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
OA D
Source: Princeton Review
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If x is a positive integer such that x^2 + 5x − 14 = 0, wh
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BTGmoderatorDC
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Brent@GMATPrepNow
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GIVEN: x² + 5x − 14 = 0BTGmoderatorDC 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
Factor: (x + 7)(x - 2) = 0
So, EITHER x = -7 OR x = 2
Since we're told x is POSITIVE, the correct answer is D
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Brent
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\begin{align*}
x^2+5x-14 &=0 \\
x^2+7x-2x-14&=0 \\
x(x+7)-2(x+7)&=0\\
(x-2)(x+7)&=0
\end{align*}
Hence
either \(x-2=0 \Rightarrow x=2\)
or \(x+7=0 \Rightarrow x=-7\)
But it is mentioned in the question statement that \(x\) is positive.
Therefore, \(x=2\).
x^2+5x-14 &=0 \\
x^2+7x-2x-14&=0 \\
x(x+7)-2(x+7)&=0\\
(x-2)(x+7)&=0
\end{align*}
Hence
either \(x-2=0 \Rightarrow x=2\)
or \(x+7=0 \Rightarrow x=-7\)
But it is mentioned in the question statement that \(x\) is positive.
Therefore, \(x=2\).
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Scott@TargetTestPrep
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x^2 + 5x − 14 = 0BTGmoderatorDC 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
OA D
Source: Princeton Review
(x + 7)(x - 2) = 0
x = -7 or x = 2
Since x must be positive, 2 is the correct answer.
Alternate solution:
We can eliminate choices A to C since they are not positive. Now, let's check choice D by substituting 2 for the value of x.
2^2 + 5(2) - 14 = 4 + 10 - 14 = 0
We see that choice D is the correct answer.
Answer: D
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