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A regular polygon can be constructed with a compass and straightedge

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

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New post 05 Nov 2019, 01:43
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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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Re: A regular polygon can be constructed with a compass and straightedge  [#permalink]

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New post 05 Nov 2019, 01:45
Answer B
as 18=2*3*3

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

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New post 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

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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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A regular polygon can be constructed with a compass and straightedge

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