Last visit was: 31 Aug 2026, 17:42 It is currently 31 Aug 2026, 17:42
Home
Messages
Tests
Schools
Events
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
Back to Forum
Create Topic
705-805 (Hard)|   Geometry|      
User avatar
GMATBusters
User avatar
GMAT Tutor
Joined: 27 Oct 2017
Last visit: 21 Aug 2026
Posts: 1,924
Own Kudos:
7,027
 [4]
Given Kudos: 242
WE:General Management (Education)
Expert
Expert reply
Posts: 1,924
Kudos: 7,027
 [4]
Equilateral triangle BDF is inscribed in equilateral triangle ACE, as 13 Oct 2018, 10:34
Kudos
Add Kudos
4
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

85% (hard)

Question Stats:

46% (02:50) correct 54% (02:11) wrong based on 63 sessions

History

Date
Time
Result
Not Attempted Yet
Attachment:
Q.jpg
Q.jpg [ 6.61 KiB | Viewed 3076 times ]
Equilateral triangle BDF is inscribed in equilateral triangle ACE, as shown in the figure above. The shaded region is what fraction of the area of triangle ACE ?
(1) ∠DFE = 90°
(2) The length of AF is \(10\sqrt{3}\)

Weekly Quant Quiz #4 Ques 8

ShowHide Answer
Official Answer
A
User avatar
Archit3110
User avatar
Major Poster
Joined: 18 Aug 2017
Last visit: 31 Aug 2026
Posts: 8,808
Own Kudos:
5,328
Given Kudos: 243
Status:You learn more from failure than from success.
Location: India
Concentration: Sustainability, Marketing
GMAT Focus 1: 545 Q79 V79 DI73
GMAT Focus 2: 645 Q83 V82 DI81
GPA: 4
WE:Marketing (Energy)
GMAT Focus 2: 645 Q83 V82 DI81
Posts: 8,808
Kudos: 5,328
Equilateral triangle BDF is inscribed in equilateral triangle ACE, as 13 Oct 2018, 10:41
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Equilateral triangle BDF is inscribed in equilateral triangle ACE, as shown in the figure above. The shaded region is what fraction of the area of triangle ACE ?
(1) ∠DFE = 90°
(2) The length of AF is 103‾√

C
User avatar
Gladiator59
User avatar
Joined: 16 Sep 2016
Last visit: 18 Mar 2026
Posts: 829
Own Kudos:
2,773
Given Kudos: 269
Status:It always seems impossible until it's done.
GMAT 1: 740 Q50 V40
GMAT 2: 770 Q51 V42
Products:
My Reviews
GMAT 2: 770 Q51 V42
Posts: 829
Kudos: 2,773
Equilateral triangle BDF is inscribed in equilateral triangle ACE, as 13 Oct 2018, 10:48
Kudos
Add Kudos
Bookmarks
Bookmark this Post
THe answer to this question could be (A) . Please find my solution attached.

Regards,
GLadi
Attachments

Q4_8.jpeg
Q4_8.jpeg [ 117.39 KiB | Viewed 2988 times ]

User avatar
sushforgmat
User avatar
Joined: 26 Dec 2017
Last visit: 30 Jul 2021
Posts: 72
Own Kudos:
35
 [1]
Given Kudos: 92
Location: India
Concentration: Technology, Marketing
Schools: Tepper '22 (WL) Kelley '22 (A$) Jones '22 (A$) Foster '22 (A$) Darden '22 (D) McCombs '22 (A) Kenan-Flagler '22 (A$) ISB '21 (A) Marshall '22 (A$)
WE:General Management (Internet and New Media)
Schools: Tepper '22 (WL) Kelley '22 (A$) Jones '22 (A$) Foster '22 (A$) Darden '22 (D) McCombs '22 (A) Kenan-Flagler '22 (A$) ISB '21 (A) Marshall '22 (A$)
Posts: 72
Kudos: 35
 [1]
Equilateral triangle BDF is inscribed in equilateral triangle ACE, as 13 Oct 2018, 10:50
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Statement 1:
We know Angle DEF = 60, Angle DFE=90 so Angle EDF = 30. This basically gives us the ratio of sides DF:FE:ED = Sqrt3:1:2. From this we can derive the ratio of the sides of the Bigger triangle. And we can easily get the area of the shaded region.

Eliminate B, C, E.

Statement 2:
Tells only about AF and nothing about any other sides or angles. So there might be many triangles with this length of AF.
Insufficient.

Answer = A
User avatar
u1983
User avatar
Current Student
Joined: 24 Aug 2016
Last visit: 06 Jun 2021
Posts: 700
Own Kudos:
882
Given Kudos: 97
GMAT 1: 540 Q49 V16
GMAT 2: 680 Q49 V33
Products:
My Reviews
GMAT 2: 680 Q49 V33
Posts: 700
Kudos: 882
Equilateral triangle BDF is inscribed in equilateral triangle ACE, as 13 Oct 2018, 11:11
Kudos
Add Kudos
Bookmarks
Bookmark this Post
(1) ∠DFE = 90° .......NS........ will not get the area
(2) The length of AF is 10root 3 .......NS...... will not get the area

1+2) can calculate all the areas of the trangles.....thus Suff Ans C
User avatar
mohagar
User avatar
Joined: 14 Aug 2017
Last visit: 15 May 2021
Posts: 63
Own Kudos:
35
Given Kudos: 136
Location: India
Concentration: Other, General Management
Schools: Kelley '22 Duke '22 Johnson '22 McDonough '22 DeGroote "22 Katz '22 Schulich(Jan) '22 (A) Sauder '22
GMAT 1: 640 Q48 V29
Schools: Kelley '22 Duke '22 Johnson '22 McDonough '22 DeGroote "22 Katz '22 Schulich(Jan) '22 (A) Sauder '22
GMAT 1: 640 Q48 V29
Posts: 63
Kudos: 35
Equilateral triangle BDF is inscribed in equilateral triangle ACE, as 13 Sep 2019, 06:28
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Gladiator59
THe answer to this question could be (A) . Please find my solution attached.

Regards,
GLadi
Show more


howw long did u take to solve this question
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 39,210
Own Kudos:
1,156
Posts: 39,210
Kudos: 1,156
Equilateral triangle BDF is inscribed in equilateral triangle ACE, as 04 Jul 2023, 18:05
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:
Bunuel
Math Expert
113036 posts
FrozenDragon
DI Forum Moderator
410 posts