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Math Expert V
Joined: 02 Sep 2009
Posts: 60506
If (x + 3)(x − 2) − (x − 2)(x − 2) = y(x − 2), what is the value of x?  [#permalink]

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Difficulty:   65% (hard)

Question Stats: 41% (01:55) correct 59% (02:08) wrong based on 30 sessions

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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

_________________
GMAT Club Legend  V
Joined: 18 Aug 2017
Posts: 5700
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
If (x + 3)(x − 2) − (x − 2)(x − 2) = y(x − 2), what is the value of x?  [#permalink]

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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.
Senior Manager  P
Joined: 13 Feb 2018
Posts: 495
GMAT 1: 640 Q48 V28
Re: If (x + 3)(x − 2) − (x − 2)(x − 2) = y(x − 2), what is the value of x?  [#permalink]

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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
GMAT Club Legend  V
Joined: 18 Aug 2017
Posts: 5700
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: If (x + 3)(x − 2) − (x − 2)(x − 2) = y(x − 2), what is the value of x?  [#permalink]

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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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Senior Manager  P
Joined: 12 Dec 2015
Posts: 474
Re: If (x + 3)(x − 2) − (x − 2)(x − 2) = y(x − 2), what is the value of x?  [#permalink]

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1
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 Re: If (x + 3)(x − 2) − (x − 2)(x − 2) = y(x − 2), what is the value of x?   [#permalink] 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?  