Last visit was: 15 Jul 2025, 09:48 It is currently 15 Jul 2025, 09:48
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.
Close
Request Expert Reply
Confirm Cancel
User avatar
MathRevolution
User avatar
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Last visit: 27 Sep 2022
Posts: 10,078
Own Kudos:
18,746
 [7]
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
Expert
Expert reply
GMAT 1: 760 Q51 V42
Posts: 10,078
Kudos: 18,746
 [7]
Kudos
Add Kudos
7
Bookmarks
Bookmark this Post
User avatar
dave13
Joined: 09 Mar 2016
Last visit: 23 Nov 2024
Posts: 1,114
Own Kudos:
1,087
 [1]
Given Kudos: 3,851
Posts: 1,114
Kudos: 1,087
 [1]
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
User avatar
rahul16singh28
Joined: 31 Jul 2017
Last visit: 09 Jun 2020
Posts: 430
Own Kudos:
493
 [2]
Given Kudos: 752
Location: Malaysia
GPA: 3.95
WE:Consulting (Energy)
Posts: 430
Kudos: 493
 [2]
Kudos
Add Kudos
2
Bookmarks
Bookmark this Post
User avatar
MathRevolution
User avatar
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Last visit: 27 Sep 2022
Posts: 10,078
Own Kudos:
18,746
 [2]
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
Expert
Expert reply
GMAT 1: 760 Q51 V42
Posts: 10,078
Kudos: 18,746
 [2]
Kudos
Add Kudos
2
Bookmarks
Bookmark this Post
=>

\(\frac{a^2}{(a-b)}=b\)
\(⇔ a^2=b(a-b)\)
\(⇔ a^2=ab – b^2\)
\(⇔ a^2 - ab + b^2 = 0\)
Since \(a≠b\), one of a and b is not zero.
If \(a ≠ 0\) or \(b ≠ 0\), \(a^2 - ab + b^2\) cannot be zero for the following reason:
\(a^2 - ab + b^2 = a^2 – 2a(\frac{b}{2}) + b^2 = a2 – 2a(\frac{b}{2}) + \frac{b^2}{3} + (\frac{3}{4})b^2\)
\(= (a – \frac{b}{2})^2 + (\frac{3}{4})b^2 > 0\)
Thus, there is no pair of real numbers \((a,b)\) satisfying the equation \(a^2 - ab + b^2 = 0.\)

Therefore, \(a\) cannot exist, and the answer is E.
Answer: E
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 37,404
Own Kudos:
Posts: 37,404
Kudos: 1,013
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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.
Moderators:
Math Expert
102579 posts
PS Forum Moderator
691 posts