NEW HERE? LEARN MORE
closeclose
It is currently 19 Apr 2024, 12:46
Register
GMAT Focus Tests
Decision Tracker
My Rewards
New posts
New comers' posts

Close
GMAT 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 GMAT 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

If (x-p)^2 - (x-t)^2 / t-p = x-t and

8 posts Go to First Unread Post
Print view
NEW TOPIC
POST REPLY
Question banks

GMAT Question Banks

Downloads
My Bookmarks
Reviews
SORT BY:
Date
Kudos
avatar
xhimi
Intern
Intern
Joined: 17 Jul 2013
Status:Hulk
Posts: 11
Location: Singapore
Concentration: Entrepreneurship, Finance
Schools: Insead '14 (M)
GMAT 1: 600 Q44 V30
GMAT 2: 650 Q45 V34
GMAT 3: 690 Q49 V34
If (x-p)^2 - (x-t)^2 / t-p = x-t and [#permalink] New post  05 Dec 2013, 20:41
1
Kudos
9
Bookmarks
00:00
A
B
C
D
E

Difficulty:

45% (medium)

Question Stats:

72% (02:19) correct 28% (02:53) wrong based on 281 sessions
Hide Show timer Statistics
If \(\frac{(x-p)^2 - (x-t)^2}{t-p} = x-t\) and \(t\neq{p}\) , then x=

A) p
B) t
C) p-2t
D) t+p
E) t-p

What is the best approach to solve for x?
ShowHide Answer
Official Answer
Official Answer and Stats are available only to registered users. Register/Login.
Most Helpful Reply
User avatar
B
mau5
Verbal Forum Moderator
Joined: 10 Oct 2012
Posts: 485
Re: If (x-p)^2 - (x-t)^2 / t-p = x-t and [#permalink] New post  05 Dec 2013, 21:48
5
Kudos
3
Bookmarks
xhimi wrote:
If \(\frac{(x-p)^2 - (x-t)^2}{t-p} = x-t\) and \(t\neq{p}\) , then x=

A) p
B) t
C) p-2t
D) t+p
E) t-p

What is the best approach to solve for x?


We know that\(a^2-b^2 = (a-b)*(a+b)\)

Thus, \(\frac{(x-p)^2 - (x-t)^2}{t-p} = \frac{(x-p+x-t)*[(x-p)-(x-t)])}{t-p} \to \frac{(2x-p-t)*(t-p)}{t-p}\)

As \(t\neq{p}\) , we can cancel it from both Numerator and Denominator, and we get \(2x-p-t = x-t \to x = p\)

A.
_________________
All that is equal and not-Deep Dive In-equality

Hit and Trial for Integral Solutions
Signature Read More
General Discussion
User avatar
L
KarishmaB
Tutor
Joined: 16 Oct 2010
Posts: 14815
Location: Pune, India
Re: If (x-p)^2 - (x-t)^2 / t-p = x-t and [#permalink] New post  05 Dec 2013, 21:42
3
Kudos
1
Bookmarks
Expert Reply
xhimi wrote:
If \(\frac{(x-p)^2 - (x-t)^2}{t-p} = x-t\) and \(t\neq{p}\) , then x=

A) p
B) t
C) p-2t
D) t+p
E) t-p

What is the best approach to solve for x?


I would put values for t and p such that each option gives a different answer. Say, t= 3, p = 1. Every option gives a different answer so when I put these values in the equation, I will get my answer for sure.

\(\frac{(x-1)^2 - (x-3)^2}{3-1} = x-3\)

\(\frac{4x - 8}{3-1} = x-3\)

\(2x - 4 = x - 3\)

x = 1
Only option (A) gives 1 when we put t = 3, p = 1 in the options. So x must be equal to p (which is option (A))

Answer (A)
avatar
xhimi
Intern
Intern
Joined: 17 Jul 2013
Status:Hulk
Posts: 11
Location: Singapore
Concentration: Entrepreneurship, Finance
Schools: Insead '14 (M)
GMAT 1: 600 Q44 V30
GMAT 2: 650 Q45 V34
GMAT 3: 690 Q49 V34
Re: If (x-p)^2 - (x-t)^2 / t-p = x-t and [#permalink] New post  05 Dec 2013, 21:59
I got lost in the algebraic approach, so thanks for showing both ways Karishma and Mau5
avatar
PareshGmat
SVP
SVP
Joined: 27 Dec 2012
Status:The Best Or Nothing
Posts: 1563
Location: India
Concentration: General Management, Technology
WE:Information Technology (Computer Software)
Re: If (x-p)^2 - (x-t)^2 / t-p = x-t and [#permalink] New post  11 Apr 2014, 01:44
1
Kudos
\(x^2 - 2xp + p^2 - (x^2 - 2xt + t^2) = xt - xp - t^2 + pt\)

(2x - x) * (t-p) = p * (t-p)

x = p

Answer = A
User avatar
B
PerfectScores
Tutor
Joined: 20 Dec 2013
Posts: 104
Re: If (x-p)^2 - (x-t)^2 / t-p = x-t and [#permalink] New post  11 Apr 2014, 02:25
1
Bookmarks
Expert Reply
xhimi wrote:
If \(\frac{(x-p)^2 - (x-t)^2}{t-p} = x-t\) and \(t\neq{p}\) , then x=

A) p
B) t
C) p-2t
D) t+p
E) t-p

What is the best approach to solve for x?


If t = 3 and p = 2 then

(x - 2)^2 - (x - 3)^2 = (x - 3) (3 - 2)

x^2 + 4 - 4x - x^2 - 9 + 6x = x - 3


2x - 5 = x - 3

x = 2

Hence x = p
User avatar
G
chrtpmdr
Current Student
Joined: 24 Jul 2019
Posts: 207
Schools: HSG MBF "23 (A) UniBocconi MFin "23 (A)
GMAT 1: 730 Q46 V45
GPA: 3.9
Re: If (x-p)^2 - (x-t)^2 / t-p = x-t and [#permalink] New post  28 Jul 2020, 06:12
Any similar questions?
_________________
Let's get some
Signature Read More
User avatar
bumpbot
Non-Human User
Joined: 09 Sep 2013
Posts: 32544
Re: If (x-p)^2 - (x-t)^2 / t-p = x-t and [#permalink] New post  07 Jun 2023, 10:24
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources
Signature Read More
GMAT Club Bot
gmatclubot
Re: If (x-p)^2 - (x-t)^2 / t-p = x-t and [#permalink]
07 Jun 2023, 10:24
NEW TOPIC
POST REPLY
Downloads
My Bookmarks
Reviews
Moderators:
Bunuel
Math Expert
92760 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

cron

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions