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If x is a positive integer such that

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If x is a positive integer such that [#permalink]

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New post 17 Feb 2017, 04:31
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Question Stats:

93% (00:30) correct 7% (00:14) wrong based on 41 sessions

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If x is a positive integer such that x^2 + 5x − 14 = 0, what is the value of x ?

A. −7
B. −5
C. 0
D. 2
E. 5
[Reveal] Spoiler: OA

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Re: If x is a positive integer such that [#permalink]

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New post 17 Feb 2017, 06:16
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SajjadAhmad wrote:
If x is a positive integer such that x² + 5x − 14 = 0, what is the value of x ?

A. −7
B. −5
C. 0
D. 2
E. 5


Given: x² + 5x − 14 = 0,
Factor: (x + 7)(x - 2) = 0
We can conclude that EITHER x + 7 = 0 OR x - 2 = 0

If x + 7 = 0, then x = -7
If x - 2 = 0, then x = 2

We have two different solutions, but the question asks for the POSITIVE solution, which is 2

Answer: D

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Brent
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Re: If x is a positive integer such that [#permalink]

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New post 17 Feb 2017, 11:23
SajjadAhmad wrote:
If x is a positive integer such that x^2 + 5x − 14 = 0, what is the value of x ?

A. −7
B. −5
C. 0
D. 2
E. 5


Solving the Quadratic equation :
x^2 + 5x − 14 = 0
(x + 7) (x - 2) = 0
x = -7 or 2
As x is a positive number , x = 2

Answer is D .
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Re: If x is a positive integer such that [#permalink]

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New post 17 Feb 2017, 13:34
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x^2+5x-14=0
x^2+7x-2x-14=0
x(x+7)-2(x+7)=0
(x-2)(x+7)=0

Hence
either x-2=0 => x=2
or x+7=0 => x=-7

But it is mentioned in the question statement that x is positive.

So x=2.

Answer D
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Re: If x is a positive integer such that [#permalink]

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New post 17 Feb 2017, 13:52
Just to post a different approach, the question is for positive value of 2...so Only D or E will be the answer. Substitute these in the equation to see which satisfies.

Answer is 2 (D)
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Re: If x is a positive integer such that [#permalink]

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New post 18 Feb 2017, 03:41
SajjadAhmad wrote:
If x is a positive integer such that \(x^2 + 5x − 14 = 0\), what is the value of x ?

A. −7
B. −5
C. 0
D. 2
E. 5


\(x^2 + 5x − 14 = 0\)

Or, \(x^2 + 7x − 2x − 14 = 0\)

Or, \(x ( x + 7 ) − 2 ( x + 7 ) = 0\)

Or, \(( x + 7 ) ( x − 2 ) = 0\)

So, \(x = 2\) or \(x = −7\)

Answer will be (D) \(x = 2\)
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Re: If x is a positive integer such that [#permalink]

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New post 23 Feb 2017, 09:21
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SajjadAhmad wrote:
If x is a positive integer such that x^2 + 5x − 14 = 0, what is the value of x ?

A. −7
B. −5
C. 0
D. 2
E. 5


x^2 + 5x − 14 = 0

(x + 7)(x - 2) = 0

x = -7 or x = 2

Since x must be positive, 2 is the correct answer.

Answer: D
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Re: If x is a positive integer such that   [#permalink] 23 Feb 2017, 09:21
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