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

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Manager
Joined: 09 Feb 2013
Posts: 118
A regular polygon can be constructed with a compass and stra  [#permalink]

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12 Mar 2013, 08:35
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Difficulty:

55% (hard)

Question Stats:

67% (02:07) correct 33% (01:48) wrong based on 188 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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Manager
Joined: 24 Jan 2013
Posts: 72
Re: A regular polygon can be constructed with a compass and stra  [#permalink]

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13 Mar 2013, 09:05
3
a) 15: the product of the distinct prime numbers 3 and 5 (i.e. 3x5)
b) 18
c) 48: the product of the 4th power of 2, and the prime number 3 (i.e. 16x3)
d) 51: the product of the distinct prime numbers 3 and 17 (i.e. 3x17)
e) 60: the product of the 2nd power of 2, and the distinct prime numbers 5 and 3 (i.e. 4x5x3)

By the way, decomposing 18 gives: 2x3x3 ----> prime number 3 is repeated, so this does not satisfy the conditions to build a regular polygon with a compass and straightedge.

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

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01 Apr 2014, 02:09
I think following wording is ambiguous :

"the product of any power of 2 and any of the five distinct primes"

1st interpretation :

$$2^n * any-of-the-prime-from-set[ 3, 5, 17, 257, 65537 ]$$

Option E (A 60-sided regular polygon) does not qualifies for above interpretation.

60= 2^n * {3 or 5}

2nd interpretation :

$$2^n * any-product-of-the-prime-from-set[ 3, 5, 17, 257, 65537 ]$$

Option E (A 60-sided regular polygon) qualifies for above interpretation.

60= 2^n * {3 and 5}

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

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26 Jul 2014, 23:02
yes the wordings in the question is ambiguous ....esp coz of option E
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Re: A regular polygon can be constructed with a compass and stra  [#permalink]

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06 Jun 2016, 22:06
18 = 2*3*3
an additional 3 , therefore B
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Re: A regular polygon can be constructed with a compass and stra  [#permalink]

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06 Jun 2016, 22:48
sivaspurthy wrote:
yes the wordings in the question is ambiguous ....esp coz of option E

"any" means "one or more"

So when we say "the product of any power of 2 and any of the five distinct primes," it means one or more of the 5 distinct primes could be taken.
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Re: A regular polygon can be constructed with a compass and stra  [#permalink]

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28 Oct 2017, 07:36
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Re: A regular polygon can be constructed with a compass and stra &nbs [#permalink] 28 Oct 2017, 07:36
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