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# A regular polygon can be constructed with a compass and straightedge

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Math Expert
Joined: 02 Sep 2009
Posts: 60647
A regular polygon can be constructed with a compass and straightedge  [#permalink]

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05 Nov 2019, 01:43
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Difficulty:

25% (medium)

Question Stats:

73% (02:09) correct 27% (02:21) wrong based on 56 sessions

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A regular polygon can be constructed with a compass and straightedge if its number of sides is either any power of 2, any product of the five distinct primes 3, 5, 17, 257, and 65537, or the product of any power of 2 and any of the five distinct primes. Which of the following regular polygons is NOT constructable with a compass and straightedge?

A. A 15-sided regular polygon
B. An 18-sided regular polygon
C. A 48-sided regular polygon
D. A 51-sided regular polygon
E. A 60-sided regular polygon

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Joined: 17 May 2019
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Re: A regular polygon can be constructed with a compass and straightedge  [#permalink]

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05 Nov 2019, 01:45
as 18=2*3*3

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Joined: 20 Jul 2017
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Re: A regular polygon can be constructed with a compass and straightedge  [#permalink]

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05 Nov 2019, 10:43
Bunuel wrote:
A regular polygon can be constructed with a compass and straightedge if its number of sides is either any power of 2, any product of the five distinct primes 3, 5, 17, 257, and 65537, or the product of any power of 2 and any of the five distinct primes. Which of the following regular polygons is NOT constructable with a compass and straightedge?

A. A 15-sided regular polygon
B. An 18-sided regular polygon
C. A 48-sided regular polygon
D. A 51-sided regular polygon
E. A 60-sided regular polygon

Are You Up For the Challenge: 700 Level Questions

A regular polygon can be constructed if the number of sides is product of
Any 5 distinct prime numbers 3, 5, 17, 257 and 65537
3*5 = 15
3*17 = 51

Or product of any power of 2 and any of the above prime numbers
—> 2^4*3 = 16*3 = 48
—> 2^2*3*5 = 4*15 = 60

So, only option left is 18. (B)

IMO Option B

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Re: A regular polygon can be constructed with a compass and straightedge   [#permalink] 05 Nov 2019, 10:43
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