If \(x\) is a number such that \(x^2 + 2x - 24 = 0\) and \(x^2 + 5x - 6 = 0,\) then \(x =\) - The Beat The GMAT Forum

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If \(x\) is a number such that \(x^2 + 2x - 24 = 0\) and \(x^2 + 5x - 6 = 0,\) then \(x =\)

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Gmat_mission: Legendary Member; Posts: 1622; Joined: Thu Mar 01, 2018 7:22 am; Followed by:2 members

If \(x\) is a number such that \(x^2 + 2x - 24 = 0\) and \(x^2 + 5x - 6 = 0,\) then \(x =\)

by Gmat_mission » Sun Apr 26, 2020 11:46 am

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If \(x\) is a number such that \(x^2 + 2x - 24 = 0\) and \(x^2 + 5x - 6 = 0,\) then \(x =\)

A. -6
B. -4
C. -3
D. 3
E. 6

[spoiler]OA=A[/spoiler]

Source: Magoosh

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Source: Beat The GMAT — Problem Solving | Sun Apr 26, 2020 11:46 am

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8088; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

Re: If \(x\) is a number such that \(x^2 + 2x - 24 = 0\) and \(x^2 + 5x - 6 = 0,\) then \(x =\)

by Scott@TargetTestPrep » Sun May 03, 2020 5:31 am

Gmat_mission wrote: ↑
Sun Apr 26, 2020 11:46 am
If \(x\) is a number such that \(x^2 + 2x - 24 = 0\) and \(x^2 + 5x - 6 = 0,\) then \(x =\)

A. -6
B. -4
C. -3
D. 3
E. 6

[spoiler]OA=A[/spoiler]

Source: Magoosh

We can solve each equation and look for the value of x that satisfies both equations. Or we can set the left hand side of the equations equal to each other since they are both equal to 0. Let’s do the latter since it’s easier:

x^2 + 2x - 24 = x^2 + 5x - 6

2x - 24 = 5x - 6

-3x = 18

x = -6

Answer: A

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