Events & Promotions
|
|
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
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Sep 2312:30 AM EDT
-01:30 AM EDT
Learn how Keshav, a Chartered Accountant, scored an impressive 705 on GMAT in just 30 days with GMATWhiz's expert guidance. In this video, he shares preparation tips and strategies that worked for him, including the mock, time management, and more
Sep 2401:30 AM EDT
-01:30 AM EDT
Tejas studied hard but kept repeating the same mistakes. After 3 attempts at 645, a focused 4-week strategy helped him identify and fix what was holding him back—leading to a 695 with just 12–15 hours of study per week.
Sep 2606:00 PM PDT
-07:00 PM PDT
Free- full-length test + 15 concept videos + 150+ short videos + study plan!
05 May 2020, 11:55
Kudos
Bookmarks
D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
37% (02:04) correct
63%
(02:05)
wrong
based on 68
sessions
History
Date
Time
Result
Not Attempted Yet
If ABCDEFGH is a regular octagon, what fraction of the octagon is shaded?
A) 1/12
B) 1/8
C) 1/6
D) 1/4
E) 3/8
06 May 2020, 05:14
Kudos
Bookmarks
BrentGMATPrepNow
If we focus on rectangle BCFG, we might recognize that the area of the shaded portion is half the area of the rectangle BCFG
How do we know this?
Well, we know that the area of the rectangle = (base)(height)
And we know that the area of the triangle = (base)(height)/2
Since both shapes have the same base and height, it must be the case that the area of the shaded portion is half the area of the rectangle BCFG
With this in mind, let's divide rectangle BCFG into TWO EQUAL rectangles.
From here, we can add two smaller triangles.
Since the area of each small triangle is HALF the area of each small rectangle, we can conclude that the combined areas of the two small triangles is HALF the combined areas of the two small rectangles.
In other words, the combined area of the two shaded triangles is the same as the area of the original triangle (triangle YGF)
At this point, when we add a couple of extra diagonals to the diagram...
.... we can see that the shaded portions account for 2/8 of the entire octagon.
Since 2/8 = 1/4, the correct answer is D.
Cheers,
Brent
General Discussion
05 May 2020, 18:24
Kudos
Bookmarks
As base and height of triangle YGF is equal to those of triangle BGY, Area of triangle YGF = Area of triangle BGY = 1/2 (area of rectangle BCGF)
\(BI = AI = \frac{a}{\sqrt{2}}\)
Hence area of rectangle BCGF = \(2*a*\frac{a}{\sqrt{2}} + a^2= (\sqrt{2}+1)a^2\)
Area of octagon = \(2*(\sqrt{2}+1)a^2 \)= 2*area of rectangle BCGF =2*2*(Area of triangle YGF)
(Area of triangle YGF)/Area of octagon = 1/4
\(BI = AI = \frac{a}{\sqrt{2}}\)
Hence area of rectangle BCGF = \(2*a*\frac{a}{\sqrt{2}} + a^2= (\sqrt{2}+1)a^2\)
Area of octagon = \(2*(\sqrt{2}+1)a^2 \)= 2*area of rectangle BCGF =2*2*(Area of triangle YGF)
(Area of triangle YGF)/Area of octagon = 1/4
BrentGMATPrepNow
Attachments
Untitled.png [ 5.24 KiB | Viewed 10847 times ]
