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If (x + 3)(x − 2) − (x − 2)(x − 2) = y(x − 2), what is the value of x?

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Bunuel
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If (x + 3)(x − 2) − (x − 2)(x − 2) = y(x − 2), what is the value of x? [#permalink] New post   09 Dec 2019, 00:37
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If \((x+3)(x−2)−(x−2)(x−2)=y(x−2)\), what is the value of x?


(1) \(y^2 = 25\)

(2) \(y < 1\)


Are You Up For the Challenge: 700 Level Questions
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B
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Archit3110
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If (x + 3)(x − 2) − (x − 2)(x − 2) = y(x − 2), what is the value of x? [#permalink] New post   Updated on: 09 Dec 2019, 09:30
given

\((x+3)(x−2)−(x−2)(x−2)=y(x−2)\)
y=5 or x=2

#1

\(y^2 = 25\)
y=+/-5
insufficient
#2
y<1
y is not 5 so x =2
Sufficient


IMO B



Bunuel wrote:
If \((x+3)(x−2)−(x−2)(x−2)=y(x−2)\), what is the value of x?


(1) \(y^2 = 25\)

(2) \(y < 1\)


Are You Up For the Challenge: 700 Level Questions

Originally posted by Archit3110 on 09 Dec 2019, 03:04.
Last edited by Archit3110 on 09 Dec 2019, 09:30, edited 1 time in total.
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LevanKhukhunashvili
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Re: If (x + 3)(x − 2) − (x − 2)(x − 2) = y(x − 2), what is the value of x? [#permalink] New post   09 Dec 2019, 09:24
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Tricky and confusing. I thought a lot

After simplifying the stem I got
5(x-2)=y(x-2)
Archit3110 made a mistake dividing both sides by x-2 as we are not sure that x-2 does not equal to 0

So there are two cases
y=5 then x can be any number
y is not 5, then x must be 2

1 stm --> y=+-5; both cases possible. Insufficient
2 stm --> y is not 5, so x must be 2. Sufficient

P.s Dont underestimate big "B", when he warns you about the challenge : ))

IMO
Ans: B
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Re: If (x + 3)(x − 2) − (x − 2)(x − 2) = y(x − 2), what is the value of x? [#permalink] New post   09 Dec 2019, 09:32
LevanKhukhunashvili
Thanks..
Even i myself was confused as why question has asked value of x but simplifying solution is giving value for y..
No wonder it's 700 level..


LevanKhukhunashvili wrote:
Tricky and confusing. I thought a lot

After simplifying the stem I got
5(x-2)=y(x-2)
Archit3110 made a mistake dividing both sides by x-2 as we are not sure that x-2 does not equal to 0

So there are two cases
y=5 then x can be any number
y is not 5, then x must be 2

1 stm --> y=+-5; both cases possible. Insufficient
2 stm --> y is not 5, so x must be 2. Sufficient

P.s Dont underestimate big "B", when he warns you about the challenge : ))

IMO
Ans: B


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Re: If (x + 3)(x − 2) − (x − 2)(x − 2) = y(x − 2), what is the value of x? [#permalink] New post   09 Dec 2019, 09:33
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If \((x+3)(x−2)−(x−2)(x−2)=y(x−2)\), what is the value of x?
Solution:
\((x+3)(x−2)−(x−2)(x−2)=y(x−2)\)
=> \((x-2)* ( (x+3)−(x−2) - y)= 0\)
=> \((x-2)* ( y-5)= 0\)
=> x=2 or y=5

(1) \(y^2 = 25\) --> insuff: y = +5 (or y=-5), so we don't know the value of x

(2) \(y < 1\) --> suff --> y < 1, so y not equal to 5, so x= 2

Answer: B
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Re: If (x + 3)(x − 2) − (x − 2)(x − 2) = y(x − 2), what is the value of x? [#permalink] New post   29 Jun 2021, 00:51
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Re: If (x + 3)(x − 2) − (x − 2)(x − 2) = y(x − 2), what is the value of x? [#permalink]
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