A regular polygon can be constructed with a compass and

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vinni.k: Master | Next Rank: 500 Posts; Posts: 421; Joined: Sun Apr 17, 2011 4:27 amFollowed by: 2 members; Location: India; Thanked: 6 times; GMAT Score:620

by vinni.k » Sun Apr 15, 2018 8:23 am

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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

OA is B

Above question is from veritas. What does "Any product of the five distinct primes 3, 5, 17, 257, and 65537" really mean ?

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Source: Beat The GMAT — Problem Solving | Sun Apr 15, 2018 8:23 am

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by [email protected] » Sun Apr 15, 2018 11:32 am

Hi vinni.k,

We're told that 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. We're asked which of the following regular polygons is NOT constructable with a compass and straightedge.

While this question is complex-looking, the math behind it is actually fairly simple (just multiplication) and we can use the Answers to our advantage. Once we find the one answer that we CANNOT get to based on the above 'restrictions', we can stop working. Let's start with Answer A...

Answer A: 15 sides

Can we get to 15 by multiplying any of the above numbers as described? Yes we can - if we take the product of 3 and 5, we'll get 15. Eliminate Answer A.

Answer B: 18 sides

Can we get to 18 by multiplying any of the above numbers as described? No we cannot; 18 can be prime factored into (2)(3)(3), but there's no way to get those pieces from the above list of numbers. Answer B must be the answer, so we can stop working.

For the sake of thoroughness, here's how you can get to the remaining three answers:
Answer C: 48 sides.... (3)(16) = (3)(2^4) = (3)(a power of 2)
Answer D: 51 sides.... (3)(17)
Answer E: 60 sides.... (3)(5)(4) = (3)(5)(2^2) = (3)(5)(a power of 2)

Final Answer: B

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Rich

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regor60: Master | Next Rank: 500 Posts; Posts: 416; Joined: Thu Oct 15, 2009 11:52 am; Thanked: 27 times

by regor60 » Mon Apr 16, 2018 6:37 am

The wording seems ambigous to me.

If you're permitted to use only one instance of a prime number in pairing it with a power of 2, the problem should say "any ONE of the distinct..."

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Mon Apr 16, 2018 6:49 am

regor60 wrote:The wording seems ambigous to me.

If you're permitted to use only one instance of a prime number in pairing it with a power of 2, the problem should say "any ONE of the distinct..."

I agree with you, regor60.

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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