Find all School-related info fast with the new School-Specific MBA Forum

It is currently 23 Jul 2014, 04:52

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

If the two regions above have the same area, what is the

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Manager
Manager
User avatar
Affiliations: CFA L3 Candidate, Grad w/ Highest Honors
Joined: 03 Nov 2007
Posts: 130
Location: USA
Schools: Chicago Booth R2 (WL), Wharton R2 w/ int, Kellogg R2 w/ int
WE 1: Global Operations (Futures & Portfolio Financing) - Hedge Fund ($10bn+ Multi-Strat)
WE 2: Investment Analyst (Credit strategies) - Fund of Hedge Fund ($10bn+ Multi-Strat)
Followers: 1

Kudos [?]: 22 [0], given: 9

If the two regions above have the same area, what is the [#permalink] New post 11 Oct 2009, 09:03
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

85% (01:50) correct 15% (01:24) wrong based on 73 sessions
Attachment:
Triangle and square.gif
Triangle and square.gif [ 4.55 KiB | Viewed 1123 times ]
If the two regions above have the same area, what is the ratio of t:s?

A. 2 : 3
B. 16 : 3
C. 4 : (3)^(1/2)
D. 2 : (3)^(1/4)
E. 4 : (3)^(1/4)
[Reveal] Spoiler: OA

Last edited by Bunuel on 09 Jul 2013, 09:10, edited 1 time in total.
Renamed the topic and edited the question.
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 18693
Followers: 3233

Kudos [?]: 22244 [0], given: 2602

Re: Good Geometry Question.... [#permalink] New post 11 Oct 2009, 09:25
Expert's post
Image
If the two regions above have the same area, what is the ratio of t:s?

A. 2 : 3
B. 16 : 3
C. 4 : (3)^(1/2)
D. 2 : (3)^(1/4)
E. 4 : (3)^(1/4)

Area of equilateral triangle is area_{equilateral}=t^2*\frac{\sqrt{3}}{4};

Area of square is area_{square}=s^2;

As areas are equal, then t^2*\frac{\sqrt{3}}{4}=s^2 --> \frac{t^2}{s^2}=\frac{4}{\sqrt{3}} --> \frac{t}{s}=\frac{2}{\sqrt[4]{3}}.

Answer: D.

_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership


Last edited by Bunuel on 11 Oct 2009, 14:59, edited 1 time in total.
Manager
Manager
User avatar
Affiliations: CFA L3 Candidate, Grad w/ Highest Honors
Joined: 03 Nov 2007
Posts: 130
Location: USA
Schools: Chicago Booth R2 (WL), Wharton R2 w/ int, Kellogg R2 w/ int
WE 1: Global Operations (Futures & Portfolio Financing) - Hedge Fund ($10bn+ Multi-Strat)
WE 2: Investment Analyst (Credit strategies) - Fund of Hedge Fund ($10bn+ Multi-Strat)
Followers: 1

Kudos [?]: 22 [0], given: 9

Re: Good Geometry Question.... [#permalink] New post 11 Oct 2009, 09:46
thanks, I was curious, how did you get 1/4 as part of the solution? When i was doing the problem I kept ending up with 2^(1/2) : 3^(1/4)
Manager
Manager
User avatar
Joined: 18 Jul 2009
Posts: 170
Location: India
Schools: South Asian B-schools
Followers: 2

Kudos [?]: 58 [0], given: 37

GMAT Tests User
Re: Good Geometry Question.... [#permalink] New post 14 Oct 2009, 04:27
Sqr (S) = Sqrt (3) / 4 * sqr (T)
on simplification T/S = 2 : (3)^(1/4)
OA D

_________________

Bhushan S.
If you like my post....Consider it for Kudos :-D

Manager
Manager
avatar
Joined: 30 May 2010
Posts: 191
Followers: 3

Kudos [?]: 41 [0], given: 32

GMAT Tests User
Re: Geometry problem - Equal areas between triangle and square [#permalink] New post 15 Aug 2010, 22:31
A(triangle) = 1/2 * t * (t/2)*sqrt{3} = (t^2sqrt{3}) / 4

A(square) = s^2

(t^2 sqrt{3}) / 4 = s^2 Areas are equal.

t^2 = 4s^2 / sqrt{3} Isolate t.

t = sqrt{4s^2 / 3^{1/2}} Take the square root of both sides.

t = sqrt{4s^2)} / sqrt{3^{1/2}} Square root of a fraction: sqrt{a/b} = sqrt{a} / sqrt{b}

t = 2s / 3^{1/4} Simplify.

t/s = 2 / 3^{1/4} Finally, the ratio.

Last edited by jpr200012 on 15 Aug 2010, 22:38, edited 1 time in total.
Manager
Manager
avatar
Joined: 30 May 2010
Posts: 191
Followers: 3

Kudos [?]: 41 [0], given: 32

GMAT Tests User
Re: Geometry problem - Equal areas between triangle and square [#permalink] New post 15 Aug 2010, 22:32
I thought this was a good problem. I overlooked that the triangle was equilateral the first time. I was looking at the shape and not the labels. One reason to always redraw figures!
Manager
Manager
User avatar
Joined: 22 Oct 2009
Posts: 242
GMAT 1: 760 Q49 V44
GPA: 3.88
Followers: 6

Kudos [?]: 60 [0], given: 1

GMAT Tests User
Re: Geometry problem - Equal areas between triangle and square [#permalink] New post 15 Aug 2010, 22:56
I find this problem to be really easy if you just plug in numbers.

Let's find the area of the triangle first, since finding the area of a square is easier to do with a given value.

Say t =2

Area of equilateral triangle with side of 2 = \sqrt{3}

Set this area equal to s^2 and take the square root of both sides

s = 3^(1/4)

Put t over s, and you have your answer!
Manager
Manager
avatar
Joined: 30 May 2010
Posts: 191
Followers: 3

Kudos [?]: 41 [0], given: 32

GMAT Tests User
Re: Good Geometry Question.... [#permalink] New post 16 Aug 2010, 08:08
YourDreamTheater: That works really fast, too. I've been using plugging in numbers more lately for saving time.

Bunuel: How the heck do you keep track of all these topics? :) Can you add GMAT Prep tag to this topic?
Manager
Manager
avatar
Joined: 20 Apr 2010
Posts: 237
Location: Hyderabad
WE 1: 4.6 years Exp IT prof
Followers: 8

Kudos [?]: 43 [0], given: 36

Re: Good Geometry Question.... [#permalink] New post 16 Aug 2010, 14:19
Simple question I got it wrong :(

_________________

I will give a Fight till the End

"To dream anything that you want to dream, that is the beauty of the human mind. To do anything that you want to do, that is the strength of the human will. To trust yourself, to test your limits, that is the courage to succeed."
- Bernard Edmonds

A person who is afraid of Failure can never succeed -- Amneet Padda

Don't Forget to give the KUDOS

Expert Post
Veritas Prep GMAT Instructor
User avatar
Joined: 16 Oct 2010
Posts: 4566
Location: Pune, India
Followers: 1029

Kudos [?]: 4455 [0], given: 162

Re: PS - Same Area, Ratio? [#permalink] New post 13 Dec 2010, 20:45
Expert's post
consultinghokie wrote:
(imagine a picture of an equilateral triangle with sides T and a square with sides S)

If the two regions above have the same area, what is the ratio of T:S?

2:3

16:3

4: sq root 3

2: fourth root 3

4: third root 3


Area of an equilateral triangle of side T = (\sqrt{3}/4)T^2

Area of square of side S = S^2

Given: (\sqrt{3}/4)T^2 = S^2

T^2/S^2 = 4/\sqrt{3}

T/S = 2/fourth root 3

_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Save $100 on Veritas Prep GMAT Courses And Admissions Consulting
Enroll now. Pay later. Take advantage of Veritas Prep's flexible payment plan options.

Veritas Prep Reviews

Manager
Manager
avatar
Joined: 05 Nov 2010
Posts: 63
Followers: 1

Kudos [?]: 1 [0], given: 5

Re: PS - Same Area, Ratio? [#permalink] New post 13 Dec 2010, 21:18
one quick question where I am stumped. When you square root a square root is that where you are getting the 4th root?
Expert Post
Veritas Prep GMAT Instructor
User avatar
Joined: 16 Oct 2010
Posts: 4566
Location: Pune, India
Followers: 1029

Kudos [?]: 4455 [0], given: 162

Re: PS - Same Area, Ratio? [#permalink] New post 13 Dec 2010, 21:26
Expert's post
spyguy wrote:
one quick question where I am stumped. When you square root a square root is that where you are getting the 4th root?


Yes.

\sqrt{3} = 3^{\frac{1}{2}}

When you take the root again, you get (3^{\frac{1}{2}})^{\frac{1}{2}} which is equal to 3^{\frac{1}{4}}
In other words, it the fourth root of 3.

_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Save $100 on Veritas Prep GMAT Courses And Admissions Consulting
Enroll now. Pay later. Take advantage of Veritas Prep's flexible payment plan options.

Veritas Prep Reviews

Manager
Manager
avatar
Joined: 05 Nov 2010
Posts: 63
Followers: 1

Kudos [?]: 1 [0], given: 5

Re: PS - Same Area, Ratio? [#permalink] New post 13 Dec 2010, 21:31
Thank you very much Karishma. Kudos! +1!
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 18693
Followers: 3233

Kudos [?]: 22244 [0], given: 2602

Re: geometry [#permalink] New post 14 Dec 2010, 00:19
Expert's post
Re: geometry   [#permalink] 14 Dec 2010, 00:19
    Similar topics Author Replies Last post
Similar
Topics:
1 Experts publish their posts in the topic What is the area of the rectangular region above? Bunuel 6 26 Feb 2014, 01:31
1 Experts publish their posts in the topic What is the area of the shaded region above, if ABCD goodyear2013 3 11 Jan 2014, 07:16
2 Experts publish their posts in the topic What is the area of triangular region ABC above? Walkabout 4 03 Dec 2012, 03:54
6 Experts publish their posts in the topic What is the area of the rectangular region above? heygirl 6 24 Feb 2011, 10:39
two regions have same area, what is the ratio of t:s? t = sushom101 1 16 Oct 2005, 16:19
Display posts from previous: Sort by

If the two regions above have the same area, what is the

  Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Privacy Policy| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.