Last visit was: 23 Apr 2026, 06:17 It is currently 23 Apr 2026, 06:17
Home
Messages
Tests
Schools
Events
Close
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
Your Progress

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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
Back to Forum
Create Topic
605-655 (Medium)|   Geometry|      
User avatar
calreg11
User avatar
Joined: 27 Oct 2011
Last visit: 07 Mar 2013
Posts: 84
Own Kudos:
1,161
 [46]
Given Kudos: 4
Location: United States
Concentration: Finance, Strategy
Schools: HBS '15 (D) Marshall '15 (II) Anderson '15 (S) Stanford '15 (S) Haas '15 (S)
GPA: 3.7
WE:Account Management (Consumer Packaged Goods)
Schools: HBS '15 (D) Marshall '15 (II) Anderson '15 (S) Stanford '15 (S) Haas '15 (S)
Posts: 84
Kudos: 1,161
 [46]
If Polygon X has fewer than 9 sides, how many sides does 11 Feb 2012, 18:15
5
Kudos
Add Kudos
41
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

45% (medium)

Question Stats:

68% (02:03) correct 32% (01:59) wrong based on 887 sessions

History

Date
Time
Result
Not Attempted Yet
If Polygon X has fewer than 9 sides, how many sides does Polygon X have?

(1) The sum of the interior angles of Polygon X is divisible by 16.

(2) The sum of the interior angles of Polygon X is divisible by 15.
ShowHide Answer
Official Answer
A
Most Helpful Reply
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 23 Apr 2026
Posts: 109,778
Own Kudos:
810,776
 [27]
Given Kudos: 105,853
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 109,778
Kudos: 810,776
 [27]
If Polygon X has fewer than 9 sides, how many sides does 11 Feb 2012, 18:28
14
Kudos
Add Kudos
12
Bookmarks
Bookmark this Post
If Polygon X has fewer than 9 sides, how many sides does Polygon X have?

Sum of inner angles of polygon=180*(x-2), where x is # of sides. Given x<9. Question x=?

(1) The sum of the interior angles of Polygon X is divisible by 16 --> 180*(x-2)=16k --> 45(x-2)=4k --> x-2 must be a multiple of 4 (as 45 is not) --> since x<9 then the only acceptable value of x is 6. Sufficient.

(2) The sum of the interior angles of Polygon X is divisible by 15 --> 180*(x-2)=15m --> 12(x-2)=m --> x can be any integer from 3 to 8, inclusive. Not sufficient. (We could even not consider this statement at all: as sum of inner angles of polygon is 180*(x-2) and 180 is a multiple of 15, then all polygons will have the sum of the interior angles divisible by 15.)

Answer: A.
General Discussion
User avatar
Jp27
User avatar
Joined: 22 Dec 2011
Last visit: 25 Dec 2013
Posts: 171
Own Kudos:
1,194
 [1]
Given Kudos: 32
Posts: 171
Kudos: 1,194
 [1]
If Polygon X has fewer than 9 sides, how many sides does 15 Oct 2012, 07:47
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
If Polygon X has fewer than 9 sides, how many sides does Polygon X have?

Sum of inner angles of polygon=180*(x-2), where x is # of sides. Given x<9. Question x=?

(1) The sum of the interior angles of Polygon X is divisible by 16 --> 180*(x-2)=16k --> 45(x-2)=4k --> x-2 must be a multiple of 4 (as 45 is not) --> since x<9 then the only acceptable value of x is 6. Sufficient.

(2) The sum of the interior angles of Polygon X is divisible by 15 --> 180*(x-2)=15m --> 12(x-2)=m --> x can be any integer from 3 to 8, inclusive. Not sufficient. (We could even not consider this statement at all: as sum of inner angles of polygon is 180*(x-2) and 180 is a multiple of 15, then all polygons will have the sum of the interior angles divisible by 15.)

Answer: A.
Show more

Hi Bunuel - Could you please correct me! I got stuck in statement 2, after seeing your sol it makes more sense. But still want to know what's wrong in the below

Stat 1 -> 180*(x-2)=16k

x-2 = 16k/180
x-2 = 2^2 * k / 3^2 * 5 (after canceling out all the primes)
so for the min value of k = 3^2 * 5 we get x -2 = 2^2 and x= 6

As A can have other primes as well let assume k has another 2 in it, then (x-2) = 2^2 * 2 we get x=10 -> this is not possible as we are constrained by the question stem . So this is sufficient

Stat 2 -> 180*(x-2)=15m
x-2 = m/ 12
so the min value of m can be 12 hence the nos of sides become 14. this is not possible as per the question stem. how to proceed from there?
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 23 Apr 2026
Posts: 109,778
Own Kudos:
810,776
Given Kudos: 105,853
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 109,778
Kudos: 810,776
If Polygon X has fewer than 9 sides, how many sides does 15 Oct 2012, 07:56
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Jp27
Bunuel
If Polygon X has fewer than 9 sides, how many sides does Polygon X have?

Sum of inner angles of polygon=180*(x-2), where x is # of sides. Given x<9. Question x=?

(1) The sum of the interior angles of Polygon X is divisible by 16 --> 180*(x-2)=16k --> 45(x-2)=4k --> x-2 must be a multiple of 4 (as 45 is not) --> since x<9 then the only acceptable value of x is 6. Sufficient.

(2) The sum of the interior angles of Polygon X is divisible by 15 --> 180*(x-2)=15m --> 12(x-2)=m --> x can be any integer from 3 to 8, inclusive. Not sufficient. (We could even not consider this statement at all: as sum of inner angles of polygon is 180*(x-2) and 180 is a multiple of 15, then all polygons will have the sum of the interior angles divisible by 15.)

Answer: A.

Hi Bunuel - Could you please correct me! I got stuck in statement 2, after seeing your sol it makes more sense. But still want to know what's wrong in the below

Stat 1 -> 180*(x-2)=16k

x-2 = 16k/180
x-2 = 2^2 * k / 3^2 * 5 (after canceling out all the primes)
so for the min value of k = 3^2 * 5 we get x -2 = 2^2 and x= 6

As A can have other primes as well let assume k has another 2 in it, then (x-2) = 2^2 * 2 we get x=10 -> this is not possible as we are constrained by the question stem . So this is sufficient

Stat 2 -> 180*(x-2)=15m
x-2 = m/ 12
so the min value of m can be 12 hence the nos of sides become 14. this is not possible as per the question stem. how to proceed from there?
Show more

If m=12, then x-2=12/12=1 --> x=3.
If m=24, then x-2=24/12=2 --> x=4.
...

Hope it's clear.
User avatar
Jp27
User avatar
Joined: 22 Dec 2011
Last visit: 25 Dec 2013
Posts: 171
Own Kudos:
1,194
Given Kudos: 32
Posts: 171
Kudos: 1,194
If Polygon X has fewer than 9 sides, how many sides does 15 Oct 2012, 08:07
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
Jp27
Bunuel
If Polygon X has fewer than 9 sides, how many sides does Polygon X have?

Sum of inner angles of polygon=180*(x-2), where x is # of sides. Given x<9. Question x=?

(1) The sum of the interior angles of Polygon X is divisible by 16 --> 180*(x-2)=16k --> 45(x-2)=4k --> x-2 must be a multiple of 4 (as 45 is not) --> since x<9 then the only acceptable value of x is 6. Sufficient.

(2) The sum of the interior angles of Polygon X is divisible by 15 --> 180*(x-2)=15m --> 12(x-2)=m --> x can be any integer from 3 to 8, inclusive. Not sufficient. (We could even not consider this statement at all: as sum of inner angles of polygon is 180*(x-2) and 180 is a multiple of 15, then all polygons will have the sum of the interior angles divisible by 15.)

Answer: A.

Hi Bunuel - Could you please correct me! I got stuck in statement 2, after seeing your sol it makes more sense. But still want to know what's wrong in the below

Stat 1 -> 180*(x-2)=16k

x-2 = 16k/180
x-2 = 2^2 * k / 3^2 * 5 (after canceling out all the primes)
so for the min value of k = 3^2 * 5 we get x -2 = 2^2 and x= 6

As A can have other primes as well let assume k has another 2 in it, then (x-2) = 2^2 * 2 we get x=10 -> this is not possible as we are constrained by the question stem . So this is sufficient

Stat 2 -> 180*(x-2)=15m
x-2 = m/ 12
so the min value of m can be 12 hence the nos of sides become 14. this is not possible as per the question stem. how to proceed from there?

If m=12, then x-2=12/12=1 --> x=3.
If m=24, then x-2=24/12=2 --> x=4.
...

Hope it's clear.
Show more

I so sorry for posting such a dumb question. I guess too much math today... all nos are appearing blurry now!
User avatar
GC14
User avatar
Joined: 09 May 2012
Last visit: 23 Feb 2013
Posts: 9
Own Kudos:
22
Given Kudos: 7
Posts: 9
Kudos: 22
If Polygon X has fewer than 9 sides, how many sides does 16 Nov 2012, 19:43
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Is this regular polygon, Because I was informed that , we can use (2n-4)*90-Sum of interior angles for regular polygon.

Please somebody correct me.
avatar
ARUNPLDb
avatar
Joined: 09 Jul 2012
Last visit: 14 Jan 2015
Posts: 6
Own Kudos:
24
Given Kudos: 6
Posts: 6
Kudos: 24
If Polygon X has fewer than 9 sides, how many sides does 18 Sep 2013, 12:44
Kudos
Add Kudos
Bookmarks
Bookmark this Post
(1) SUFFICIENT: Using the relationship 180(n – 2) = (sum of interior angles), we could calculate the sum of the interior angles for all the polygons that have fewer than 9 sides. Just the first two are shown below; it would take too long to calculate all of the possibilities.

(2) INSUFFICIENT: Statement (2) tells us that the sum of the interior angles of Polygon X is divisible by 15. Therefore, the prime factorization of the sum of the interior angles will include 3 × 5. Following the same procedure as above, we realize that both 3 and 5 are included in the prime factorization of 180. As a result, every one of the possibilities can be divided by 15 regardless of the number of sides.

The correct answer is A.
User avatar
jlgdr
User avatar
Joined: 06 Sep 2013
Last visit: 24 Jul 2015
Posts: 1,302
Own Kudos:
2,976
 [3]
Given Kudos: 355
Concentration: Finance
Schools: Wharton '17 (A) HBS '17 (WA$)
Schools: Wharton '17 (A) HBS '17 (WA$)
Posts: 1,302
Kudos: 2,976
 [3]
If Polygon X has fewer than 9 sides, how many sides does 15 Nov 2013, 14:54
3
Kudos
Add Kudos
Bookmarks
Bookmark this Post
calreg11
If Polygon X has fewer than 9 sides, how many sides does Polygon X have?

(1) The sum of the interior angles of Polygon X is divisible by 16.

(2) The sum of the interior angles of Polygon X is divisible by 15.
Show more

If you like the x-games or played tony hawk when you were a child you won't have trouble remembering that

3 sides - 180
4- 360
5-540
6-720
7-900

Statement 1, has to be divisible by 15 so by 8 and by 2 or 2^4. Only one that fits the bill is 720. Hence A is suff

Statement 2. Div by 15. More than 1 possible answer so Insuff

Hence A

Cheers!
J :)

Kudos if you like!
User avatar
tgubbay1
User avatar
Joined: 13 Nov 2014
Last visit: 04 Sep 2025
Posts: 28
Own Kudos:
15
Given Kudos: 105
Location: France
Concentration: Healthcare, Statistics
Schools: HBS '25 (D) Booth '25 (A) Wharton '25 (D) Sloan '25 (D) CBS '25 (WD) Haas '25 (WD) Stern '25 (WD) Kellogg '25 (WD) Stanford '25 (WD)
WE:Consulting (Consulting)
Schools: HBS '25 (D) Booth '25 (A) Wharton '25 (D) Sloan '25 (D) CBS '25 (WD) Haas '25 (WD) Stern '25 (WD) Kellogg '25 (WD) Stanford '25 (WD)
Posts: 28
Kudos: 15
If Polygon X has fewer than 9 sides, how many sides does 26 Apr 2015, 10:52
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
If Polygon X has fewer than 9 sides, how many sides does Polygon X have?

Sum of inner angles of polygon=180*(x-2), where x is # of sides. Given x<9. Question x=?

(1) The sum of the interior angles of Polygon X is divisible by 16 --> 180*(x-2)=16k --> 45(x-2)=4k --> x-2 must be a multiple of 4 (as 45 is not) --> since x<9 then the only acceptable value of x is 6. Sufficient.

(2) The sum of the interior angles of Polygon X is divisible by 15 --> 180*(x-2)=15m --> 12(x-2)=m --> x can be any integer from 3 to 8, inclusive. Not sufficient. (We could even not consider this statement at all: as sum of inner angles of polygon is 180*(x-2) and 180 is a multiple of 15, then all polygons will have the sum of the interior angles divisible by 15.)

Answer: A.
Show more


I used a different method, I found that 16 is 2^4; 180 only has 2^2 as prime factors so (n-2) must be a factor of 4 (8 is too big since n would be 10). Is it correct to approach it this way? can I use this moving forward? Cheers
User avatar
Harley1980
User avatar
Retired Moderator
Joined: 06 Jul 2014
Last visit: 14 Jun 2024
Posts: 997
Own Kudos:
6,769
Given Kudos: 178
Location: Ukraine
Concentration: Entrepreneurship, Technology
GMAT 1: 660 Q48 V33
GMAT 2: 740 Q50 V40
GMAT 2: 740 Q50 V40
Posts: 997
Kudos: 6,769
If Polygon X has fewer than 9 sides, how many sides does 26 Apr 2015, 11:17
Kudos
Add Kudos
Bookmarks
Bookmark this Post
tgubbay1
Bunuel
If Polygon X has fewer than 9 sides, how many sides does Polygon X have?

Sum of inner angles of polygon=180*(x-2), where x is # of sides. Given x<9. Question x=?

(1) The sum of the interior angles of Polygon X is divisible by 16 --> 180*(x-2)=16k --> 45(x-2)=4k --> x-2 must be a multiple of 4 (as 45 is not) --> since x<9 then the only acceptable value of x is 6. Sufficient.

(2) The sum of the interior angles of Polygon X is divisible by 15 --> 180*(x-2)=15m --> 12(x-2)=m --> x can be any integer from 3 to 8, inclusive. Not sufficient. (We could even not consider this statement at all: as sum of inner angles of polygon is 180*(x-2) and 180 is a multiple of 15, then all polygons will have the sum of the interior angles divisible by 15.)

Answer: A.


I used a different method, I found that 16 is 2^4; 180 only has 2^2 as prime factors so (n-2) must be a factor of 4 (8 is too big since n would be 10). Is it correct to approach it this way? can I use this moving forward? Cheers
Show more

Hello tgubbay1

It's inherently the same approach which was given by Bunuel in second comment:
Bunuel
180*(x-2)=16k --> 45(x-2)=4k --> x-2 must be a multiple of 4
Show more

You definetely can use it for moving forward:
\(n-2 = 4k\) so you should fine \(n\) that will satisfactory for statement \(2 < n < 9\)
and this will be only variant: \(6\)
User avatar
mvictor
User avatar
Board of Directors
Joined: 17 Jul 2014
Last visit: 14 Jul 2021
Posts: 2,118
Own Kudos:
1,276
 [3]
Given Kudos: 236
Location: United States (IL)
Concentration: Finance, Economics
Schools: Stanford '20 (WD)
GMAT 1: 650 Q49 V30
GPA: 3.92
WE:General Management (Transportation)
Products:
My Reviews
Schools: Stanford '20 (WD)
GMAT 1: 650 Q49 V30
Posts: 2,118
Kudos: 1,276
 [3]
If Polygon X has fewer than 9 sides, how many sides does 29 Mar 2016, 18:21
2
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
calreg11
If Polygon X has fewer than 9 sides, how many sides does Polygon X have?

(1) The sum of the interior angles of Polygon X is divisible by 16.

(2) The sum of the interior angles of Polygon X is divisible by 15.
Show more

the sum of the interior angles of a polygon is:
180(n-2)
possible # of sides: 3,4,5,6,7,8

1. tells us that 180(n-2) is divisible by 16
or 45(n-2) is divisible by 4.
it is divisible only when n-2 is divisible by 4.
only way it can be true is if n=6, or polygon X has 6 sides.
any other option does not work. so 1 is sufficient.

2. the sum of interior angles is divisible by 15.
well..180 is divisible by 15, and so is 360. first one has 3 sides, second one has 4 sides.
since more than one option is possible, 2 alone is insufficient.
User avatar
BrentGMATPrepNow
User avatar
Major Poster
Joined: 12 Sep 2015
Last visit: 31 Oct 2025
Posts: 6,733
Own Kudos:
36,449
 [2]
Given Kudos: 799
Location: Canada
Expert
Expert reply
Posts: 6,733
Kudos: 36,449
 [2]
If Polygon X has fewer than 9 sides, how many sides does 29 Apr 2018, 07:18
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
calreg11
If Polygon X has fewer than 9 sides, how many sides does Polygon X have?

(1) The sum of the interior angles of Polygon X is divisible by 16.

(2) The sum of the interior angles of Polygon X is divisible by 15.
Show more

Target question: How many sides does Polygon X have?

Given: Polygon X has fewer than 9 sides

Useful rule: The sum of the angles in an n-sided polygon = (n - 2)(180º)

Since the polygon has FEWER than 9 sides, there are are exactly SIX possible cases:
case a: There are 8 sides, in which case the sum of the angles = (8 - 2)(180º) = 6(180º)
case b: There are 7 sides, in which case the sum of the angles = (7 - 2)(180º) = 5(180º)
case c: There are 6 sides, in which case the sum of the angles = (6 - 2)(180º) = 4(180º)
case d: There are 5 sides, in which case the sum of the angles = (5 - 2)(180º) = 3(180º)
case e: There are 4 sides, in which case the sum of the angles = (4 - 2)(180º) = 2(180º)
case f: There are 3 sides, in which case the sum of the angles = (3 - 2)(180º) = 180º

Statement 1: The sum of the interior angles of Polygon X is divisible by 16.
Only case c (6 sides) satisfies this condition.
4(180º) = 720, and 720 is divisible by 16.
Since no other cases satisfy the condition in statement 1, it MUST be the case that the polygon has 6 sides
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: The sum of the interior angles of Polygon X is divisible by 15.
Since 180 is divisible by 15, we can be certain that any multiple of 180 is also divisible by 15.
So, cases a through to f all satisfy the condition in statement 2.
In other words, the polygon have have 8, 7, 6, 5, 4, or 3 sides
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer: A

Cheers,
Brent
User avatar
mimajit
User avatar
Joined: 03 Aug 2017
Last visit: 24 Jun 2020
Posts: 75
Own Kudos:
28
Given Kudos: 85
Posts: 75
Kudos: 28
If Polygon X has fewer than 9 sides, how many sides does 16 May 2018, 08:46
Kudos
Add Kudos
Bookmarks
Bookmark this Post
GMATPrepNow
calreg11
If Polygon X has fewer than 9 sides, how many sides does Polygon X have?

(1) The sum of the interior angles of Polygon X is divisible by 16.

(2) The sum of the interior angles of Polygon X is divisible by 15.

Target question: How many sides does Polygon X have?

Given: Polygon X has fewer than 9 sides

Useful rule: The sum of the angles in an n-sided polygon = (n - 2)(180º)

Since the polygon has FEWER than 9 sides, there are are exactly SIX possible cases:
case a: There are 8 sides, in which case the sum of the angles = (8 - 2)(180º) = 6(180º)
case b: There are 7 sides, in which case the sum of the angles = (7 - 2)(180º) = 5(180º)
case c: There are 6 sides, in which case the sum of the angles = (6 - 2)(180º) = 4(180º)
case d: There are 5 sides, in which case the sum of the angles = (5 - 2)(180º) = 3(180º)
case e: There are 4 sides, in which case the sum of the angles = (4 - 2)(180º) = 2(180º)
case f: There are 3 sides, in which case the sum of the angles = (3 - 2)(180º) = 180º

Statement 1: The sum of the interior angles of Polygon X is divisible by 16.
Only case c (6 sides) satisfies this condition.
4(180º) = 720, and 720 is divisible by 16.
Since no other cases satisfy the condition in statement 1, it MUST be the case that the polygon has 6 sides
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: The sum of the interior angles of Polygon X is divisible by 15.
Since 180 is divisible by 15, we can be certain that any multiple of 180 is also divisible by 15.
So, cases a through to f all satisfy the condition in statement 2.
In other words, the polygon have have 8, 7, 6, 5, 4, or 3 sides
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer: A

Cheers,
Brent
Show more

Hi Brent is there a faster way to solve the same ? I understood your approach but I guess it will take a few minutes before I could arrive at the answer . Also do you think such time consuming questions can feature on test day ?
User avatar
BrentGMATPrepNow
User avatar
Major Poster
Joined: 12 Sep 2015
Last visit: 31 Oct 2025
Posts: 6,733
Own Kudos:
36,449
Given Kudos: 799
Location: Canada
Expert
Expert reply
Posts: 6,733
Kudos: 36,449
If Polygon X has fewer than 9 sides, how many sides does 16 May 2018, 09:21
Kudos
Add Kudos
Bookmarks
Bookmark this Post
mimajit
GMATPrepNow
calreg11
If Polygon X has fewer than 9 sides, how many sides does Polygon X have?

(1) The sum of the interior angles of Polygon X is divisible by 16.

(2) The sum of the interior angles of Polygon X is divisible by 15.

Target question: How many sides does Polygon X have?

Given: Polygon X has fewer than 9 sides

Useful rule: The sum of the angles in an n-sided polygon = (n - 2)(180º)

Since the polygon has FEWER than 9 sides, there are are exactly SIX possible cases:
case a: There are 8 sides, in which case the sum of the angles = (8 - 2)(180º) = 6(180º)
case b: There are 7 sides, in which case the sum of the angles = (7 - 2)(180º) = 5(180º)
case c: There are 6 sides, in which case the sum of the angles = (6 - 2)(180º) = 4(180º)
case d: There are 5 sides, in which case the sum of the angles = (5 - 2)(180º) = 3(180º)
case e: There are 4 sides, in which case the sum of the angles = (4 - 2)(180º) = 2(180º)
case f: There are 3 sides, in which case the sum of the angles = (3 - 2)(180º) = 180º

Statement 1: The sum of the interior angles of Polygon X is divisible by 16.
Only case c (6 sides) satisfies this condition.
4(180º) = 720, and 720 is divisible by 16.
Since no other cases satisfy the condition in statement 1, it MUST be the case that the polygon has 6 sides
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: The sum of the interior angles of Polygon X is divisible by 15.
Since 180 is divisible by 15, we can be certain that any multiple of 180 is also divisible by 15.
So, cases a through to f all satisfy the condition in statement 2.
In other words, the polygon have have 8, 7, 6, 5, 4, or 3 sides
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer: A

Cheers,
Brent

Hi Brent is there a faster way to solve the same ? I understood your approach but I guess it will take a few minutes before I could arrive at the answer . Also do you think such time consuming questions can feature on test day ?
Show more

I know that it LOOKS like my approach takes a lot of time but, on test day, I wouldn't write out all of those steps.
I might just create a small table with "# of sides" and "sum of angles"
We I have:
3: 180º
4: 360º
5: 540º
6: 720º
7: 900º
8: 1080º

Once we've created that table (20 seconds tops), it won't take long to deal with each statement.

Does that help?

Cheers,
Brent
User avatar
fskilnik
User avatar
Joined: 12 Oct 2010
Last visit: 03 Jan 2025
Posts: 883
Own Kudos:
1,880
Given Kudos: 57
Status:GMATH founder
Expert
Expert reply
Posts: 883
Kudos: 1,880
If Polygon X has fewer than 9 sides, how many sides does 23 Jan 2019, 05:50
Kudos
Add Kudos
Bookmarks
Bookmark this Post
calreg11
If Polygon X has fewer than 9 sides, how many sides does Polygon X have?

(1) The sum of the interior angles of Polygon X is divisible by 16.

(2) The sum of the interior angles of Polygon X is divisible by 15.
Show more
\(\sum\nolimits_N { = \left( {N - 2} \right) \cdot 180\,\,\,\,\,\,\left[ {{\rm{degrees}}} \right]}\)

\(? = N\,\,\,\,\left( {3 \le \,\,N\,\,{\mathop{\rm int}} \,\, \le 8} \right)\)

\(\left( 1 \right)\,\,\,{\mathop{\rm int}} \,\, = \,\,{{\left( {N - 2} \right) \cdot 180} \over {16}}\,\, = \,\,{{\left( {N - 2} \right) \cdot 45} \over 4}\,\,\,\,\,\mathop \Rightarrow \limits^{GCF\left( {45,4} \right)\, = \,1} \,\,\,\,\,{{N - 2} \over 4} = {\mathop{\rm int}}\)

\(\left. \matrix{\\
3 \le \,\,N\,\,{\mathop{\rm int}} \,\, \le 8\,\, \hfill \cr \\
{{N - 2} \over 4} = {\mathop{\rm int}} \hfill \cr} \right\}\,\,\,\,\,\, \Rightarrow \,\,\,\,\,N = 6\,\,\,\,\,\, \Rightarrow \,\,\,\,\,{\rm{SUFF}}.\)


\(\left( 2 \right)\,\,\,{\mathop{\rm int}} \,\, = \,\,{{\left( {N - 2} \right) \cdot 180} \over {15}}\,\, = \,\,\left( {N - 2} \right) \cdot 12\,\,\,\,\,\left\{ \matrix{\\
\,{\rm{Take}}\,\,N = 3 \hfill \cr \\
\,{\rm{Take}}\,\,N = 4 \hfill \cr} \right.\,\,\,\,\,\, \Rightarrow \,\,\,\,\,{\rm{INSUFF}}.\)


We follow the notations and rationale taught in the GMATH method.

Regards,
Fabio.
User avatar
gurmukh
User avatar
Joined: 18 Dec 2017
Last visit: 30 Dec 2025
Posts: 258
Own Kudos:
269
Given Kudos: 20
Posts: 258
Kudos: 269
If Polygon X has fewer than 9 sides, how many sides does 13 Apr 2020, 04:15
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Sum of interior angles of a polygon = (n-2)×180
Where n is the number of sides of a polygon
From first statement
180 is a multiple of 4, to make it a multiple of 16 only value of n that can be fitted is 6.
Sufficient
From second statement
180 is already a multiple of 15 so any value of n can be fitted
Insufficient
Option A is the answer

Posted from my mobile device
User avatar
Archit3110
User avatar
Major Poster
Joined: 18 Aug 2017
Last visit: 23 Apr 2026
Posts: 8,628
Own Kudos:
5,190
Given Kudos: 243
Status:You learn more from failure than from success.
Location: India
Concentration: Sustainability, Marketing
GMAT Focus 1: 545 Q79 V79 DI73
GMAT Focus 2: 645 Q83 V82 DI81
GPA: 4
WE:Marketing (Energy)
Products:
GMAT Club Tests Forum Quiz
GMAT Focus 2: 645 Q83 V82 DI81
Posts: 8,628
Kudos: 5,190
If Polygon X has fewer than 9 sides, how many sides does 12 Sep 2020, 08:14
Kudos
Add Kudos
Bookmarks
Bookmark this Post
calreg11
If Polygon X has fewer than 9 sides, how many sides does Polygon X have?

(1) The sum of the interior angles of Polygon X is divisible by 16.

(2) The sum of the interior angles of Polygon X is divisible by 15.
Show more

sum of interior angle of polygon ; 180*(n-2)

#1
The sum of the interior angles of Polygon X is divisible by 16.
180*(n-2)/16 ; 5*(n-2)/4 ;
n has to be 6 sufficient
#2
The sum of the interior angles of Polygon X is divisible by 15
180*(n-2)/15 ; 12*(n-2)
n can be any value from 1 to 8
insufficient
OPTION A is correct
User avatar
achloes
User avatar
Joined: 16 Oct 2020
Last visit: 19 May 2025
Posts: 244
Own Kudos:
221
Given Kudos: 2,382
GMAT 1: 460 Q28 V26
GMAT 2: 550 Q39 V27
GMAT 3: 610 Q39 V35
GMAT 4: 650 Q42 V38
GMAT 5: 720 Q48 V41
GMAT 5: 720 Q48 V41
Posts: 244
Kudos: 221
If Polygon X has fewer than 9 sides, how many sides does 29 Jun 2023, 04:08
Kudos
Add Kudos
Bookmarks
Bookmark this Post
180(n-2) = sum of interior angles of a polygon, where n = number of sides

We also know that n must be an integer and we can use this info to our advantage.

S1.
180(n-2) = 16 x Integer
90(n-2) = 8 x Integer
45(n-2) = 4 x Integer
45 is not divisible by 4, so n-2 must be div by 4. Acceptable value for n = 6 only, because 2<n<9
SUFFICIENT

S2.
180(n-2) = 15 x Integer
60(n-2) = 5 x Integer
60 is div by 5 so n-2 need not be div by 5
INSUFFICIENT
Moderators:
Bunuel
Math Expert
109778 posts
kingbucky
498 posts
Gmat860sanskar
212 posts