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Sub 505 (Easy)|   Algebra|      
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Bunuel
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If x is a number such that x2 + 2x - 24 = 0 and x2 + 5x - 6 = 0, then 02 Apr 2015, 04:45
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

5% (low)

Question Stats:

89% (01:12) correct 11% (01:07) wrong based on 175 sessions

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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
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A
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If x is a number such that x2 + 2x - 24 = 0 and x2 + 5x - 6 = 0, then 02 Apr 2015, 05:07
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Bunuel
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

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(x+6)(x-4)=0...x=-6 OR 4
(x+6)(x-1)=0...c=-6 OR 1

Answer: A
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If x is a number such that x2 + 2x - 24 = 0 and x2 + 5x - 6 = 0, then 02 Apr 2015, 05:16
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Bunuel
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

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for first equation
x + x = -2
x * x = -24
so x = -6 or 4

for second equation
x + x = -5
x * x = -6
so x = -6 or 1

we have one common answer for x: this is -6
and answer is A
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If x is a number such that x2 + 2x - 24 = 0 and x2 + 5x - 6 = 0, then 02 Apr 2015, 06:07
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x^2 + 2x - 24 = 0
x^2 + 5x - 6 = 0

Subtracting the two equations,
-3x = 18
So, x = -6
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If x is a number such that x2 + 2x - 24 = 0 and x2 + 5x - 6 = 0, then 02 Apr 2015, 07:27
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Bunuel
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

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Hi Bunuel,

I solved this question by equating the two equations, can you please suggest whether anything is wrong in this approach, or if I should add some steps to make this approach foolproof?

\(x^2 + 2x - 24\) = \(x^2 + 5x - 6\)
=> \(3x = -18\)
=> \(x = -6\)

IMO correct answer is A.
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If x is a number such that x2 + 2x - 24 = 0 and x2 + 5x - 6 = 0, then 02 Apr 2015, 07:43
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Bunuel
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

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X2 + 5x - 6 = 0, then x =-6, 1

Since 1 is not in option , -6 is answer.
answer a
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If x is a number such that x2 + 2x - 24 = 0 and x2 + 5x - 6 = 0, then 02 Apr 2015, 17:28
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Bunuel
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

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1st method:
Equate both the equations:
\(x^2 + 2x - 24 = x^2 + 5x - 6\)
\(3x = -18\)
\(x = -6\)
Satisfies both equations.

Answer:A

Longer method/Alternate:

Solve each equation: \(x^2 + 2x - 24 = 0\)
\(x = 4,-6\)

\(x^2 + 5x - 6 = 0,\)
\(x = 1,-6\)

Clearly x = -6 after taking the intersection and this values satisfies both equations.
Answer:A
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If x is a number such that x2 + 2x - 24 = 0 and x2 + 5x - 6 = 0, then 02 Apr 2015, 23:57
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Answer = A = -6

\(x^2 + 2x - 24 = x^2 + 5x - 6 = 0\)

-3x = 18

x = -6

Had only one equation been given, "x" would had derived 2 values. However in this case, two equations are given

So, this will yield "ONLY ONE ANSWER" for x because value of "x" has to SATISFY both equations
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If x is a number such that x2 + 2x - 24 = 0 and x2 + 5x - 6 = 0, then 03 Apr 2015, 00:29
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Bunuel
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

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Answer=A
x^2+2x-24=x^2+6x-4x-24=(x+6)(x-4)=0
x=-6 or x=4
and x^2+5x-6=x^2+6x-x-6=0
(x+6)(x-1)=0
x=-6 or x=1
Using both, x=-6
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If x is a number such that x2 + 2x - 24 = 0 and x2 + 5x - 6 = 0, then 06 Apr 2015, 06:19
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Bunuel
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

Kudos for a correct solution.
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MAGOOSH OFFICIAL SOLUTION:
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If x is a number such that x2 + 2x - 24 = 0 and x2 + 5x - 6 = 0, then 26 Oct 2022, 07:25
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