Forum Home > GMAT > Quantitative > Problem Solving (PS)
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.
Dec 1207:30 AM PST
-08:30 AM PST
Join the conversation to learn more about INSEAD vs LBS
Dec 1310:00 AM EST
-12:00 PM EST
Have you ever wondered how to score a PERFECT 805 on the GMAT? Meet Julia, a banking professional who used the Target Test Prep course to achieve this incredible feat. Julia's story is nothing short of an inspiration.
Dec 1410:00 AM EST
-12:00 PM EST
Think a 100% GMAT Verbal score is out of your reach? Target Test Prep will make you think again! Our course uses techniques such as topical study and spaced repetition to maximize knowledge retention and make studying simple and fun.
Dec 1411:00 AM IST
-01:00 PM IST
Attend this session to learn how to Deconstruct arguments, Pre-Think Author’s Assumptions, and apply Negation Test.- Dec 15
11:00 AM IST
-01:00 PM IST
Attend this free GMAT Algebra Webinar and learn how to master the most challenging Inequalities and Absolute Value problems with ease. - Dec 16
08:00 AM PST
-11:59 PM PST
GMAT Club 12 Days of Christmas is a 4th Annual GMAT Club Winter Competition based on solving questions. This is the Winter GMAT competition on GMAT Club with an amazing opportunity to win over $40,000 worth of prizes! - Dec 17
09:00 AM PST
-10:00 AM PST
Join Manhattan Prep instructor Whitney Garner for a fun—and thorough—review of logic-based (non-math) problems, with a particular emphasis on Data Sufficiency and Two-Parts. - Dec 18
10:00 AM PST
-11:00 AM PST
Here is the essential guide to securing scholarships as an MBA student! In this video, we explore the various types of scholarships available, including need-based and merit-based options.
niteshwaghray
GMAT 1: 700 Q45 V40
Posts: 59
Updated on: 25 May 2017, 14:35
Originally posted by niteshwaghray on 25 May 2017, 13:28.
Last edited by Bunuel on 25 May 2017, 14:35, edited 1 time in total.
Last edited by Bunuel on 25 May 2017, 14:35, edited 1 time in total.
Edited the question.
Kudos
Bookmarks
B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
85%
(hard)
Question Stats:
48% (03:02) correct
52%
(02:59)
wrong
based on 63
sessions
History
Date
Time
Result
Not Attempted Yet
In the figure above, a regular hexagon EFGHIJ is inscribed in the rectangle ABCD. If the ratio of the magnitudes of the area and the perimeter of the hexagon is \(\frac{√3}{2}\), what is the ratio of the magnitudes of the area and the perimeter of the rectangle ABCD?
A. \(2\sqrt{3} - 4\)
B. \(4\sqrt{3} - 6\)
C. \(2\sqrt{3} + 4\)
D. \(4\sqrt{3} + 6\)
E. None of the above
Attachment:
XFWWxun.png [ 4.75 KiB | Viewed 8518 times ]
25 May 2017, 15:13
Kudos
Bookmarks
niteshwaghray
In the figure above, a regular hexagon EFGHIJ is inscribed in the rectangle ABCD. If the ratio of the magnitudes of the area and the perimeter of the hexagon is \(\frac{√3}{2}\), what is the ratio of the magnitudes of the area and the perimeter of the rectangle ABCD?
A. \(2\sqrt{3} - 4\)
B. \(4\sqrt{3} - 6\)
C. \(2\sqrt{3} + 4\)
D. \(4\sqrt{3} + 6\)
E. None of the above
Attachment:
The attachment XFWWxun.png is no longer available
Some redundant info in the question...
Check the image below:
Each interior angle of a regular polygon is given by: \(\frac{180(n−2)}{n}\), where n is the number of sides. Thus, each interior angel in the regular hexagon = 120°. This will make triangles at the corner 30°-60°-90°. The sides are always in the ratio 1:√3:2. Notice that the smallest side (1) is opposite the smallest angle (30°), and the longest side (2) is opposite the largest angle (90°).
So, we have that one side of the rectangle is 1 + 2 + 1 = 4 and another is \(\sqrt{3}+\sqrt{3}=2\sqrt{3}\)
Area = \(4*2\sqrt{3}=8\sqrt{3}\);
Perimeter = \(2*(4+2\sqrt{3})=8+4\sqrt{3}\).
Ratio = \(\frac{8\sqrt{3}}{8+4\sqrt{3}}=\frac{2\sqrt{3}}{2+\sqrt{3}}\).
Rationalize by multiplying numerator and denominator by \(2-\sqrt{3}\):
\(\frac{2\sqrt{3}(2-\sqrt{3})}{(2+\sqrt{3})(2-\sqrt{3})}=\frac{2\sqrt{3}(2-\sqrt{3})}{4-1}=4\sqrt{3}-6\).
Answer: B.
Attachment:
Hexagon.png [ 6.04 KiB | Viewed 8217 times ]
29 Jun 2022, 19:49
Kudos
Bookmarks
niteshwaghray
In the figure above, a regular hexagon EFGHIJ is inscribed in the rectangle ABCD. If the ratio of the magnitudes of the area and the perimeter of the hexagon is \(\frac{√3}{2}\), what is the ratio of the magnitudes of the area and the perimeter of the rectangle ABCD?
A. \(2\sqrt{3} - 4\)
B. \(4\sqrt{3} - 6\)
C. \(2\sqrt{3} + 4\)
D. \(4\sqrt{3} + 6\)
E. None of the above
Attachment:
XFWWxun.png
The ratio of the area of the hexagon to the area of the perimeter of the hexagon is 1.7/2 = 0.85.
The area of the rectangle is a tiny bit bigger. The perimeter of the rectangle is also a tiny bit bigger. It's going to be SOMETHING close to 0.85.
A. \(2\sqrt{3} - 4\) = 3.4-4 Negative? Nope.
B. \(4\sqrt{3} - 6\) = 6.8-6 = 0.8 Keep it.
C. \(2\sqrt{3} + 4\) = 3.4+4 = 7.4 Huge! Nope.
D. \(4\sqrt{3} + 6\) = 6.8+6 = 14.8 HUGE! Nope.
E. None of the above
Keep it. That took less than 30 seconds. I'm good with a 50/50 on a question of this complexity level in that amount of time, would certainly go with B from a test-taker/test-writer psychology perspective, and would expect GMAC to give five numerical answer choices (the last of which could be eliminated using the same approach) if they were to have this exact question.
Answer choice B.
