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.
Apr 2308:00 PM PDT
-09:00 PM PDT
Video explanations + diagnosis of 10 weakest areas + 150+ short videos + study plan!
Apr 2301:30 AM EDT
-02:30 AM EDT
Struggling with GMAT Verbal as a non-native speaker? Harsh improved his score from 595 to 695 in just 45 days—and scored a 99 %ile in Verbal (V88)! Learn how smart strategy, clarity, and guided prep helped him gain 100 points.
Apr 2512:30 AM EDT
-01:30 AM EDT
At one point, she believed GMAT wasn’t for her. After scoring 595, self-doubt crept in and she questioned her potential. But instead of quitting, she made the right strategic changes. The result? A remarkable comeback to 695. Check out how Saakshi did it.
Apr 2610:00 AM EDT
-11:00 AM EDT
The Target Test Prep course represents a quantum leap forward in GMAT preparation, a radical reinterpretation of the way that students should study. Try before you buy with a 5-day, full-access trial of the course for FREE!
Apr 2711:00 AM EDT
-12:00 PM EDT
Prefer video-based learning? The Target Test Prep OnDemand course is a one-of-a-kind video masterclass featuring 400 hours of lecture-style teaching by Scott Woodbury-Stewart, founder of Target Test Prep and one of the most accomplished GMAT instructors
Apr 2808:00 AM PDT
-11:00 AM PDT
Whether you are just beginning your MBA journey or fine-tuning your path to a 700+ score, GMAT Day is designed to give you a competitive edge.
A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
24% (02:14) correct
76%
(02:07)
wrong
based on 331
sessions
History
Date
Time
Result
Not Attempted Yet
R is a convex polygon. Does R have at least 8 sides?
(1) Exactly 3 of the interior angles of R are greater than 80 degrees.
(2) None of the interior angles of R are less than 60 degrees.
(1) Exactly 3 of the interior angles of R are greater than 80 degrees.
(2) None of the interior angles of R are less than 60 degrees.
22 Apr 2014, 03:45
Kudos
Bookmarks
pretzel
No, the correct answer is A.
R is a convex polygon. Does R have at least 8 sides?
The Sum of Interior Angles of a polygon is \(180(n-2)\) degrees, where \(n\) is the number of sides (so is the number of angles). So, the greater the number of sides the greater is the sum of the angles.
For 8 sided polygon the sum of the angles is \(180(n-2)=180*6=1080\) degrees. The question basically asks whether the sum of the angles of the polygon is more than or equal to 1080 degrees.
(1) Exactly 3 of the interior angles of R are greater than 80 degrees. This implies that each of the remaining angles must be less than or equal to 80 degrees.
Assume that the polygon IS 8-sided. In this case, the sum of those 3 angles would be \(3*80<(sum \ of \ the \ given \ 3 \ angles)<3*180\) --> \(240<(sum \ of \ the \ given \ 3 \ angles)<540\).
Thus the sum of the reaming 5 angles must be \(1080-540<(sum \ of \ the \ remaining \ 5 \ angles)<1080-240\) --> \(540<(sum \ of \ the \ remaining \ 5 \ angles)<840\). But the sum of the reaming 5 angles must be less than or equal to 5*80=400, and not greater than 540 degrees. Therefore the assumption that the polygon could be 8-sided was wrong.
If the polygon cannot be 8-sided, then it cannot be more sided too. So, R must have less than 8 sides. Sufficient.
(2) None of the interior angles of R are less than 60 degrees. Not sufficient: consider equilateral triangle (all angles 60 degrees) and regular octagon (all angles 1080/8=135 degrees).
Answer: A.
Hope it's clear.
24 Sep 2006, 09:08
Kudos
Bookmarks
R is a convex polygon. Does R have at least 8 sides?
(1) Exactly 3 of the interior angles of R are greater than 80 degrees.
(2) None of the interior angles of R are less than 60 degrees.
What is convex polygon
A convex polygon is a simple polygon whose interior is a convex set. The following properties of a simple polygon are all equivalent to convexity:
* Every internal angle is at most 180 degrees.
* Every line segment between two vertices of the polygon does not go
exterior to the polygon
To have minimun 8 sides a polygon should have sum of angles 180(n-2)
180(8-2) = 1080
(1). Exactly 3 of the interior angles of R are greater than 80 degrees.
Lets take the greatest value for these angles- 180 and smallest for other 5 -80.
180*3+80*5= 940 < 1080 ..SUFFI
(2) None of the interior angles of R are less than 60 degrees.
Angles can have any value ..NOT SUFFI
Answer A
i hope
(1) Exactly 3 of the interior angles of R are greater than 80 degrees.
(2) None of the interior angles of R are less than 60 degrees.
What is convex polygon
A convex polygon is a simple polygon whose interior is a convex set. The following properties of a simple polygon are all equivalent to convexity:
* Every internal angle is at most 180 degrees.
* Every line segment between two vertices of the polygon does not go
exterior to the polygon
To have minimun 8 sides a polygon should have sum of angles 180(n-2)
180(8-2) = 1080
(1). Exactly 3 of the interior angles of R are greater than 80 degrees.
Lets take the greatest value for these angles- 180 and smallest for other 5 -80.
180*3+80*5= 940 < 1080 ..SUFFI
(2) None of the interior angles of R are less than 60 degrees.
Angles can have any value ..NOT SUFFI
Answer A
i hope 
