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A wagon wheel with a circumference of 14π has seven straigh

This topic has 2 expert replies and 2 member replies
vinni.k Master | Next Rank: 500 Posts
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A wagon wheel with a circumference of 14π has seven straigh

Post Tue Jan 29, 2013 8:17 am
A wagon wheel with a circumference of 14π has seven straight spokes that originate at the center of the wheel. If the distance between consecutive spokes on the wheel’s circumference is equivalent, what is the perimeter of each sector of the circle bounded by consecutive spokes?

A) 14 + 2π
B) 7π
C) 14π
D) 14 + 4π
E) 7 + 7π

Answer is A

Thanks & Regards
Vinni
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Top Reply
Post Tue Jan 29, 2013 11:50 am
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!

_________________


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Manhattan Prep GMAT & GRE instructor
EdM in Mind, Brain, and Education
Harvard Graduate School of Education


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vinni.k Master | Next Rank: 500 Posts
Joined
17 Apr 2011
Posted:
333 messages
Followed by:
1 members
Upvotes:
6
Test Date:
2016
Target GMAT Score:
700+
GMAT Score:
620
Top Reply
Post Tue Jan 29, 2013 10:41 am
Thank you.

Regards
Vinni

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Post Tue Jan 29, 2013 11:50 am
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
Manhattan Prep GMAT & GRE instructor
EdM in Mind, Brain, and Education
Harvard Graduate School of Education


Manhattan Prep instructors all have 99th+ percentile scores and expert teaching experience.
Sign up for a FREE TRIAL, and learn why we have the highest ratings in the GMAT industry!

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Free Manhattan Prep online events - The first class of every online Manhattan Prep course is free. Classes start every week.
vinni.k Master | Next Rank: 500 Posts
Joined
17 Apr 2011
Posted:
333 messages
Followed by:
1 members
Upvotes:
6
Test Date:
2016
Target GMAT Score:
700+
GMAT Score:
620
Post Tue Jan 29, 2013 10:41 am
Thank you.

Regards
Vinni

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