x is a prime number, what is the value of x? [#permalink]
22 Jun 2017, 06:17
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Bunuel
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