Last visit was: 20 Nov 2024, 07:37 It is currently 20 Nov 2024, 07:37
Decision Tracker
My Rewards
New comers' posts
New posts
Unanswered

Close

GRE Prep 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
Your Progress

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

Practice
Pays

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Go to My Error Log Learn more
Close

Request Expert Reply

Confirm Cancel
PREVIOUS TOPIC
NEXT TOPIC

If (x-1)^2=(x-2)^2, then x=

Tags :
Find Similar Topics  About  Add a Tag

Show Tags
Hide Tags

User avatar
D
Carcass
Verbal Expert
Joined: 18 Apr 2015
Posts: 29991
Own Kudos [?]: 36305 [0]
Given Kudos: 25921
Send PM
If (x-1)^2=(x-2)^2, then x= [#permalink] New post   Updated on: 03 Jan 2024, 04:36
Expert Reply
00:00

Question Stats:

100% (01:18) correct 0% (00:00) wrong based on 9 sessions

Hide Show timer Statistics

If \((x-1)^2=(x-2)^2\), then \(x=\)

A. -5/8

B. 5/3

C. 4/3

D. 3/2

E. 5/2
ShowHide Answer
Official Answer
D

Originally posted by Carcass on 11 Dec 2020, 22:19.
Last edited by Carcass on 03 Jan 2024, 04:36, edited 1 time in total.
Fixed typo
avatar
B
endurance
Manager
Manager
Joined: 06 Nov 2020
Posts: 85
Own Kudos [?]: 69 [0]
Given Kudos: 101
Send PM
Re: If (x-1)^2=(x-2)^2, then x= [#permalink] New post   12 Dec 2020, 03:17
1
the answer is 3/2 !!
avatar
G
GR3A
Manager
Manager
Joined: 02 Sep 2019
Posts: 181
Own Kudos [?]: 144 [0]
Given Kudos: 94
Concentration: Finance
GRE 1: Q151 V148
GPA: 3.14
Send PM
Re: If (x-1)^2=(x-2)^2, then x= [#permalink] New post   12 Dec 2020, 08:13
2
(x-1)^2 = (x-2)^2
Factoring each side, we get
x^2-2x+1= x^2-4x+4 subtract (x^2) for both side
-2x+1=-4x+4 add +4x for both sides and subtract 1
2x= 3 ==> x= 3/2.

and it is true that (3/2-1)^2 = (3/2-2)^2
0.5^2 = -0.5^2
avatar
logann2
Manager
Manager
Joined: 22 Aug 2019
Posts: 96
Own Kudos [?]: 85 [2]
Given Kudos: 0
Send PM
Re: If (x-1)^2=(x-2)^2, then x= [#permalink] New post   16 Dec 2020, 21:49
1
1
Bookmarks
(x-1)^2 = (x-2)^2

We know that quadratic curves are symmetric. so what number ends up same magnitude when you subtract 1 and 2 from it?

1.5 because 1.5-1 = .5 and 1.5-2 = -.5. (squaring cancels the negative 1)
User avatar
G
HarishKumar
GRE Instructor
Joined: 24 Dec 2018
Posts: 1065
Own Kudos [?]: 1425 [1]
Given Kudos: 24
Send PM
Re: If (x-1)^2=(x-2)^2, then x= [#permalink] New post   03 Jan 2024, 00:38
1
if \((x-1)^ = (x-2)^2\) then,

expanding both sides of the equation, we get

\(x^2 + 1^2 - 2\times 1\times x = x^2 + 2^2 - 2\times 2 \times x\)

\(x^2 + 1 - 2x = x^2 + 4 - 4x\)

cancelling like terms on both sides and rearranging,

\(2x - 3 = 0\)

\(2x = 3\)

\(x = \frac{3}{2}\)
avatar
QuantBusters
Intern
Intern
Joined: 27 Dec 2023
Posts: 2
Own Kudos [?]: 1 [1]
Given Kudos: 1
Send PM
Re: If (x-1)^2=(x-2)^2, then x= [#permalink] New post   03 Jan 2024, 03:09
1
Hi

There is a typo in option D. It should be 3/2.

Thanks

Carcass wrote:
If \((x-1)^2=(x-2)^2\), then \(x=\)

A. -5/8

B. 5/3

C. 4/3

D. 2/3

E. 5/2
User avatar
D
Carcass
Verbal Expert
Joined: 18 Apr 2015
Posts: 29991
Own Kudos [?]: 36305 [1]
Given Kudos: 25921
Send PM
Re: If (x-1)^2=(x-2)^2, then x= [#permalink] New post   03 Jan 2024, 04:36
1
Expert Reply
the book had the typo

thanks sir fixed
Prep Club for GRE Bot
gmatclubot
Re: If (x-1)^2=(x-2)^2, then x= [#permalink]
03 Jan 2024, 04:36
Moderators:
adewale223
GRE Instructor
81 posts
bronaugust
GRE Forum Moderator
37 posts
BrushMyQuant
Moderator
1111 posts
VibhuAnurag
GRE Instructor
234 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Main navigation

Partners

GRE Resources

www.ets.org/gre | About | Terms and Conditions and Privacy Policy | Prep Club for GRE Rules | Contact