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

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Source: — Data Sufficiency |
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Re: If y = x^2 - 6x + 9, what is the value of x?

by deloitte247 » Sun Mar 15, 2020 12:00 pm

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Statement 1: y=0
$$0=x^2-6x+9$$
$$x^2-6x+9=0$$
(x-3)(x-3)=0
x-3=0 or x-3=0
x=3 or x=3
The value of x = 3
Statement 1 is SUFFICIENT

Statement 2: x+y=3
y=3-x
$$3-x=x^2-6x+9$$
$$x^2-6x+x+9-3=0$$
$$x^2-5x+6=0$$
(x-2) (x-3) = 0
x-2 = 0 or x-3 = 0
x=2 or x=3
Since the target question cannot be answered with certainty, then statement 2 is NOT SUFFICIENT.
Therefore, only statement 1 alone is sufficient. Hence, option A is the correct answer.
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Re: If y = x^2 - 6x + 9, what is the value of x?

by Brent@GMATPrepNow » Sun Mar 15, 2020 12:29 pm

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Brent@GMATPrepNow wrote: ↑
Fri Mar 13, 2020 9:52 am
 If y = x^2 - 6x + 9, what is the value of x?

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

Answer: A
Source: Official guide
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

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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