Bunuel wrote:
FRESH GMAT CLUB TESTS QUESTION
The length of each side of equilateral triangle M is 3 times the length of each side of equilateral triangle N. What is the perimeter of equilateral triangle N ?
(1) The ratio of the area of equilateral triangle M to the area of equilateral triangle N is 9:1
(2) The sum of the circumferences of circles circumscribing triangles M and N is \(12\pi\)
\(M_{side}=3y…N_{side}=y…N_{perimeter}=3(y)=3y=M_{side}\)
(1) The ratio of the area of equilateral triangle M to the area of equilateral triangle N is 9:1 insufic.\(\frac{M_{area}}{N_{area}}=9…\frac{(3y)^2√3/4}{(y)^2√3/4}=9…\frac{9y^2}{y^2}=9…9=9…y=?\)
(2) The sum of the circumferences of circles circumscribing triangles M and N is \(12\pi\) sufic.\(Circle_M…30:60:90=altitude,side/2,radius=a:a√3:2a…\)
\(M_{side}/2=(3y)/2=a√3…a=3y/(2√3)…M_{radius}=2[3y/(2√3)]=3y/√3\)
\(Circle_N…30:60:90=a:a√3:2a…\)
\(N_{side}/2=(y)/2=a√3…a=y/(2√3)…N_{radius}=2[y/(2√3)]=y/√3\)
\(2π(M_{radius}+N_{radius})=12π…(3y/√3+y/√3)=6…4y√3/3=6…4y√3=18…y√3=9/2…y=4.5/√3\)
Answer (B)