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

 It is currently 17 Jan 2019, 22:23

### 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

## Events & Promotions

###### Events & Promotions in January
PrevNext
SuMoTuWeThFrSa
303112345
6789101112
13141516171819
20212223242526
272829303112
Open Detailed Calendar
• ### The winning strategy for a high GRE score

January 17, 2019

January 17, 2019

08:00 AM PST

09:00 AM PST

Learn the winning strategy for a high GRE score — what do people who reach a high score do differently? We're going to share insights, tips and strategies from data we've collected from over 50,000 students who used examPAL.
• ### Free GMAT Strategy Webinar

January 19, 2019

January 19, 2019

07:00 AM PST

09:00 AM PST

Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT.

# The interior angles,in degrees, of a polygon are all distinct integers

Author Message
TAGS:

### Hide Tags

Retired Moderator
Status: Preparing for GMAT
Joined: 25 Nov 2015
Posts: 986
Location: India
GPA: 3.64
The interior angles,in degrees, of a polygon are all distinct integers  [#permalink]

### Show Tags

Updated on: 19 Jan 2018, 06:39
1
00:00

Difficulty:

45% (medium)

Question Stats:

63% (01:57) correct 37% (02:42) wrong based on 42 sessions

### HideShow timer Statistics

The interior angles, in degrees, of a polygon are all distinct integers. If the greatest interior angle in the polygon is 144 deg., what is the maximum number of sides that the polygon can have?
A) 5
B) 6
C) 7
D) 8
E) 9

Source - T.I.M.E.

_________________

Please give kudos, if you like my post

When the going gets tough, the tough gets going...

Originally posted by souvonik2k on 19 Jan 2018, 06:09.
Last edited by souvonik2k on 19 Jan 2018, 06:39, edited 2 times in total.
Senior PS Moderator
Joined: 26 Feb 2016
Posts: 3334
Location: India
GPA: 3.12
The interior angles,in degrees, of a polygon are all distinct integers  [#permalink]

### Show Tags

19 Jan 2018, 06:22
souvonik2k wrote:
The interior angles, in degrees, of a polygon are all distinct integers. If the greatest interior angle in the polygon is 144 deg., what is the maximum number of sides that the polygon can have?
A) 5
B) 6
C) 7
D) 8
E) 9

If the interior angles were not distinct integers
The formula for measure of interior angle of the polygon is $$\frac{(n-2)*180}{n}$$

We are given the greatest possible angle is 144 degree.
Since the angles are distinct, the angles must be at least 1 lesser than the previous angle.
The sum for 9 such angles is 140*9(144+143+142+141+140+139+138+137+136)

Hence, the equation would not be (n-2)*180 = 1260
180n = 1260+360 => n = 9(Option E)

_________________

You've got what it takes, but it will take everything you've got

Retired Moderator
Status: Preparing for GMAT
Joined: 25 Nov 2015
Posts: 986
Location: India
GPA: 3.64
Re: The interior angles,in degrees, of a polygon are all distinct integers  [#permalink]

### Show Tags

19 Jan 2018, 06:32
pushpitkc wrote:
souvonik2k wrote:
The interior angles, in degrees, of a polygon are all distinct integers. If the greatest interior angle in the polygon is 144 deg., what is the maximum number of sides that the polygon can have?
A) 5
B) 6
C) 7
D) 8
E) 9

Kindly check the answer to the question. I think it must be 10.

The formula for measure of interior angle of the polygon is $$\frac{(n-2)*180}{n}$$
We are given the greatest possible angle is 144 degree.

Hence, $$\frac{(n-2)*180}{n} = 144$$
Solving for n we will get n=10

Hi
This formula is applicable when all the interior angles are equal.
Here all angles are distinct, so this formula will not be applicable.
_________________

Please give kudos, if you like my post

When the going gets tough, the tough gets going...

Retired Moderator
Status: Preparing for GMAT
Joined: 25 Nov 2015
Posts: 986
Location: India
GPA: 3.64
The interior angles,in degrees, of a polygon are all distinct integers  [#permalink]

### Show Tags

19 Jan 2018, 07:33
Exterior angle of the largest interior angle = 180-144 = 36 deg.
This will be the smallest exterior angle.
In order to get the largest no. of sides, let us take the exterior angles consecutive.
Sum of exterior angles of a polygon is 360 deg.
Thus, 36+37+....44=360
Maximum no. of sides = 9
Attachments

Doc1.docx [11.13 KiB]

_________________

Please give kudos, if you like my post

When the going gets tough, the tough gets going...

Senior PS Moderator
Joined: 26 Feb 2016
Posts: 3334
Location: India
GPA: 3.12
The interior angles,in degrees, of a polygon are all distinct integers  [#permalink]

### Show Tags

19 Jan 2018, 09:02
souvonik2k wrote:
Exterior angle of the largest interior angle = 180-144 = 36 deg.
This will be the smallest exterior angle.
In order to get the largest no. of sides, let us take the exterior angles consecutive.
Sum of exterior angles of a polygon is 360 deg.
Thus, 36+37+....44=360
Maximum no. of sides = 9

I agree. I missed the part about the interior angles being different. Have corrected the solution accordingly.
_________________

You've got what it takes, but it will take everything you've got

The interior angles,in degrees, of a polygon are all distinct integers &nbs [#permalink] 19 Jan 2018, 09:02
Display posts from previous: Sort by