BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem
TTP OnDemand GMAT Video Course
Featured Course

Target Test Prep GMAT OnDemand

Scott Woodbury-Stewart’s private virtual classroom — 400 hours of master-class video lessons for the GMAT Focus Edition.

  • 715+ score guarantee — highest in the industry (99th percentile)
  • 52 chapters · 1,500+ lessons · 4,000+ practice questions
  • 400 hours of video · 1,500+ instructor-led HD smartboard lessons
  • 300,000+ students accepted to Harvard, Stanford, Wharton, Booth & Sloan & more
  • 24/7 live support + weekly Zoom office hours with GMAT instructors
  • TTP AI Assist — 24/7 AI-powered virtual tutor for instant help
  • 1,200+ flashcards + AI-powered study assistant & daily calendar
  • OnDemand, LiveTeach & GMAT Bootcamp formats available
  • Also: GRE, SAT Math & Executive Assessment courses
  • MBA Admissions Consulting now available
  • 🏆 2025 EdTech Breakthrough Award: Test Prep Solution Provider of the Year
  • 200,000+ students served
  • 5-day free trial — $0 to start, no auto-billing, cancel anytime
★★★★★ 5.0 (559 reviews)
130-pt guarantee
$0 to start then $127/mo
Start Free 5-Day Trial Read 559 Reviews →

Interior angles problem

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
Source: — Problem Solving |
User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members
Location: New York, NY
Thanked: 13060 times
GMAT Score:790

by GMATGuruNY » Thu Mar 03, 2016 5:01 pm
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.
The sum of the interior angles of a polygon with n sides = (n-2)(180).

Statement 1: The sum of the interior angles of Polygon X is divisible by 16.
Thus:
(n-2)(180)/16 = positive integer.
(n-2)(45)/4 = positive integer.
Since 4 does not divide into 45, the expression on the left-hand side will yield a positive integer only if (n-2) is a multiple of 4.
If n-2 = 4, then n=6.
If n-2 = 8, then n=10.
Since the question stem requires that n<9, only the option in red is viable.
Thus, n=6.
SUFFICIENT.

Statement 2: The sum of the interior angles of Polygon X is divisible by 15.
Thus:
(n-2)(180)/15 = positive integer.
(n-2)(12) = positive integer.
The product on the left-hand side will yield a positive integer if n is equal to any of the following:
3, 4, 5, 6, 7, 8.
Since n can be different values, INSUFFICIENT.

The correct answer is A.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Master | Next Rank: 500 Posts
Posts: 163
Joined: Tue Jan 13, 2015 11:44 am
Thanked: 2 times

by didieravoaka » Thu Mar 03, 2016 5:12 pm
Thanks Mitch!
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members
Location: Vancouver, BC
Thanked: 5254 times
GMAT Score:770

by Brent@GMATPrepNow » Fri Mar 04, 2016 7:59 am
j_shreyans wrote: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
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
GMAT Instructor
Posts: 2630
Joined: Wed Sep 12, 2012 3:32 pmFollowed by: 119 members
Location: East Bay all the way
Thanked: 625 times
GMAT Score:780

by Matt@VeritasPrep » Fri Mar 04, 2016 3:25 pm
A nice way of remembering this formula is thinking of your polygon in terms of triangles.

A triangle is one triangle, obviously, so it has 180°.

A square is two triangles, so it has 180+180 = 360°.

A pentagon is three triangles, so it has 180+180+180 = 540°, etc.

You can see that the first three sides count ONCE -- they form a ∆ -- and each additional side also counts once. So if we have n sides, the first three count ONCE, the other (n - 3) count once EACH, and we're left with 1 + (n - 3) = n - 2 to count.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1