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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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Updated on: 09 Jul 2017, 01:07
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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)

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Md. Abdur Rakib

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Sentence Correction-Collection of Ron Purewal's "elliptical construction/analogies" for SC Challenges

Originally posted by AbdurRakib on 01 Jul 2016, 04:14.
Last edited by Bunuel on 09 Jul 2017, 01:07, edited 1 time in total.
Renamed the topic and edited the question.
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Re: If y = x^2 - 6x + 9, what is the value of x?  [#permalink]

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Updated on: 20 Jul 2016, 08:55
7
Top Contributor
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

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Originally posted by GMATPrepNow on 20 Jul 2016, 04:56.
Last edited by GMATPrepNow on 20 Jul 2016, 08:55, 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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01 Jul 2016, 07:17
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, 04:21
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, 06:03
1
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

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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, 06:19
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, 19:57
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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Posts: 52230
If y = x^2 - 6x + 9, what is the value of x?  [#permalink]

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09 Jul 2017, 01:10
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?

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 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, 01:37
1
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, 12:37
2
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, 02:43
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, 03:15
1
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, 04:31
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]

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21 Aug 2018, 07:19
Y=x^2 - 6x +9
Y= (x-3)^2

1) y=0
So (x-3)^2=0
x=3 SUFFICIENT

2) x+y= 3
So x-3=(x-3)^2
X^2-5x+6=0
(x-3)(x-2)=0
INSUFFIECIENT

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

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24 Oct 2018, 09:12
1
If y = x^2 - 6x + 9, what is the value of x?

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

For part (2) I did it like this:
y = x^2 - 6x + 9
y = (x-3)(x-3)
since x+y=3, y = 3-x, which can also be written as -(x-3) so:
-(x-3) = (x-3)(x-3)
cancelling x-3 on each side:
-1 = x-3
x=2 SUFFICIENT

Please can someone explain why this is wrong
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Re: If y = x^2 - 6x + 9, what is the value of x?  [#permalink]

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07 Nov 2018, 21:18
Hi Bunuel,

I am confused with statement II:

from stem I could find that X is either -3 or 3, then I substituted it into the Equation Y = x^2 -6x + 9, and got either Y is 0 or 36. Thus X + Y = 3, X either 3 or -33.

Although I got two answer, but i think something is wrong with my approach, when compared to other approaches as stated below:

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
Math Expert
Joined: 02 Sep 2009
Posts: 52230
Re: If y = x^2 - 6x + 9, what is the value of x?  [#permalink]

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07 Nov 2018, 22:38
hero_with_1000_faces wrote:
Hi Bunuel,

I am confused with statement II:

from stem I could find that X is either -3 or 3, then I substituted it into the Equation Y = x^2 -6x + 9, and got either Y is 0 or 36. Thus X + Y = 3, X either 3 or -33.

Although I got two answer, but i think something is wrong with my approach, when compared to other approaches as stated below:

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

From (1) x^2 - 6x + 9 = 0 --> (x - 3)^2 = 0 --> x = 3. So, sufficient.

Your reasoning for (2) is correct.
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Re: If y = x^2 - 6x + 9, what is the value of x?  [#permalink]

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07 Nov 2018, 23:00
but i got different answer from what others got ? why is that ?
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Re: If y = x^2 - 6x + 9, what is the value of x?  [#permalink]

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07 Nov 2018, 23:04
hero_with_1000_faces wrote:
but i got different answer from what others got ? why is that ?

What different answer did you get? For which statement?
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Re: If y = x^2 - 6x + 9, what is the value of x?  [#permalink]

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07 Nov 2018, 23:20
Bunuel wrote:
hero_with_1000_faces wrote:
Hi Bunuel,

I am confused with statement II:

from stem I could find that X is either -3 or 3, then I substituted it into the Equation Y = x^2 -6x + 9, and got either Y is 0 or 36. Thus X + Y = 3, X either 3 or -33.

Although I got two answer, but i think something is wrong with my approach, when compared to other approaches as stated below:

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

From (1) x^2 - 6x + 9 = 0 --> (x - 3)^2 = 0 --> x = 3. So, sufficient.

Your reasoning for (2) is correct.

From Statement II :

I got X is either 3 or -33

While some other users got X = 3 or 2
Re: If y = x^2 - 6x + 9, what is the value of x? &nbs [#permalink] 07 Nov 2018, 23:20

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