Last visit was: 22 Apr 2026, 18:20 It is currently 22 Apr 2026, 18:20
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
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 22 Apr 2026
Posts: 109,754
Own Kudos:
Given Kudos: 105,823
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 109,754
Kudos: 810,671
 [16]
1
Kudos
Add Kudos
15
Bookmarks
Bookmark this Post
Most Helpful Reply
User avatar
bidskamikaze
Joined: 07 Jan 2018
Last visit: 29 Oct 2022
Posts: 251
Own Kudos:
307
 [7]
Given Kudos: 160
Location: India
GMAT 1: 710 Q49 V38
GMAT 1: 710 Q49 V38
Posts: 251
Kudos: 307
 [7]
6
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
General Discussion
User avatar
pandajee
Joined: 27 Nov 2018
Last visit: 17 Dec 2022
Posts: 56
Own Kudos:
46
 [2]
Given Kudos: 70
Posts: 56
Kudos: 46
 [2]
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
User avatar
nick1816
User avatar
Retired Moderator
Joined: 19 Oct 2018
Last visit: 12 Mar 2026
Posts: 1,841
Own Kudos:
8,508
 [2]
Given Kudos: 707
Location: India
Posts: 1,841
Kudos: 8,508
 [2]
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
two lines are making 60 degrees angle with line x=1 and all three lines create an equilateral triangle, that means if one line has +ve slope, other line must have -ve slope.
Equation of a line, having -ve slope, passing through origin and making 60 degrees with line x=1 is
y=-(1/√3)x
Intersection point of x=1 and y=-(1/√3)x= (1, -1/√3)
Intersection point of x=1 and y=1+(√3/3)x= {1, 1+(√3/3)}
distance between (1, -1/√3) and {1, 1+(√3/3)}= (3+2√3)/3
perimeter of equilateral triangle= 3*side = 3* (3+2√3)/3 = (3+2√3)
User avatar
Crytiocanalyst
Joined: 16 Jun 2021
Last visit: 27 May 2023
Posts: 943
Own Kudos:
Given Kudos: 309
Posts: 943
Kudos: 214
Kudos
Add Kudos
Bookmarks
Bookmark this Post
2 lines make 60 degree angle one has positive slope and other negative slope
m=-1/3^(1/2) since 60 degree and negative slope
c=0 passing through origin
y=-(1/√3)x
The meeting of the lines of:
x=1 and y=-(1/√3)x= (1, -1/√3)
The meeting of the lines of:
x=1 and y=1+(√3/3)x= (1, 1+(√3/3))
one side of the equilateral triangle being the distance between
(1, -1/√3) and (1, 1+(√3/3))= (3+2√3)/3
perimeter of the triangle being=3* (3+2√3)/3 = (3+2√3)(equilateral triangle )
Hence IMO D
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 38,964
Own Kudos:
Posts: 38,964
Kudos: 1,117
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Automated notice from GMAT Club BumpBot:

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

This post was generated automatically.
Moderators:
Math Expert
109754 posts
Tuck School Moderator
853 posts