Brent and Hemant are both correct, but there's a way that you could quickly guess on this problem.
When we're looking for the perimeter of one section, we know we're going to have 2 straight pieces (2 spokes), and one curved piece (the edge of the wheel). We know that the circumference of the wheel is in terms of pi, so any piece of that circumference will also be something*pi.
However, those straight pieces (the spokes) won't have a pi. So if we're adding 2 spokes + 1 curved piece, we know the answer has to be "something + something*pi." We could eliminate B and C.
We know that the GMAT likes to include trap answers, so looking at 14 or 7... you can bet that 7 is the trap answer for people who only counted 1 spoke, not 2. Now looking at 2pi or 4pi, 4pi is probably the trap for people who accidentally counted 2 curved pieces instead of 1.
So if we just had to quickly guess, we'd guess A here. And we'd be right!
Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
