GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

It is currently 02 Jun 2020, 08:00

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

Let a, b, and c be positive integers with a> b > c such that a^2 - b^2

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 64172
Let a, b, and c be positive integers with a> b > c such that a^2 - b^2  [#permalink]

Show Tags

New post 18 Apr 2019, 00:01
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

18% (02:12) correct 82% (03:29) wrong based on 11 sessions

HideShow timer Statistics

VP
VP
User avatar
V
Joined: 28 Jul 2016
Posts: 1020
Location: India
Concentration: Finance, Human Resources
Schools: ISB '18 (D)
GPA: 3.97
WE: Project Management (Investment Banking)
Reviews Badge
Re: Let a, b, and c be positive integers with a> b > c such that a^2 - b^2  [#permalink]

Show Tags

New post 18 Apr 2019, 00:22
Awaiting explanation by someone:
I was able to add two equations and come up with

\(a^2−b^2−c^2+ab=2011\)
\(a^2+3b^2+3c^2−3ab−2ac−2bc=−1997\)
------------------------------------------------
\(2a^2+2b^2+2c^2−2ab−2ac−2bc =14\)
or
\(a^2+b^2+c^2−ab−ac−bc =7\)

and
\(a^3+b^3+c^3−3abc=(a+b+c)[a^2+b^2+c^2−ab−bc−ac]\)

\(a^3+b^3+c^3−3abc=7(a+b+c)\)

But could not solve further
_________________

Keep it simple. Keep it blank
Intern
Intern
avatar
B
Joined: 18 Nov 2018
Posts: 27
Re: Let a, b, and c be positive integers with a> b > c such that a^2 - b^2  [#permalink]

Show Tags

New post 18 Apr 2019, 03:24
IMO E

Combine two equations and we have
a^2 + b^2 + c^2 - 2ab - 2ac - 2bc = 14
(a-b)^2 + (b-c)^2 + (a-c)^2 = 14

Since a>b>c and all three are integer, (a-c)^2 is 9 while (b-c)^2 and (a-b)^2 can be either 1 and 4.

Two scenarios: either a=c+3 & b=c+2 or a=c+3 & b=c+1

Replace the scenarios into the equation a^2 -b^2 -c^2 +ab = 2011 and we get only 1 integer solution for c which is 250. a=250+3=253.

Posted from my mobile device
GMAT Club Bot
Re: Let a, b, and c be positive integers with a> b > c such that a^2 - b^2   [#permalink] 18 Apr 2019, 03:24

Let a, b, and c be positive integers with a> b > c such that a^2 - b^2

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





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