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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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Joined: 22 Jun 2014
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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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06 Dec 2018, 09:10
1
00:00

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

Project PS Butler : Question #61

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Joined: 12 Sep 2015
Posts: 3511
Re: If x is a number such that x^2 - 3x + 2 = 0 and x^2 - x - 2 = 0  [#permalink]

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06 Dec 2018, 09:19
1
Top Contributor
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

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

Cheers,
Brent
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Joined: 09 Mar 2016
Posts: 1277
Re: If x is a number such that x^2 - 3x + 2 = 0 and x^2 - x - 2 = 0  [#permalink]

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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

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
Manager
Joined: 24 Dec 2017
Posts: 184
Location: India
Concentration: Strategy, Real Estate
Schools: Johnson '21
Re: If x is a number such that x^2 - 3x + 2 = 0 and x^2 - x - 2 = 0  [#permalink]

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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
CEO
Joined: 12 Sep 2015
Posts: 3511
Re: If x is a number such that x^2 - 3x + 2 = 0 and x^2 - x - 2 = 0  [#permalink]

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06 Dec 2018, 11:38
1
1
Top Contributor
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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Manager
Joined: 24 Dec 2017
Posts: 184
Location: India
Concentration: Strategy, Real Estate
Schools: Johnson '21
Re: If x is a number such that x^2 - 3x + 2 = 0 and x^2 - x - 2 = 0  [#permalink]

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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?
CEO
Joined: 12 Sep 2015
Posts: 3511
Re: If x is a number such that x^2 - 3x + 2 = 0 and x^2 - x - 2 = 0  [#permalink]

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07 Dec 2018, 07:41
1
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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Manager
Joined: 24 Dec 2017
Posts: 184
Location: India
Concentration: Strategy, Real Estate
Schools: Johnson '21
If x is a number such that x^2 - 3x + 2 = 0 and x^2 - x - 2 = 0  [#permalink]

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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
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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