gracie wrote:
The number of diagonals of two different regular polygons each consists of two identical digits.
The square root of the sum of the sides of both polygons equals the number of sides of a
A. nonagon
B. hendecagon
C. heptagon
D. pentagon
E. triskaidecagon
source:me
Dear
gracie,
I'm happy to respond.
As an intriguing math question, I would give this a B+.
As a GMAT-like math question, I would give this a D-.
First of all, I would say that the wording of the first sentence is problematic. At first, I took you to mean that the two different numbers were of the form AB and BA. I think it would be much much easier to specify that the two numbers are both multiples of 11. If you don't want to mention 11 explicitly, I think a better wording would be as follows:
"
The number of diagonals of two different regular polygons each is number in which the tens digits and the ones digit are identical."
Recognizing the significance of 11 is key. The number of diagonals in an n-sided polygon is n(n-3)/2, and the only way this will be divisible by 11 is if n = 11 or n - 3 = 11, that is, n = 14. A regular 11-sided polygon has 44 diagonals, and a regular 14-sided polygon has 77 diagonals.
11 + 14 = 25
The square root = 5.
A five-sided polygon is a pentagon. Answer =
(D) With better wording, this would be genuinely intriguing problem. Unfortunately, this is not at all like a hard GMAT math problem. What makes a hard math problem specifically a GMAT-like hard math problem is quite subtle.
Among other things, I don't know that I have seen any official question that requires students both to know the number of diagonals equation and to do further calculations with that equation. GMAT students should know the "
pentagon," but all the rest of the shape names, while perfectly correct from the point of view of geometry, are beyond what the GMAT expects students to know.
If a problem is hard simply because it uses math beyond what the GMAT expects students to know, then it is hard but not GMAT-like. The trick is to stay well within the limits of what GMAT students clearly and unambiguously need to know, and yet produce a problem that is tricky despite the fact that all the math is straightforward.
Does all this make sense?
Mike