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If x is a number such that x^2 - 3x + 2 = 0 and x^2 - x - 2 = 0

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If x is a number such that x^2 - 3x + 2 = 0 and x^2 - x - 2 = 0  [#permalink]

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New post 06 Dec 2018, 09:10
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E

Difficulty:

  5% (low)

Question Stats:

88% (00:49) correct 13% (00:42) wrong based on 77 sessions

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If \(x\) is a number such that \(x^2 - 3x + 2 = 0\) and \(x^2 - x - 2 = 0\), what is the value of \(x\)?

(A) -2
(B) -1
(C) 0
(D) 1
(E) 2

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Re: If x is a number such that x^2 - 3x + 2 = 0 and x^2 - x - 2 = 0  [#permalink]

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New post 06 Dec 2018, 09:19
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HKD1710 wrote:
If \(x\) is a number such that \(x^2 - 3x + 2 = 0\) and \(x^2 - x - 2 = 0\), what is the value of \(x\)?

(A) -2
(B) -1
(C) 0
(D) 1
(E) 2

Project PS Butler : Question #61


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Since both equation are set equal to 0, we can write: x² - 3x + 2 = x² - x - 2
Subtract x² from both sides to get: -3x + 2 = -x - 2
Add 3x to both sides to get: 2 = 2x - 2
Add 2 to both sides to get: 4 = 2x
Solve: x = 2

Answer: E

Cheers,
Brent
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Re: If x is a number such that x^2 - 3x + 2 = 0 and x^2 - x - 2 = 0  [#permalink]

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New post 06 Dec 2018, 09:27
HKD1710 wrote:
If \(x\) is a number such that \(x^2 - 3x + 2 = 0\) and \(x^2 - x - 2 = 0\), what is the value of \(x\)?

(A) -2
(B) -1
(C) 0
(D) 1
(E) 2

Project PS Butler : Question #61


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i solved it differently


\(x^2 - 3x + 2 = 0\)
(x-1)(x-2)
x =1 ; x=2


\(x^2 - x - 2 = 0\)
(x-2)(x+1)
x =2; x =-1

so both equations have in common 2

hence E
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Re: If x is a number such that x^2 - 3x + 2 = 0 and x^2 - x - 2 = 0  [#permalink]

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New post 06 Dec 2018, 09:46
2 ways to get to the answer.

1. POE (Approximately 1 min and 30 secs to solve it)
2. Find the roots of the equation. (Close to 2 mins)

\(x^2\)-3x+2=0
x=2 or x=1

\(x^2\)-x-2=0
x=2 or x=-1

2 is common in both. Hence IMO E
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Re: If x is a number such that x^2 - 3x + 2 = 0 and x^2 - x - 2 = 0  [#permalink]

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New post 06 Dec 2018, 11:38
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Aside: Finding the roots of each equation, and then identifying the root that the equations have in common will work.
However, this approach COULD be a time killer, if the equations are not so forgiving.

For example: 4x² - 9x - 9 = 0 and 4x² + 19x + 12 = 0

Cheers,
Brent
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Re: If x is a number such that x^2 - 3x + 2 = 0 and x^2 - x - 2 = 0  [#permalink]

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New post 06 Dec 2018, 21:26
GMATPrepNow wrote:
Aside: Finding the roots of each equation, and then identifying the root that the equations have in common will work.
However, this approach COULD be a time killer, if the equations are not so forgiving.

For example: 4x² - 9x - 9 = 0 and 4x² + 19x + 12 = 0

Cheers,
Brent


So whats the best method?
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Re: If x is a number such that x^2 - 3x + 2 = 0 and x^2 - x - 2 = 0  [#permalink]

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New post 07 Dec 2018, 07:41
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Top Contributor
ArjunJag1328 wrote:
GMATPrepNow wrote:
Aside: Finding the roots of each equation, and then identifying the root that the equations have in common will work.
However, this approach COULD be a time killer, if the equations are not so forgiving.

For example: 4x² - 9x - 9 = 0 and 4x² + 19x + 12 = 0

Cheers,
Brent


So whats the best method?


GIVEN: 4x² - 9x - 9 = 0 and 4x² + 19x + 12 = 0
Since both equations are set equal to 0, we can write: 4x² - 9x - 9 = 4x² + 19x + 12
Subtract 4x² from both sides: -9x - 9 = 19x + 12
Subtract 19x from both sides: -28x - 9 = 12
Add 9 to both sides: -28x = 21
Solve: x = -21/28 = -3/4

Cheers,
Brent
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If x is a number such that x^2 - 3x + 2 = 0 and x^2 - x - 2 = 0  [#permalink]

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New post 07 Dec 2018, 21:47
GMATPrepNow wrote:
ArjunJag1328 wrote:
GMATPrepNow wrote:
Aside: Finding the roots of each equation, and then identifying the root that the equations have in common will work.
However, this approach COULD be a time killer, if the equations are not so forgiving.

For example: 4x² - 9x - 9 = 0 and 4x² + 19x + 12 = 0

Cheers,
Brent


So whats the best method?


GIVEN: 4x² - 9x - 9 = 0 and 4x² + 19x + 12 = 0
Since both equations are set equal to 0, we can write: 4x² - 9x - 9 = 4x² + 19x + 12
Subtract 4x² from both sides: -9x - 9 = 19x + 12
Subtract 19x from both sides: -28x - 9 = 12
Add 9 to both sides: -28x = 21
Solve: x = -21/28 = -3/4

Cheers,
Brent


=> \(x^2\)-3x+2=\(x^2\)-x-2

=>\(x^2\)-\(x^2\)-3x+x+2+2=0

=>-2x+4=0

=>-2x=-4

=>x=\(\frac{4}{2}\)

=>x=2

Thanks GMATPrepNow
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If x is a number such that x^2 - 3x + 2 = 0 and x^2 - x - 2 = 0   [#permalink] 07 Dec 2018, 21:47
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