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Does regular polygon X have more than 6 sides?

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Does regular polygon X have more than 6 sides?  [#permalink]

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New post 21 Jul 2017, 04:01
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Fresh GMAT Club Tests' Challenge Question:



Does regular polygon X have more than 6 sides?

(1) The ratio of the length of the longest line that can be drawn between two vertices of polygon X to the length of any one side of polygon X is greater than 2.
(2) The degree measure of an interior angle of polygon X is NOT an integer.

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Re: Does regular polygon X have more than 6 sides?  [#permalink]

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New post 21 Jul 2017, 04:52
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IMO D.

Statement 1: As we move from Triangle to hexagon we can see that this ratio increases from 1 ----> 1.732, hence for ratio to be 2, the polygon should be the one with more than 6 sides

Statement 2: As we move from triangle to hexagon we can see that the interior angle will always be integer. But as soon as we have more than 6 sides the interior angle becomes non Integer.

Mathematically, any interior angle can be given by [ ( N-2)/N x 180], where N= number of sides of the regular polygon. All values of N from 3 to 6 are factor of 180.
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Re: Does regular polygon X have more than 6 sides?  [#permalink]

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New post 21 Jul 2017, 05:52
Bunuel wrote:

Fresh GMAT Club Tests' Challenge Question:



Does regular polygon X have more than 6 sides?

(1) The ratio of the length of the longest line that can be drawn between two vertices of polygon X to the length of any one side of polygon X is greater than 2.
(2) The degree measure of an interior angle of polygon X is NOT an integer.



The regular polygon has
Exterior angle = 360/n = 360/6 = 60 degrees
Interior angle = 180-Exterior = 180-(360/n) = 180-60 = 120 degrees
Length of Diagonal = 2*Length of side


Statement 1: The ratio of the length of the longest line that can be drawn between two vertices of polygon X to the length of any one side of polygon X is greater than 2.
Since the longest diagonal in a hexagon is twice the length of side therefore the polygon discussed in Question is definitely not a six sided polygon
SUFFICIENT

Statement 2: The degree measure of an interior angle of polygon X is NOT an integer.
But we have already seen that the degree measure of a six sided polygon is 120 hence it's definitely not a six sided polygon
SUFFICIENT

Answer: Option D
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Does regular polygon X have more than 6 sides?  [#permalink]

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New post 21 Jul 2017, 08:03
Bunuel wrote:

Fresh GMAT Club Tests' Challenge Question:



Does regular polygon X have more than 6 sides?

(1) The ratio of the length of the longest line that can be drawn between two vertices of polygon X to the length of any one side of polygon X is greater than 2.
(2) The degree measure of an interior angle of polygon X is NOT an integer.


The question asks "Does regular polygon X have more than 6 sides?"

(1)
Let's take a square. The length of the longest line is the diameter of the square. So the ratio of diameter to the side increases because the length of the diameter is constant, and the length of the side (chord) decreases.

As the question is concerned with a 6-sided polygon, let's take a regular hexagon - 6 sided regular polygon.
The sum of its angles is (n-2)x180=720. So, each angle is 720/6=120 degrees.
The length of the longest line is the diameter of the circumscribed circle, i.e. AD.
Angle OAF = angle OFA= 60 degrees => triangle AOF is equilateral. So, AF is equal to the length of the radius => 1/2 of the diameter.
Per st.1, the ratio of diagonal is more than 2, so the polygon must have more than 6 angles.
Sufficient.

(2)
Angle of a triangle = 180/3 = 60
Angle of a square = 360/4 = 90
Pentagon: Sum of angles = (n-2) x 180 = 540. Angle of pentagon = 540/5 = 108
Angle of hexagon, as mentioned above, is 120 degrees.

Sufficient, we can stop here and move on.

The asnwer is D

Just to prove, the sum of angles of the 7 sided polygon (heptagon) = (7-3)x180=900. 900/7=128 4/7

Hence D
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hexagon-long-diagonals.png
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Re: Does regular polygon X have more than 6 sides?  [#permalink]

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New post 24 Dec 2018, 03:13
Bunuel wrote:

Fresh GMAT Club Tests' Challenge Question:



Does regular polygon X have more than 6 sides?

(1) The ratio of the length of the longest line that can be drawn between two vertices of polygon X to the length of any one side of polygon X is greater than 2.
(2) The degree measure of an interior angle of polygon X is NOT an integer.


Par of GMAT CLUB'S New Year's Quantitative Challenge Set


_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

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Re: Does regular polygon X have more than 6 sides?  [#permalink]

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New post 06 Jan 2019, 12:00
GMATinsight wrote:
Bunuel wrote:

Fresh GMAT Club Tests' Challenge Question:



Does regular polygon X have more than 6 sides?

(1) The ratio of the length of the longest line that can be drawn between two vertices of polygon X to the length of any one side of polygon X is greater than 2.
(2) The degree measure of an interior angle of polygon X is NOT an integer.



The regular polygon has
Exterior angle = 360/n = 360/6 = 60 degrees
Interior angle = 180-Exterior = 180-(360/n) = 180-60 = 120 degrees
Length of Diagonal = 2*Length of side


Statement 1: The ratio of the length of the longest line that can be drawn between two vertices of polygon X to the length of any one side of polygon X is greater than 2.
Since the longest diagonal in a hexagon is twice the length of side therefore the polygon discussed in Question is definitely not a six sided polygon
SUFFICIENT

Statement 2: The degree measure of an interior angle of polygon X is NOT an integer.
But we have already seen that the degree measure of a six sided polygon is 120 hence it's definitely not a six sided polygon
SUFFICIENT

Answer: Option D





This post, I think does not fit here. The question asks for whether the polygon has more than 6 sides, while this reply by GMATInsight proves that it is not a Hexagon/6 sided polygon.
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Re: Does regular polygon X have more than 6 sides?  [#permalink]

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New post 08 Jan 2019, 07:35
Bunuel wrote:

Fresh GMAT Club Tests' Challenge Question:



Does regular polygon X have more than 6 sides?

(1) The ratio of the length of the longest line that can be drawn between two vertices of polygon X to the length of any one side of polygon X is greater than 2.
(2) The degree measure of an interior angle of polygon X is NOT an integer.



For the 2nd option,

If the polygon has 12 sides,

interior angle = (n-2/n)*180 = (10/12)*180 = 150 which is an integer.

So only 1st option is correct according to me.
Let me know if I am wrong.
Thanks!
GMAT Club Bot
Re: Does regular polygon X have more than 6 sides? &nbs [#permalink] 08 Jan 2019, 07:35
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