GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 20 Jul 2018, 11:44

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

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

Author Message
TAGS:

### Hide Tags

Director
Status: I don't stop when I'm Tired,I stop when I'm done
Joined: 11 May 2014
Posts: 551
GPA: 2.81
If y = x^2 - 6x + 9, what is the value of x?  [#permalink]

### Show Tags

Updated on: 09 Jul 2017, 02:07
2
8
00:00

Difficulty:

25% (medium)

Question Stats:

69% (00:58) correct 31% (00:56) wrong based on 449 sessions

### HideShow timer Statistics

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)

_________________

Md. Abdur Rakib

Please Press +1 Kudos,If it helps
Sentence Correction-Collection of Ron Purewal's "elliptical construction/analogies" for SC Challenges

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.
CEO
Joined: 12 Sep 2015
Posts: 2633
Re: If y = x^2 - 6x + 9, what is the value of x?  [#permalink]

### Show Tags

Updated on: 20 Jul 2016, 09:55
6
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

RELATED VIDEO

_________________

Brent Hanneson – Founder of gmatprepnow.com

Originally posted by GMATPrepNow on 20 Jul 2016, 05:56.
Last edited by GMATPrepNow on 20 Jul 2016, 09:55, edited 2 times in total.
##### General Discussion
Senior Manager
Joined: 02 Mar 2012
Posts: 334
Schools: Schulich '16
Re: If y = x^2 - 6x + 9, what is the value of x?  [#permalink]

### Show Tags

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
Intern
Joined: 28 Apr 2015
Posts: 19
GMAT 1: 600 Q46 V27
GMAT 2: 630 Q47 V30
Re: If y = x^2 - 6x + 9, what is the value of x?  [#permalink]

### Show Tags

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?
Intern
Joined: 28 Apr 2015
Posts: 19
GMAT 1: 600 Q46 V27
GMAT 2: 630 Q47 V30
Re: If y = x^2 - 6x + 9, what is the value of x?  [#permalink]

### Show Tags

20 Jul 2016, 07:03
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

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.
CEO
Joined: 12 Sep 2015
Posts: 2633
Re: If y = x^2 - 6x + 9, what is the value of x?  [#permalink]

### Show Tags

20 Jul 2016, 07:19
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
_________________

Brent Hanneson – Founder of gmatprepnow.com

Intern
Joined: 07 Jun 2017
Posts: 10
Re: If y = x^2 - 6x + 9, what is the value of x?  [#permalink]

### Show Tags

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?

Sent from my SM-G900F using GMAT Club Forum mobile app
Math Expert
Joined: 02 Sep 2009
Posts: 47157
If y = x^2 - 6x + 9, what is the value of x?  [#permalink]

### Show Tags

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?

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.
_________________
Intern
Joined: 07 Jun 2017
Posts: 10
Re: If y = x^2 - 6x + 9, what is the value of x?  [#permalink]

### Show Tags

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!

Sent from my SM-G900F using GMAT Club Forum mobile app
Retired Moderator
Joined: 19 Mar 2014
Posts: 971
Location: India
Concentration: Finance, Entrepreneurship
GPA: 3.5
Re: If y = x^2 - 6x + 9, what is the value of x?  [#permalink]

### Show Tags

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

_________________

"Nothing in this world can take the place of persistence. Talent will not: nothing is more common than unsuccessful men with talent. Genius will not; unrewarded genius is almost a proverb. Education will not: the world is full of educated derelicts. Persistence and determination alone are omnipotent."

Best AWA Template: https://gmatclub.com/forum/how-to-get-6-0-awa-my-guide-64327.html#p470475

Intern
Joined: 15 Jul 2017
Posts: 7
Re: If y = x^2 - 6x + 9, what is the value of x?  [#permalink]

### Show Tags

07 Sep 2017, 03:43
The question is asking about the value of x, so X could not has two different values?
Math Expert
Joined: 02 Sep 2009
Posts: 47157
Re: If y = x^2 - 6x + 9, what is the value of x?  [#permalink]

### Show Tags

07 Sep 2017, 04:15
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.
_________________
Senior Manager
Joined: 29 Jun 2017
Posts: 497
GPA: 4
WE: Engineering (Transportation)
Re: If y = x^2 - 6x + 9, what is the value of x?  [#permalink]

### Show Tags

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

_________________

Give Kudos for correct answer and/or if you like the solution.

Re: If y = x^2 - 6x + 9, what is the value of x? &nbs [#permalink] 07 Sep 2017, 05:31
Display posts from previous: Sort by

# Events & Promotions

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.