BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem
TTP OnDemand GMAT Video Course
Featured Course

Target Test Prep GMAT OnDemand

Scott Woodbury-Stewart’s private virtual classroom — 400 hours of master-class video lessons for the GMAT Focus Edition.

  • 715+ score guarantee — highest in the industry (99th percentile)
  • 52 chapters · 1,500+ lessons · 4,000+ practice questions
  • 400 hours of video · 1,500+ instructor-led HD smartboard lessons
  • 300,000+ students accepted to Harvard, Stanford, Wharton, Booth & Sloan & more
  • 24/7 live support + weekly Zoom office hours with GMAT instructors
  • TTP AI Assist — 24/7 AI-powered virtual tutor for instant help
  • 1,200+ flashcards + AI-powered study assistant & daily calendar
  • OnDemand, LiveTeach & GMAT Bootcamp formats available
  • Also: GRE, SAT Math & Executive Assessment courses
  • MBA Admissions Consulting now available
  • 🏆 2025 EdTech Breakthrough Award: Test Prep Solution Provider of the Year
  • 200,000+ students served
  • 5-day free trial — $0 to start, no auto-billing, cancel anytime
★★★★★ 5.0 (559 reviews)
130-pt guarantee
$0 to start then $127/mo
Start Free 5-Day Trial Read 559 Reviews →

Jeff is painting two murals on the front of an old apartment

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
User avatar
Master | Next Rank: 500 Posts
Posts: 235
Joined: Wed Oct 26, 2016 9:21 pmFollowed by: 5 members
Thanked: 3 times
by Anaira Mitch » Fri Dec 30, 2016 4:38 am
Jeff is painting two murals on the front of an old apartment building that he is renovating. One mural will cover the quadrilateral face ABCD while the other will cover the circular face (shown to the right, with radius XY). Assuming that the thickness of the coats of paint is negligible, will each mural require the same amount of paint? Note: Figures are not drawn to scale.

(1) AB = BC = CD = DA and AB= XY sqrt pie

(2) AC = BD and AC= XY sqrt 2*pie

Please help with this problem.
Attachments
mural.PNG
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Source: — Data Sufficiency |
User avatar
Master | Next Rank: 500 Posts
Posts: 235
Joined: Wed Oct 26, 2016 9:21 pmFollowed by: 5 members
Thanked: 3 times

by Anaira Mitch » Fri Dec 30, 2016 9:19 am
Anyone?
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
GMAT Instructor
Posts: 2630
Joined: Wed Sep 12, 2012 3:32 pmFollowed by: 119 members
Location: East Bay all the way
Thanked: 625 times
GMAT Score:780

by Matt@VeritasPrep » Fri Jan 20, 2017 1:16 am
We're essentially asked (in a more fun way) if the area of the circle = the area of the square, so let's try to answer that.

S1::

Since the quadrilateral has four equal sides, it is either a square or a rhombus. If the side is s, then the area is either s² or unknown, if we have a rhombus.

Naming the radius of the circle r, we've also got r√π = s, or r = s/√π. So we know the area of the circle is π * (s/√π)², or s².

So if the quadrilateral is a circle, the murals have equal area, but if it's only a rhombus they may not: INSUFFICIENT.

S2::

Since the quadrilateral has equal diagonals, it could be a square, a rectangle, or an isosceles trapezoid. We don't know which, so we can't find the area of the quadrilateral: INSUFFICIENT.

S1 + S2::

Together, we know from S1 that we've got either a square or a rhombus, and that each side = r√π. From S2, we know that the diagonal of the quadrilateral = r * √2π. If our quadrilateral is a square, we'd apply the Pythagorean Theorem: Side² + Side² = Diagonal². Here, that gives us

(r√π)² + (r√π)² = (r√2π)²

or

2r²π = 2r²π

Success! So it's a square, and we're set: SUFFICIENT.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1