BIB BOOK TEST 1 Problem

GRE Quant Problem Solving
1

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Source: Big book
Ans B
Please help me know how and why?

Thank you

2

So this was my approach to the problem:

  1. First, I focused on the word “equilateral”. From this you can discern all three circles have equal radii. This would help us find the perimeter, which would be 2r + 2r + 2r (r being the radii of each circle)

NOTE: The circles meeting at one point, perpendicularly bisect each triangle’s side. This is why the side lengths are 2r each.

  1. Circumference of circle Q would be 2pi(r) which is approximately 6.28*r

Thus B would be slightly bigger than A. (6.28>6)

Now as to how you can verify if all three circles have equal radii, make one circle bigger than the other two, with the other two having equal radii. The triangle would end up being isosceles. So, the only way the triangle PQR would remain equilateral was if all three circles had equal radii.

Hope this helps.