Events & Promotions
|
|
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
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Aug 2710:00 AM EDT
-11:00 AM EDT
We’ve worked incredibly hard to build TTP into the best test prep experience possible, and it would mean a lot to us to win Newsweek’s 2026 Readers’ Choice Award for Best Test Prep. If TTP has helped you, we’d be incredibly grateful for your vote.
Sep 0410:00 AM PDT
-11:00 AM PDT
What does test anxiety really look like on the GMAT? For many test takers, it does not look like a panic attack. Instead, it shows up as brain fog, rereading, negative comparisons, mental noise....
Sep 0609:30 AM EDT
-12:30 PM EST
Top scores are possible when you enroll in a powerful EA course, taught live online + 6 months access to TTP OnDemand video courses included! Perfect class schedule and easy course access for working professionals. Class starts Sundays Sept. 6, 2026.- Sep 07
12:01 AM PDT
-11:59 PM PDT
On the 7th, GMAT Club Tests will be Free! Including all the Quizzes, Questions, and Tests. 12 AM - 11:59 PM PDT - Sep 09
07:00 AM PDT
-10:00 AM PDT
Meet AdComs and explore top Master’s programs - MiM, MiF, MSc, MSBA and more. - Application Fee Waivers - Free 1-Week of GMAT Club Tests: - Master's Application Toolkit - Grand Prize Giveaway 
Sep 1507:00 PM EDT
-09:00 PM EST
Elite scores are possible when you enroll in a powerful GMAT course, taught live online + 6 months access to TTP OnDemand video courses included! Class starts Tues/Thurs Sept. 15, 2026 - Nov. 15, 2027, 7:00pm-9:00pm EST
Sep 2108:00 PM EDT
-10:00 PM EDT
Boost your GMAT score in less than one month in a live online class + 6 months access to TTP OnDemand video courses included! Class starts Mon, Tues, Wed, Thur, Fri Sept. 21, 2026 - Oct. 9, 2027, 7:00pm-10:00pm EST
BillyZ
Current Student
Joined: 14 Nov 2016
Last visit: 06 Jun 2026
Posts: 1,134
Given Kudos: 926
Location: Malaysia
Concentration: General Management, Strategy
Schools: Sloan '23 (D) Tuck '23 (D) Darden '23 (D) Ross '23 (D) Kellogg '23 (D) Wharton '23 (D) Booth '23 (D) Fuqua '24 (A) Harvard '24 (D) Stanford '24 (D)
GMAT 1: 750 Q51 V40 (Online)
GPA: 3.53
Products:
Schools: Sloan '23 (D) Tuck '23 (D) Darden '23 (D) Ross '23 (D) Kellogg '23 (D) Wharton '23 (D) Booth '23 (D) Fuqua '24 (A) Harvard '24 (D) Stanford '24 (D)
GMAT 1: 750 Q51 V40 (Online)
Posts: 1,134
30 Mar 2017, 18:37
Kudos
Bookmarks
rxs0005
OFFICIAL SOLUTION
We are told that the smallest angle measures 136 degrees--this is the first term in the consecutive set. If the polygon has S sides, then the largest angle--the last term in the consecutive set--will be (S - 1) more than 136 degrees.
The sum of consecutive integers = (Average Term) * (# of Term)= \(\frac{First + Last}{2}\) * (# of Terms).
Given that there are S terms in the set, we can plug in for the first and last term as follows:
\(\frac{136 + 136 + (S-1)}{2} * S\) = sum of the angles in the polygon.
We also know that the sum of the angles in a polygon = 180 (S-2) where S represents the number of sides.
Therefore: \(180(S-2) = \frac{136+136+(S-1)}{2} * S\). We can solve
for S by cross-multiplying and simplifying as follows:
\(2(180)(S-2) = [272 + (S-1)] S\)
\(360S - 720 = (271 + S)S\)
\(360S - 720 = 271S + S^2\)
\(S^2 - 89S + 720 = 0\)
A look at the answer choices tells you to try (S - 8), (S - 9), or (S - 10) in factoring.
As it turns out (S-9)(S-80)=0, which means S can be 9 or 80. However S cannot be 80 because this creates a polygon with angles greater than 180.
Therefore S equals 9; there are 9 sides in the polygon.
The correct answer is B.
24 Apr 2017, 06:20
Kudos
Bookmarks
Reverse Approach using external angle
We are given : smallest internal angle = 136 deg ;
to find : number of sides 'n'
Solution : We know that, internal angle = (n - 2)*180;
But, we dont know value of n. However, we know one thing for sure. Irrespective of the value of n, Sum of all the external angles will be 360 deg.
So, Corresponding external angle for internal angle of 136 deg = 180 - 136 = 44 deg. (Since, Sum of internal + external angle = 180 deg)
As internal angle increases by 1 external angle decreases by 1.
So, now 2nd external angle will be 43 deg, 3rd external angle will be 42 deg, 4th will be 41 deg and so on. We keep doing this till the point our sum of all external angles turns out to be 360 deg.
So, 44 + 43 + 42 + 41 + 40 + 39 + 38 + 37 + 36 = 360
total number of terms in above equation is 9. So the number of sides of polygon = 9
( We can also use concept of AP. All the terms are in AP. We know S = 360, t1 = 44, d = -1, n=?
360 = n/2* (2*44 + (n-1)*-1) => n^2 - 89n + 720 = 0 => n = 80 or n = 9)
We are given : smallest internal angle = 136 deg ;
to find : number of sides 'n'
Solution : We know that, internal angle = (n - 2)*180;
But, we dont know value of n. However, we know one thing for sure. Irrespective of the value of n, Sum of all the external angles will be 360 deg.
So, Corresponding external angle for internal angle of 136 deg = 180 - 136 = 44 deg. (Since, Sum of internal + external angle = 180 deg)
As internal angle increases by 1 external angle decreases by 1.
So, now 2nd external angle will be 43 deg, 3rd external angle will be 42 deg, 4th will be 41 deg and so on. We keep doing this till the point our sum of all external angles turns out to be 360 deg.
So, 44 + 43 + 42 + 41 + 40 + 39 + 38 + 37 + 36 = 360
total number of terms in above equation is 9. So the number of sides of polygon = 9
( We can also use concept of AP. All the terms are in AP. We know S = 360, t1 = 44, d = -1, n=?
360 = n/2* (2*44 + (n-1)*-1) => n^2 - 89n + 720 = 0 => n = 80 or n = 9)
02 Sep 2019, 01:53
Kudos
Bookmarks
I still think that the fastest (though may not be the best way as expounded extensively in this post) to solve this question is to make use of the fact that 180(n-2) will always have Unit Digit = 0 (try n=3,4,...etc)
The fact is that we are given a starting number of 136, and we know for SURE that all angles are consecutive numbers. That would mean (pun intended) that the mean * n must = UD of 0.
We can narrow down to 9 or 10, but a surer bet would be to use the fact that the MEAN would always have a UD of zero i.e. only 140 is the nearest possible answer we have here. Then, multiplying by number of sides would always yield UD zero.
Hence (B).
The fact is that we are given a starting number of 136, and we know for SURE that all angles are consecutive numbers. That would mean (pun intended) that the mean * n must = UD of 0.
We can narrow down to 9 or 10, but a surer bet would be to use the fact that the MEAN would always have a UD of zero i.e. only 140 is the nearest possible answer we have here. Then, multiplying by number of sides would always yield UD zero.
Hence (B).
