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pahwa: Community Manager; Posts: 117; Joined: Tue Feb 27, 2007 11:49 pm; Thanked: 9 times

by pahwa » Fri Oct 26, 2007 7:18 am

1. if a

c = 2:3:4, then what is 1/a:1/b:1/c?

2. In a regular pentagon ABCDE, what is measure of angle ABE?
a. 36
b. 72
c. 108
d. 54
e. 90

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Source: Beat The GMAT — Problem Solving | Fri Oct 26, 2007 7:18 am

gmatrant: Master | Next Rank: 500 Posts; Posts: 416; Joined: Wed Oct 03, 2007 9:08 amFollowed by: 1 member; Thanked: 10 times

solution

by gmatrant » Fri Oct 26, 2007 9:40 am

1. if a

c = 2:3:4, then what is 1/a:1/b:1/c?
1/2:1/3:1/4
taking LCM for 2,3,4 is 12
hence they are in ratio 6:4:3

2. Angle ABE is 36 degrees
In a regular pentagon by formula (n-2)*180/5 we get each interior of the regulat polygon. So angle EAB is 108 degrees. ----- (1)
In the triangle EAB. EA is of the same length of AB, thereby their angles are also same , hence angle EAB + 2 angle ABE = 180 degrees
From (1) above we know that EAB is 108, so ABE = 36 degrees

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