GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 09 Dec 2019, 10:59 ### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # Does regular polygon X have more than 6 sides?

Author Message
TAGS:

### Hide Tags

Math Expert V
Joined: 02 Sep 2009
Posts: 59623
Does regular polygon X have more than 6 sides?  [#permalink]

### Show Tags 00:00

Difficulty:   95% (hard)

Question Stats: 39% (02:08) correct 61% (01:58) wrong based on 134 sessions

### HideShow timer Statistics

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.

_________________
Manager  B
Joined: 02 Mar 2017
Posts: 71
GMAT 1: 700 Q51 V34 Re: Does regular polygon X have more than 6 sides?  [#permalink]

### Show Tags

1
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.
CEO  D
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2977
Location: India
GMAT: INSIGHT
Schools: Darden '21
WE: Education (Education)
Re: Does regular polygon X have more than 6 sides?  [#permalink]

### Show Tags

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

_________________
Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION
VP  V
Joined: 30 Jan 2016
Posts: 1174
Does regular polygon X have more than 6 sides?  [#permalink]

### Show Tags

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
Attachments hexagon-long-diagonals.png [ 8.04 KiB | Viewed 1811 times ]

_________________
Non progredi est regredi
Math Expert V
Joined: 02 Sep 2009
Posts: 59623
Re: Does regular polygon X have more than 6 sides?  [#permalink]

### Show Tags

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.

_________________
Intern  B
Joined: 02 Oct 2016
Posts: 4
Re: Does regular polygon X have more than 6 sides?  [#permalink]

### Show Tags

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

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.
Intern  B
Joined: 30 Sep 2018
Posts: 1
Re: Does regular polygon X have more than 6 sides?  [#permalink]

### Show Tags

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!
Intern  B
Joined: 02 Jan 2018
Posts: 41
GMAT 1: 710 Q50 V36 GMAT 2: 710 Q48 V40 GMAT 3: 720 Q50 V37 Re: Does regular polygon X have more than 6 sides?  [#permalink]

### Show Tags

I have a question.
If it's a 10 sided poly then the interior angles are [(10-2)/10]=144 which is an integer so shouldn't A be the answer?
Manager  S
Joined: 19 Jan 2019
Posts: 110
Re: Does regular polygon X have more than 6 sides?  [#permalink]

### Show Tags

chinmaysawant 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.

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!

Take n= 7 or 11..

You won't get an integral value for the interior angles.. infact all the values of n between 3 and 6 will give an integral value, and n is nothing but the number of sides of the polygon... so n > 6 will give you atleast one non integral value of the interior angles.. and that's all what you need.

Posted from my mobile device Re: Does regular polygon X have more than 6 sides?   [#permalink] 27 Feb 2019, 19:29
Display posts from previous: Sort by

# Does regular polygon X have more than 6 sides?  