It is currently 17 Oct 2017, 03:13

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

Events & Promotions in June
Open Detailed Calendar

In the diagram above, triangle ABC is equilateral, figure SQRE is a sq

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

Hide Tags

Expert Post
2 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 41871

Kudos [?]: 128512 [2], given: 12179

In the diagram above, triangle ABC is equilateral, figure SQRE is a sq [#permalink]

Show Tags

New post 04 May 2015, 06:03
2
This post received
KUDOS
Expert's post
10
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  85% (hard)

Question Stats:

61% (02:42) correct 39% (02:54) wrong based on 181 sessions

HideShow timer Statistics

Image
In the diagram above, triangle ABC is equilateral, figure SQRE is a square, and A is the midpoint of SQ. If the perimeter of triangle ABC is 6 inches, what is the length, in inches, of segment RY ?

A) 0.5

B) 1.5

C) \(\sqrt{3}-1.5\)

D) \(2-\sqrt{3}\)

E) \(\frac{\sqrt{3}}{2}\)

[Reveal] Spoiler:
Attachment:
PS_3.gif
PS_3.gif [ 2.5 KiB | Viewed 3486 times ]


Kudos for a correct solution.
[Reveal] Spoiler: OA

_________________

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

Kudos [?]: 128512 [2], given: 12179

1 KUDOS received
Senior Manager
Senior Manager
avatar
Joined: 02 Mar 2012
Posts: 362

Kudos [?]: 88 [1], given: 4

Schools: Schulich '16
In the diagram above, triangle ABC is equilateral, figure SQRE is a sq [#permalink]

Show Tags

New post 04 May 2015, 07:04
1
This post received
KUDOS
its C.

side of triangle is 2.draw a perpendicular from A to the bottom opf the square.Take it as point Z.

since AC =2,AE=sqrt3(30,60,90 trianghoe)


now AQ is sqrt3/2 (as it half side of sqare)

now AQY is 30,60,90 triangle too. with AQ=sqrt3/2

so QY=3/2(sqrt3 *sqrt3/2)

yr=qr-qy=sqrt3/2-3/2

option C

Kudos [?]: 88 [1], given: 4

1 KUDOS received
Intern
Intern
avatar
Joined: 20 Jan 2015
Posts: 5

Kudos [?]: 3 [1], given: 4

Concentration: Finance, Economics
GMAT 1: 560 Q38 V30
Re: In the diagram above, triangle ABC is equilateral, figure SQRE is a sq [#permalink]

Show Tags

New post 04 May 2015, 14:40
1
This post received
KUDOS
find side of triangle: 6/3 = 2 inch per side
find area of equilateral triangle: 2²* sqrt(3) / 4 = sqrt (3)
find height: area of triangle = sqrt(3) = 1/2 * base * height -> solve for height: sqrt (3) = 1/2 * 2 * height -> height= sqrt (3)
find third side: its a 90° triangle -> ratio is 1:sqrt(3):2 -> third site = 1 inch.
find RB: (2 - sqrt(3)) / 2
find RY: use Thales' theorem -> 1 / sqrt(3) = RB / RY -> 1 / sqrt(3) = ((2 - sqrt(3)) / 2) / RY -> solve for RY -> RY = sqrt(3) - 1.5

C

Kudos [?]: 3 [1], given: 4

4 KUDOS received
Manager
Manager
User avatar
Joined: 18 Nov 2013
Posts: 82

Kudos [?]: 63 [4], given: 63

Concentration: General Management, Technology
GMAT 1: 690 Q49 V34
Premium Member
Re: In the diagram above, triangle ABC is equilateral, figure SQRE is a sq [#permalink]

Show Tags

New post 05 May 2015, 01:26
4
This post received
KUDOS
Image

Perimeter of equilateral \(\triangle\) = 6
Side of triangle = AB=BC=AC = 2

Side of Square = \(\sqrt{3}\)/2 * a = \(\sqrt{3}\)/2 * 2 = \(\sqrt{3}\)

Now \(\triangle\)YQA and \(\triangle\)YRB are similar triangles ; ----> As one angle \(90^{\circ}\), \(\angle\)y vertically opposite; all angles equal (AAA).

As \(\triangle\)YQA ~ \(\triangle\)YRB ; implies ratio of sides equal \(\frac{YR}{RB} = \frac{YQ}{AQ}\)

let YR = x , YQ = \(\sqrt{3}\) - x ; ----> ( as QR = \(\sqrt{3}\) )

AQ = \(\sqrt{3}\)/2 , RB =(2-\(\sqrt{3}\))/2 ;

\(\frac{YR}{RB} = \frac{YQ}{AQ}\)

\(\frac{x}{(2-\sqrt{3})/2}\) = \(\frac{\sqrt3-x}{(\sqrt{3}/2)}\)

x = \(\frac{(2\sqrt3 - 3 )}{2}\)

x = \(\sqrt3 - 1.5\)

Ans : C
_________________

_______
- Cheers


+1 kudos if you like

Kudos [?]: 63 [4], given: 63

Manager
Manager
avatar
Joined: 06 Mar 2014
Posts: 103

Kudos [?]: 20 [0], given: 3

Re: In the diagram above, triangle ABC is equilateral, figure SQRE is a sq [#permalink]

Show Tags

New post 01 Jun 2015, 10:11
hsbinfy :
Can you please explain how did you get QY=3/2.I am getting it as 1/2.
Please explain how did you apply 30-6-90 to that triangle and how did you got tht value.

Thanks

Kudos [?]: 20 [0], given: 3

1 KUDOS received
Manager
Manager
avatar
Joined: 12 Nov 2014
Posts: 60

Kudos [?]: 95 [1], given: 3

Re: In the diagram above, triangle ABC is equilateral, figure SQRE is a sq [#permalink]

Show Tags

New post 01 Jun 2015, 11:16
1
This post received
KUDOS
Shree9975 wrote:
hsbinfy :
Can you please explain how did you get QY=3/2.I am getting it as 1/2.
Please explain how did you apply 30-6-90 to that triangle and how did you got tht value.

Thanks


See the attachment.

For 30-60-90 triangle, sides are in the ratio 1 : √3 : 2.
You just have to apply this rule to the triangles in the figure.

You will see that RY = √3 - 1.5

Answer C
Attachments

tria.jpg
tria.jpg [ 35.17 KiB | Viewed 2727 times ]


_________________

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Kindly press Kudos if the explanation is clear.
Thank you
Ambarish

Kudos [?]: 95 [1], given: 3

Expert Post
1 KUDOS received
e-GMAT Representative
User avatar
S
Joined: 04 Jan 2015
Posts: 746

Kudos [?]: 2069 [1], given: 123

Re: In the diagram above, triangle ABC is equilateral, figure SQRE is a sq [#permalink]

Show Tags

New post 02 Jun 2015, 07:15
1
This post received
KUDOS
Expert's post
Here's the step-by-step guide to thinking through this question. :)

Let the length of RY be x inches.

Image

We are given that Triangle ABC is equilateral. This means, Angle ABC = 60 degrees

In right triangle BRY,

\(\frac{RY}{BR} = tan60 =\sqrt{3}\)

That is, \(\frac{x}{BR} = \sqrt{3}\) . . . (1)

If we can find the value of BR, we will be able to find the value of x.

So, let's try to find more about BR now.

We are given that the perimeter of the equilateral triangle ABC = 6 inches

This means, each side of triangle ABC = 6/3 = 2 inches

Now, let each side of square QRES be 2a units.

Since we are given that A is the mid-point of side QS, this means that equilateral triangle ABC is placed symmetrically about the square QRES.

Therefore, \(CE = BR = \frac{(2 - 2a)}{2} = 1 - a\) . . . (2)

Substituting (2) in (1), we get:

\(\frac{x}{(1-a)} = \sqrt{3}\) . . . (3)

Equation 3 contains two unknowns: x and a. So, to find a unique value of x, we now know that we should try to find another relation involving x and/or a.

We get it by dropping a perpendicular from A on side BC.

In right triangle APB,

\(\frac{AP}{BP} = tan60 = \sqrt{3}\)

That is, \(\frac{2a}{1} = \sqrt{3}\)

That is, \(a = \frac{(sqrt3)}{2}\) . . . (4)

By solving (3) and (4), we get \(x = \sqrt{3} - 1.5\)

Hope this helped! :)

Best Regards

Japinder
_________________












| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com

Kudos [?]: 2069 [1], given: 123

Expert Post
SVP
SVP
User avatar
G
Joined: 08 Jul 2010
Posts: 1834

Kudos [?]: 2272 [0], given: 51

Location: India
GMAT: INSIGHT
WE: Education (Education)
Reviews Badge
Re: In the diagram above, triangle ABC is equilateral, figure SQRE is a sq [#permalink]

Show Tags

New post 02 Jun 2015, 07:53
Expert's post
4
This post was
BOOKMARKED
Bunuel wrote:
Image
In the diagram above, triangle ABC is equilateral, figure SQRE is a square, and A is the midpoint of SQ. If the perimeter of triangle ABC is 6 inches, what is the length, in inches, of segment RY ?

A) 0.5

B) 1.5

C) \(\sqrt{3}-1.5\)

D) \(2-\sqrt{3}\)

E) \(\frac{\sqrt{3}}{2}\)

[Reveal] Spoiler:
Attachment:
The attachment PS_3.gif is no longer available


Kudos for a correct solution.


Answer: Option
[Reveal] Spoiler:
C

Attachments

File comment: www.GMATinsight.com
sol1.jpg
sol1.jpg [ 240.74 KiB | Viewed 2684 times ]


_________________

Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION

Kudos [?]: 2272 [0], given: 51

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 41871

Kudos [?]: 128512 [0], given: 12179

Re: In the diagram above, triangle ABC is equilateral, figure SQRE is a sq [#permalink]

Show Tags

New post 02 Jun 2015, 08:37
Bunuel wrote:
Image
In the diagram above, triangle ABC is equilateral, figure SQRE is a square, and A is the midpoint of SQ. If the perimeter of triangle ABC is 6 inches, what is the length, in inches, of segment RY ?

A) 0.5

B) 1.5

C) \(\sqrt{3}-1.5\)

D) \(2-\sqrt{3}\)

E) \(\frac{\sqrt{3}}{2}\)

[Reveal] Spoiler:
Attachment:
PS_3.gif


Kudos for a correct solution.


Similar questions to practice:
in-the-figure-above-pqrs-is-a-square-and-ab-ac-is-the-area-of-tria-192330.html
in-the-figure-above-sqre-is-a-square-ab-ac-and-as-aq-161814.html
_________________

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

Kudos [?]: 128512 [0], given: 12179

Manager
Manager
avatar
B
Joined: 20 Apr 2014
Posts: 116

Kudos [?]: [0], given: 23

Re: In the diagram above, triangle ABC is equilateral, figure SQRE is a sq [#permalink]

Show Tags

New post 19 Nov 2015, 15:28
I can not understand how we get 1.5 i understand how we got Square root 3 please expert help. thank you in advance.

Kudos [?]: [0], given: 23

1 KUDOS received
Manager
Manager
avatar
B
Joined: 23 May 2013
Posts: 191

Kudos [?]: 107 [1], given: 42

Location: United States
Concentration: Technology, Healthcare
Schools: Stanford '19 (M)
GMAT 1: 760 Q49 V45
GPA: 3.5
GMAT ToolKit User
Re: In the diagram above, triangle ABC is equilateral, figure SQRE is a sq [#permalink]

Show Tags

New post 20 Jun 2016, 12:43
1
This post received
KUDOS
1
This post was
BOOKMARKED
All of you are doing this problem incorrectly if you even begin to do the algebra or geometry.

If you know that the side of the triangle is 2 inches, then you know the length of RY has to be significantly less than that, so take a look at the answer choices.

A) 1/2 - way too big.
B) 1.5 - way too big.
C) .2 - close, keep this in mind
D) .3 - close, but still too big.
E) .85 - way too big.

The answer is between C and D, and because that segment looks a lot closer to 1/5 than to 1/3, go with answer C.

Time ~20 seconds

Kudos [?]: 107 [1], given: 42

Manager
Manager
User avatar
G
Joined: 01 Sep 2016
Posts: 208

Kudos [?]: 167 [0], given: 33

GMAT 1: 690 Q49 V35
GMAT ToolKit User Reviews Badge CAT Tests
Re: In the diagram above, triangle ABC is equilateral, figure SQRE is a sq [#permalink]

Show Tags

New post 21 Sep 2017, 01:04
1
This post was
BOOKMARKED
Here is my solution. Since, this one had a diagram and lot of rules, I posted an image. Hope this helps.
Attachments

21903586_10207991228218545_79220063_n.jpg
21903586_10207991228218545_79220063_n.jpg [ 74.7 KiB | Viewed 348 times ]


_________________

we shall fight on the beaches,
we shall fight on the landing grounds,
we shall fight in the fields and in the streets,
we shall fight in the hills;
we shall never surrender!

Kudos [?]: 167 [0], given: 33

Re: In the diagram above, triangle ABC is equilateral, figure SQRE is a sq   [#permalink] 21 Sep 2017, 01:04
Display posts from previous: Sort by

In the diagram above, triangle ABC is equilateral, figure SQRE is a sq

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


cron

GMAT Club MBA Forum Home| About| Terms and Conditions| 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®.