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

Question

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

OG Q 2017 New Question(Book Question: 230)

BrentGMATPrepNow · Accepted Answer

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

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ydmuley · Answer

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 Did you like the answer? 1 Kudos Please :good

mariachi0204 · Answer

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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Bunuel · Answer

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.

mrmortezajafari · Answer

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

Bunuel · Answer

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.

hero_with_1000_faces · Answer

From Statement II :

I got X is either 3 or -33

While some other users got X = 3 or 2

Bunuel · Answer

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!

Kinshook · Answer

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

LeenaSai · Answer

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

Bunuel · Answer

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.

LeenaSai · Answer

Thanks for the prompt reply Bunuel ,

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

Bunuel · Answer

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.

Kritisood · Answer

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?

BrentGMATPrepNow · Answer

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.

ScottTargetTestPrep · Answer

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

CrackverbalGMAT · Answer

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

Thanks,
Clifin J Francis
GMAT SME

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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?

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