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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] If y = x^2 - 6x + 9, what is the value of x?   Updated on: 09 Jul 2017, 02:07
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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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A

Originally posted by AbdurRakib on 01 Jul 2016, 05:14.
Last edited by Bunuel on 09 Jul 2017, 02:07, edited 1 time in total.
Renamed the topic and edited the question.
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If y = x^2 - 6x + 9, what is the value of x? [#permalink] If y = x^2 - 6x + 9, what is the value of x?   Updated on: 15 Mar 2020, 13:29
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AbdurRakib
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

Answer: A

RELATED VIDEO

Originally posted by BrentGMATPrepNow on 20 Jul 2016, 05:56.
Last edited by BrentGMATPrepNow on 15 Mar 2020, 13:29, edited 3 times in total.
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Re: If y = x^2 - 6x + 9, what is the value of x? [#permalink] If y = x^2 - 6x + 9, what is the value of x?   16 Jul 2017, 13:37
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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? [#permalink] If y = x^2 - 6x + 9, what is the value of x?   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] If y = x^2 - 6x + 9, what is the value of x?   09 Jul 2017, 02:10
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mariachi0204
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] If y = x^2 - 6x + 9, what is the value of x?   07 Sep 2017, 03:43
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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] If y = x^2 - 6x + 9, what is the value of x?   07 Sep 2017, 04:15
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mrmortezajafari
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] If y = x^2 - 6x + 9, what is the value of x?   08 Nov 2018, 00:20
Bunuel
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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
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Re: If y = x^2 - 6x + 9, what is the value of x? [#permalink] If y = x^2 - 6x + 9, what is the value of x?   08 Nov 2018, 00:29
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Bunuel
hero_with_1000_faces
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

I don't see how you got that.

The statement (2) is actually quite easy and should not be confusing:

The stem says that y = x^2 - 6x + 9
(2) says that x + y = 3, so y = 3 - x.

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

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

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

\((3- x)(3- x - 1) = 0\)

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

\(x = 3\) or \(x = 2\).

Hope it's clear!
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Re: If y = x^2 - 6x + 9, what is the value of x? [#permalink] If y = x^2 - 6x + 9, what is the value of x?   17 Sep 2019, 06:29
AbdurRakib
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)

If y = x^2 - 6x + 9, what is the value of x?
\(y = (x-3)^2\)

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

(2) x + y = 3
Since value of y is unknown
NOT SUFFICIENT

IMO A
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Re: If y = x^2 - 6x + 9, what is the value of x? [#permalink] If y = x^2 - 6x + 9, what is the value of x?   05 Nov 2019, 05:31
GMATPrepNow
AbdurRakib
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

Answer =
Show Spoiler
A

RELATED VIDEO


Hi ,

I have a doubt while considering statement 2
Why can’t we form the equation as stated below :
Y = 3-X
And then put and solve ,

3-X = (X-3)^2
Or , 3-X = (3-X)^2 Because (x-3)^2 = (3-x)^2

Then X=3

So Answer D

Kindly help

Posted from my mobile device
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Re: If y = x^2 - 6x + 9, what is the value of x? [#permalink] If y = x^2 - 6x + 9, what is the value of x?   05 Nov 2019, 05:45
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LeenaSai
GMATPrepNow
AbdurRakib
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

Answer =
Show Spoiler
A

RELATED VIDEO


Hi ,

I have a doubt while considering statement 2
Why can’t we form the equation as stated below :
Y = 3-X
And then put and solve ,

3-X = (X-3)^2
Or , 3-X = (3-X)^2 Because (x-3)^2 = (3-x)^2

Then X=3

So Answer D

Kindly help

Posted from my mobile device

From the stem: y = (3 - x)^2
From (2): y = 3 - x.

So, (3 - x)^2 = 3 - x.
(3 - x)^2 - (3 - x) = 0;
(3 - x)(3 - x - 1) = 0;
(3 - x)(2 - x) = 0;
x = 3 or x = 2.
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If y = x^2 - 6x + 9, what is the value of x? [#permalink] If y = x^2 - 6x + 9, what is the value of x?   Updated on: 05 Nov 2019, 05:55
Thanks for the prompt reply Bunuel ,

But I am stuck that why can’t we cancel the common (3-x) from both sides ?

Originally posted by LeenaSai on 05 Nov 2019, 05:48.
Last edited by LeenaSai on 05 Nov 2019, 05:55, edited 1 time in total.
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Re: If y = x^2 - 6x + 9, what is the value of x? [#permalink] If y = x^2 - 6x + 9, what is the value of x?   05 Nov 2019, 05:55
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LeenaSai
Thanks for the prompt reply Bunuel ,

But I am stuck that why can’t we cancel the common (3-x ) from both sides ?

You cannot reduce (3 - x)^2 = 3 - x by 3 -x because 3 - x can be 0 and we cannot divide by 0. By doing so you loose a root, namely x = 3.

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.

By the way, all this is already explained on previous two pages. I suggest to re-read the whole thread.

Hope it helps.
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Re: If y = x^2 - 6x + 9, what is the value of x? [#permalink] If y = x^2 - 6x + 9, what is the value of x?   13 Mar 2020, 08:45
GMATPrepNow
AbdurRakib
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

Answer =
Show Spoiler
A

RELATED VIDEO

Hi GMATPrepNow thanks for the valuable video :) I had a question; as per the videos, does it then mean that every time we must solve the entire question to ensure that the variable doesn't disappear and also solve the quadratic equation every time to ensure whether or not it has two solutions?
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Re: If y = x^2 - 6x + 9, what is the value of x? [#permalink] If y = x^2 - 6x + 9, what is the value of x?   13 Mar 2020, 09:52
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Hi GMATPrepNow thanks for the valuable video :) I had a question; as per the videos, does it then mean that every time we must solve the entire question to ensure that the variable doesn't disappear and also solve the quadratic equation every time to ensure whether or not it has two solutions?

When it comes to DS questions where we need to find some value from an equation, we must always ensure that there's only one possible answer to the target question.
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Re: If y = x^2 - 6x + 9, what is the value of x? [#permalink] If y = x^2 - 6x + 9, what is the value of x?   30 Jun 2021, 11:49
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AbdurRakib
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)
Solution:

Question Stem Analysis:

We need to determine the value of x.

Statement One Alone:

Since y = 0, we can solve the equation:

x^2 - 6x + 9 = 0

(x - 3)^2 = 0

x - 3 = 0

x = 3

Statement one alone is sufficient.

Statement Two Alone:

Since x + y = 3, y = 3 - x and we can solve the equation:

x^2 - 6x + 9 = 3 - x

x^2 - 5x + 6 = 0

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

x = 3 or x = 2

Since x can be either 3 or 2, statement two alone is not sufficient.

Answer: A
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Re: If y = x^2 - 6x + 9, what is the value of x? [#permalink] If y = x^2 - 6x + 9, what is the value of x?   30 Aug 2021, 10:55
Top Contributor
Statement 1: y=0

\( x^2 - 6x + 9 =0\)
\((x-3)^2 = 0\)
\( x=3\)
Since you get a definite value of x, statement 1 is sufficient.

Statement 2: x + y = 3 ===> y= 3-x
\( y = x^2 - 6x + 9\)
\(3-x=x^2 - 6x + 9\)
\(x^2 - 5x + 6=0\)
\((x-3)(x-2)=0\)
\(x=3,2\)
Since two values are possible for x, statement 2 is insufficient

Option A is the answer

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