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

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If y = x^2 - 6x + 9, what is the value of x? [#permalink]

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01 Jul 2016, 05:14
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If y = x^2 - 6x + 9, what is the value of x?

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

OG Q 2017 New Question(Book Question: 230)
[Reveal] Spoiler: OA

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Re: If y = x^2 - 6x + 9, what is the value of x? [#permalink]

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01 Jul 2016, 08:17
A
1)y=(x-3)^2 andn y=0 so x=3

2)x+y=3.not suff for finding x

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Re: If y = x^2 - 6x + 9, what is the value of x? [#permalink]

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20 Jul 2016, 05:21
AbdurRakib wrote:
If y=$$x^2$$-6x+9,what is the value of x?

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

OG Q 2017 New Question(Book Question: 230)

Why can't it be D?

Y=0. Obvious.

x+y=3. Substitute y=3-x in the equation to get (x-2)(x-3)=0 to get x=2 or 3.

Is it for that x has two values, we chose option A?

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Re: If y = x^2 - 6x + 9, what is the value of x? [#permalink]

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20 Jul 2016, 05:56
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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

[Reveal] Spoiler:
A

RELATED VIDEO

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Last edited by GMATPrepNow on 20 Jul 2016, 09:55, edited 2 times in total.

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Re: If y = x^2 - 6x + 9, what is the value of x? [#permalink]

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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

[Reveal] Spoiler:
A

RELATED VIDEO

I think you've made a small mistake when re-arranging x+y=3 to y=x-3. Shouldn't it be y=3-x?

Nevertheless, Point made. X should have one definite value to confirm the option.

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Re: If y = x^2 - 6x + 9, what is the value of x? [#permalink]

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20 Jul 2016, 07:19
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Top Contributor
siv wrote:
I think you've made a small mistake when re-arranging x+y=3 to y=x-3. Shouldn't it be y=3-x?

Nevertheless, Point made. X should have one definite value to confirm the option.

Good catch!
I've edited my response.

Cheers,
Brent
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Re: If y = x^2 - 6x + 9, what is the value of x? [#permalink]

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08 Jul 2017, 20:57
I'm getting SUFFICIENT for statement 2. Here's how:

Given, x+y = 3
X = 3 - y
Substituting for X in the equation;

Y = (3-y)^2 - 6 (3-y) + 9
Y = 9 - 6y + y^2 - 18 + 6y + 9
Cancel out terms,
Y=y^2

Implies y = 1
Therefore x=2

Am I missing something?

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If y = x^2 - 6x + 9, what is the value of x? [#permalink]

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09 Jul 2017, 02:10
mariachi0204 wrote:
I'm getting SUFFICIENT for statement 2. Here's how:

Given, x+y = 3
X = 3 - y
Substituting for X in the equation;

Y = (3-y)^2 - 6 (3-y) + 9
Y = 9 - 6y + y^2 - 18 + 6y + 9
Cancel out terms,
Y=y^2
Implies y = 1

Therefore x=2

Am I missing something?

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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 cannot divide by zero.
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Re: If y = x^2 - 6x + 9, what is the value of x? [#permalink]

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09 Jul 2017, 02:37
Bunuel wrote:
mariachi0204 wrote:
I'm getting SUFFICIENT for statement 2. Here's how:

Given, x+y = 3
X = 3 - y
Substituting for X in the equation;

Y = (3-y)^2 - 6 (3-y) + 9
Y = 9 - 6y + y^2 - 18 + 6y + 9
Cancel out terms,
Y=y^2
Implies y = 1

Therefore x=2

Am I missing something?

Sent from my SM-G900F using GMAT Club Forum mobile app

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!

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Re: If y = x^2 - 6x + 9, what is the value of x? [#permalink]

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16 Jul 2017, 13:37
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

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Re: If y = x^2 - 6x + 9, what is the value of x? [#permalink]

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07 Sep 2017, 03:43
The question is asking about the value of x, so X could not has two different values?

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Re: If y = x^2 - 6x + 9, what is the value of x? [#permalink]

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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".

Hope it helps.
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Re: If y = x^2 - 6x + 9, what is the value of x? [#permalink]

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07 Sep 2017, 05:31
AbdurRakib wrote:
If y = x^2 - 6x + 9, what is the value of x?

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

OG Q 2017 New Question(Book Question: 230)

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

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Re: If y = x^2 - 6x + 9, what is the value of x?   [#permalink] 07 Sep 2017, 05:31
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