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Re: If y = x^2 - 6x + 9, what is the value of x?
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Updated on: 20 Jul 2016, 09:55

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AbdurRakib wrote:

If y = x² - 6x + 9, what is the value of x?

(1) y = 0 (2) x + y = 3

Target question:What is the value of x?

Given: y = x² - 6x + 9

Statement 1: y = 0 This tells us that 0 = x² - 6x + 9 Factor the right side to get: 0 = (x - 3)(x - 3) So, it MUST be the case that x = 3 Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: x + y = 3 Rearrange this equation to get: y = 3 - x We're also told that y = x² - 6x + 9 So, it must be true that x² - 6x + 9 = 3 - x Rearrange to get: x² - 5x + 6 = 0 Factor: (x - 2)(x - 3) = 0 So, EITHER x = 2 OR x = 3 Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Re: If y = x^2 - 6x + 9, what is the value of x?
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20 Jul 2016, 07:03

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GMATPrepNow wrote:

AbdurRakib wrote:

If y = x² - 6x + 9, what is the value of x?

(1) y = 0 (2) x + y = 3

Target question:What is the value of x?

Given: y = x² - 6x + 9

Statement 1: y = 0 This tells us that 0 = x² - 6x + 9 Factor the right side to get: 0 = (x - 3)(x - 3) So, it MUST be the case that x = 3 Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: x + y = 3 Rearrange this equation to get: y = x - 3 We're also told that y = x² - 6x + 9 So, it must be true that x² - 6x + 9 = x - 3 Rearrange to get: x² - 7x + 12 = 0 Factor: (x - 3)(x - 4) = 0 So, EITHER x = 3 OR x = 4 Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

From y = y^2 it follows that y(y - 1) = 0, so y = 1 or y = 0.

You cannot reduce y = y^2 by y because y can be 0 and we cannot divide by 0. By doing so you loose a root, namely y = 0.

Never reduce equation by variable (or expression with variable), if you are not certain that variable (or expression with variable) doesn't equal to zero. We cannot divide by zero.
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From y = y^2 it follows that y(y - 1) = 0, so y = 1 or y = 0.

You cannot reduce y = y^2 by y because y can be 0 and we cannot divide by 0. By doing so you loose a root, namely y = 0.

Never reduce equation by variable (or expression with variable), if you are not certain that variable (or expression with variable) doesn't equal to zero. We can not divide by zero.

Oh yes! Noted, will keep that in mind. Thanks a lot Bunuel!

Re: If y = x^2 - 6x + 9, what is the value of x?
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16 Jul 2017, 13:37

1

If \(y = x^2 - 6x + 9\), what is the value of x?

(1) \(y = 0\)

\(y = x^2 - 6x + 9\)

\(0 = x^2 - 6x + 9\)

\((x-3) (x-3) = 0\)

\(x = 3\)

Hence, (1) ===== is SUFFICIENT

(2) \(x + y = 3\)

\(y = 3 - x\)

\(y = x^2 - 6x + 9\)

\(3 - x = x^2 - 6x + 9\)

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

\((x - 3) (x - 2) = 0\)

\(x = 3\) Or

\(x = 2\)

Hence, (2) ===== is NOT SUFFICIENT

Hence, Answer is A

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Re: If y = x^2 - 6x + 9, what is the value of x?
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07 Sep 2017, 04:15

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mrmortezajafari wrote:

The question is asking about the value of x, so X could not has two different values?

When a DS question asks about the value of some variable, then the statement(s) is sufficient ONLY if you can get the single numerical value of this variable.

In a Yes/No Data Sufficiency questions, statement(s) is sufficient if the answer is “always yes” or “always no” while a statement(s) is insufficient if the answer is "sometimes yes" and "sometimes no".

y = x^2 - 6x + 9 1) y=0 => y = x^2 - 6x + 9=0 => (x-3)^2 =0 => x=3 , single definite Ans A / D selected

2) x+y=3 or y=3-x => 3-x = y = x^2 - 6x + 9 => 3-x = x^2 - 6x + 9 => x^2-5x+6 =0 => (x-2)(x-3) =0 x=2 and x = 3 x=2,y=1 and if x=3,y=0 both are satisfying equation y = x^2 - 6x + 9 so x has 2 values => REJECTED D

ANSWER is A _________________

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