Problem Solving

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

GMAT assassins aren't born, they're made,
Rich