If x is a positive integer such that x^2 + 5x âˆ’ 14 = 0, wh

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by Brent@GMATPrepNow » Sun Jul 07, 2019 5:50 am

BTGmoderatorDC wrote:If x is a positive integer such that xÂ² + 5x âˆ’ 14 = 0, what is the value of x ?

A. âˆ’7
B. âˆ’5
C. 0
D. 2
E. 5

GIVEN: xÂ² + 5x âˆ’ 14 = 0
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

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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swerve: Legendary Member; Posts: 2499; Joined: Sun Oct 29, 2017 2:04 pm; Followed by:6 members

by swerve » Sun Jul 07, 2019 9:47 am

\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, \(x=2\).

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Thu Jul 11, 2019 6:54 pm

BTGmoderatorDC wrote:If x is a positive integer such that x^2 + 5x âˆ’ 14 = 0, what is the value of x ?

A. âˆ’7
B. âˆ’5
C. 0
D. 2
E. 5

OA D

Source: Princeton Review

x^2 + 5x âˆ’ 14 = 0

(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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