GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 14 Nov 2018, 05:31

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.

Close

Request Expert Reply

Confirm Cancel
Events & Promotions in November
PrevNext
SuMoTuWeThFrSa
28293031123
45678910
11121314151617
18192021222324
2526272829301
Open Detailed Calendar
  • $450 Tuition Credit & Official CAT Packs FREE

     November 15, 2018

     November 15, 2018

     10:00 PM MST

     11:00 PM MST

    EMPOWERgmat is giving away the complete Official GMAT Exam Pack collection worth $100 with the 3 Month Pack ($299)
  • Free GMAT Strategy Webinar

     November 17, 2018

     November 17, 2018

     07:00 AM PST

     09:00 AM PST

    Nov. 17, 7 AM PST. Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT.

If the two regions above have the same area, what is the ratio of t:s?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Manager
Manager
User avatar
Affiliations: CFA L3 Candidate, Grad w/ Highest Honors
Joined: 03 Nov 2007
Posts: 125
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)
If the two regions above have the same area, what is the ratio of t:s?  [#permalink]

Show Tags

New post Updated on: 08 Dec 2017, 22:01
2
5
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

78% (01:42) correct 22% (02:30) wrong based on 540 sessions

HideShow timer Statistics

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)


Attachment:
Triangle and square.gif
Triangle and square.gif [ 4.55 KiB | Viewed 10108 times ]

Originally posted by robertrdzak on 11 Oct 2009, 09:03.
Last edited by Bunuel on 08 Dec 2017, 22:01, edited 2 times in total.
Renamed the topic and edited the question.
Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50580
Re: If the two regions above have the same area, what is the ratio of t:s?  [#permalink]

Show Tags

New post Updated on: 11 Oct 2009, 14:59
3
2
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 the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

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?
Extra-hard Quant Tests with Brilliant Analytics


Originally posted by Bunuel on 11 Oct 2009, 09:25.
Last edited by Bunuel on 11 Oct 2009, 14:59, edited 1 time in total.
General Discussion
Manager
Manager
User avatar
Affiliations: CFA L3 Candidate, Grad w/ Highest Honors
Joined: 03 Nov 2007
Posts: 125
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)
Re: If the two regions above have the same area, what is the ratio of t:s?  [#permalink]

Show Tags

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: 164
Location: India
Schools: South Asian B-schools
Re: If the two regions above have the same area, what is the ratio of t:s?  [#permalink]

Show Tags

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: 179
Re: If the two regions above have the same area, what is the ratio of t:s?  [#permalink]

Show Tags

New post Updated on: 15 Aug 2010, 22:38
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.

Originally posted by jpr200012 on 15 Aug 2010, 22:31.
Last edited by jpr200012 on 15 Aug 2010, 22:38, edited 1 time in total.
Manager
Manager
avatar
Joined: 30 May 2010
Posts: 179
Re: If the two regions above have the same area, what is the ratio of t:s?  [#permalink]

Show Tags

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
B
Joined: 22 Oct 2009
Posts: 235
GMAT 1: 760 Q49 V44
GPA: 3.88
Re: If the two regions above have the same area, what is the ratio of t:s?  [#permalink]

Show Tags

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: 179
Re: If the two regions above have the same area, what is the ratio of t:s?  [#permalink]

Show Tags

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?
Veritas Prep GMAT Instructor
User avatar
P
Joined: 16 Oct 2010
Posts: 8527
Location: Pune, India
Re: If the two regions above have the same area, what is the ratio of t:s?  [#permalink]

Show Tags

New post 13 Dec 2010, 20:45
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

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >

GMAT self-study has never been more personalized or more fun. Try ORION Free!

Intern
Intern
avatar
Joined: 05 Nov 2010
Posts: 43
Re: If the two regions above have the same area, what is the ratio of t:s?  [#permalink]

Show Tags

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?
Veritas Prep GMAT Instructor
User avatar
P
Joined: 16 Oct 2010
Posts: 8527
Location: Pune, India
Re: If the two regions above have the same area, what is the ratio of t:s?  [#permalink]

Show Tags

New post 13 Dec 2010, 21:26
1
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

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >

GMAT self-study has never been more personalized or more fun. Try ORION Free!

Senior Manager
Senior Manager
avatar
Joined: 15 Sep 2011
Posts: 329
Location: United States
WE: Corporate Finance (Manufacturing)
GMAT ToolKit User
Re: If the two regions above have the same area, what is the ratio of t:s?  [#permalink]

Show Tags

New post 29 Jun 2015, 15:51
A. 2 : 3 formula of area for equilateral triangles includes irrational number and area of square is the sides squared, a result without irrational number. One side must have an irrational number and therefore 2:3 cannot not be correct.
B. 16 : 3 same reasoning as above.
C. 4 : (3)^(1/2) Trick to see whether the final root was taken
D. 2 : (3)^(1/4) True statement
E. 4 : (3)^(1/4) Trick to test whether you're precise enough when selecting answer choices.

IMO D
Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 8768
Premium Member
Re: If the two regions above have the same area, what is the ratio of t:s?  [#permalink]

Show Tags

New post 08 Dec 2017, 15:08
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

GMAT Club Bot
Re: If the two regions above have the same area, what is the ratio of t:s? &nbs [#permalink] 08 Dec 2017, 15:08
Display posts from previous: Sort by

If the two regions above have the same area, what is the ratio of t:s?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


Copyright

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

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

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®.