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Sub 505 (Easy)|   Algebra|            
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HKD1710
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If x is a number such that x^2 - 3x + 2 = 0 and x^2 - x - 2 = 0 06 Dec 2018, 09:10
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E
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87% (00:53) correct 13% (01:03) wrong based on 1426 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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E
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BrentGMATPrepNow
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If x is a number such that x^2 - 3x + 2 = 0 and x^2 - x - 2 = 0 06 Dec 2018, 09:19
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HKD1710
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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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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dave13
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If x is a number such that x^2 - 3x + 2 = 0 and x^2 - x - 2 = 0 06 Dec 2018, 09:27
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HKD1710
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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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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If x is a number such that x^2 - 3x + 2 = 0 and x^2 - x - 2 = 0 06 Dec 2018, 09:46
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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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If x is a number such that x^2 - 3x + 2 = 0 and x^2 - x - 2 = 0 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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If x is a number such that x^2 - 3x + 2 = 0 and x^2 - x - 2 = 0 06 Dec 2018, 21:26
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GMATPrepNow
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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So whats the best method?
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If x is a number such that x^2 - 3x + 2 = 0 and x^2 - x - 2 = 0 07 Dec 2018, 07:41
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ArjunJag1328
GMATPrepNow
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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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 07 Dec 2018, 21:47
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ArjunJag1328
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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

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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=> \(x^2\)-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 26 Mar 2025, 09:55
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