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

It is currently 21 Oct 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

BC=BD=DC=AD. If AB= 10, what is the length of AC?

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
4 KUDOS received
Manager
Manager
avatar
Joined: 09 Feb 2013
Posts: 121
Followers: 1

Kudos [?]: 266 [4] , given: 17

BC=BD=DC=AD. If AB= 10, what is the length of AC? [#permalink] New post 11 Mar 2013, 23:42
4
This post received
KUDOS
3
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

55% (02:59) correct 45% (01:44) wrong based on 118 sessions
Attachment:
1.jpg
1.jpg [ 7.3 KiB | Viewed 4208 times ]
Note: figure not drawn to scale

BC=BD=DC=AD. If AB= 10, what is the length of AC?

A. 20
B. 10\sqrt{3}
C. 20\sqrt{3}/3
D. 10
E. 10\sqrt{3}/3
[Reveal] Spoiler: OA

_________________

Kudos will encourage many others, like me.
Good Questions also deserve few KUDOS.

Expert Post
1 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 23351
Followers: 3602

Kudos [?]: 28702 [1] , given: 2809

Re: BC=BD=DC=AD. If AB= 10, what is the length of AC? [#permalink] New post 12 Mar 2013, 02:40
1
This post received
KUDOS
Expert's post
emmak wrote:
Attachment:
The attachment 1.jpg is no longer available
Note: figure not drawn to scale

BC=BD=DC=AD. If AB= 10, what is the length of AC?

A. 20
B. 10\sqrt{3}
C. 20\sqrt{3}/3
D. 10
E. 10\sqrt{3}/3


This question CAN be solved without trigonometry. In fact trigonometry is NOT tested on the GMAT, which means that EVERY GMAT geometry question can be solved without it.

Look at the figure below:
Attachment:
Triangle.png
Triangle.png [ 18.53 KiB | Viewed 4159 times ]
Notice that triangle ABE is 30°-60°-90° right triangle (E=90° and A=30°), thus its sides are in the ratio 1 : \sqrt{3}: 2 (\sqrt{3} corresponds with AE and 2 corresponds with AB).

Now, since AE=2x+x=3x, then AE:AB=\sqrt{3}: 2 --> 3x:10=\sqrt{3}: 2 --> x=\frac{5\sqrt{3}}{3} --> AC=4x=\frac{20\sqrt{3}}{3}.

Answer: C.

For more check Triangles chapter of Math Book: math-triangles-87197.html

Hope it's clear.
_________________

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

1 KUDOS received
Manager
Manager
avatar
Joined: 08 Dec 2012
Posts: 64
Location: United Kingdom
GMAT 1: 710 Q0 V0
WE: Engineering (Consulting)
Followers: 1

Kudos [?]: 57 [1] , given: 31

Re: BC=BD=DC=AD. If AB= 10, what is the length of AC? [#permalink] New post 18 Mar 2013, 13:38
1
This post received
KUDOS
A step shorter than Bunuel's method :)

Triangle BCD is equilateral. Triangle ADB is isosceles (with angle ADB =120).

Therefore, ABC is a right angle triangle, with angle BAC=30; ACB=60 & ABC=90.

We know that a right angle triangle with 30-60-90 combination has sides of ratio 1x:\sqrt{3}x:2x, with \sqrt{3}x corresponding to AB; 1x corresponding to BC; and 2x corresponding to AC.

Since we know AB = 10, so AC = \frac{20}{\sqrt{3}} which can also be written as 20\sqrt{3}/3

Answer is C

Hope this makes sense.
Expert Post
Veritas Prep GMAT Instructor
User avatar
Joined: 16 Oct 2010
Posts: 4876
Location: Pune, India
Followers: 1150

Kudos [?]: 5348 [0], given: 165

Re: BC=BD=DC=AD. If AB= 10, what is the length of AC? [#permalink] New post 18 Mar 2013, 20:21
Expert's post
emmak wrote:
Attachment:
1.jpg
Note: figure not drawn to scale

BC=BD=DC=AD. If AB= 10, what is the length of AC?

A. 20
B. 10\sqrt{3}
C. 20\sqrt{3}/3
D. 10
E. 10\sqrt{3}/3


You can do it using just the Pythagorean theorem too.
Notice that you have an equilateral triangle BCD. If its side is a, its altitude BE (shown by Bunuel in the diagram) will be \sqrt{3}a/2.
Also the base AE will be a + a/2 (Since altitude of equilateral triangle bisects the base)

So 10^2 = (3a/2)^2 + (\sqrt{3}a/2)^2
100 = 12a^2/4
a = 10\sqrt{3}/3

Length of AC = 2a = 20\sqrt{3}/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: 26 Feb 2013
Posts: 54
Concentration: Strategy, General Management
GMAT 1: 660 Q50 V30
WE: Consulting (Telecommunications)
Followers: 0

Kudos [?]: 4 [0], given: 16

Re: BC=BD=DC=AD. If AB= 10, what is the length of AC? [#permalink] New post 19 Mar 2013, 08:13
From BC=BD=DC, we know angle DBC= 60 and Angle BDA=120.
And AD=AB so angle ABD=30.
Therefor triangle ABC is right angle trangle with angle B=90 and Angle A=30.

now Cos(A)= AB/AC=10/AC=Sqrt3/2

hence AC=20/srt3 or (20*srt3)/3
Expert Post
Veritas Prep GMAT Instructor
User avatar
Joined: 16 Oct 2010
Posts: 4876
Location: Pune, India
Followers: 1150

Kudos [?]: 5348 [0], given: 165

Re: BC=BD=DC=AD. If AB= 10, what is the length of AC? [#permalink] New post 27 Mar 2013, 19:51
Expert's post
rakeshd347 wrote:
Hi There

I understood your approach but I solved this problem with another approach which is right but I am getting the different result. Can you tell me what is wrong with this approach.

angle BDC,BCD and DBC are all 60 degrees as it is equilateral triangle.
Now in the triangle BAD angle BDA will be 120 because of straight line. so the rest of the two angles will be 30 each which makes the angle ABC a rectangle. So the triangle ABC is rectangle and if you solve it with this approach you will get the answer 10multiply by root3/3

Can you please tell me whats wrong with this.
Thanks


You are right that triangle ABC is right angled at B.
Also, AC = 2*BC, AB = 10

BC^2 + 10^2 = AB^2 = (2BC)^2
10^2 = 3(BC)^2
BC = 10\sqrt{3}/3

But the question asks you the length of AC.

AC = 2*BC = 20\sqrt{3}/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
User avatar
Joined: 28 Apr 2013
Posts: 172
Location: India
GPA: 4
WE: Medicine and Health (Health Care)
Followers: 0

Kudos [?]: 27 [0], given: 84

Re: BC=BD=DC=AD. If AB= 10, what is the length of AC? [#permalink] New post 25 Nov 2013, 06:45
emmak wrote:
Attachment:
1.jpg
Note: figure not drawn to scale

BC=BD=DC=AD. If AB= 10, what is the length of AC?

A. 20
B. 10\sqrt{3}
C. 20\sqrt{3}/3
D. 10
E. 10\sqrt{3}/3


Another way; since BD=BC=DC, triangle BDC equilateral triangle hence angle BCA = 60 degrees. it mens that other angles angle ABC + angle BAC = 180-60 = 120. Which means that AB = < AC. Which means AC >=10. Let BC = X ; Therefore AC= 2X.
Using pythagoreus theorem AC^2 = AB^2 + BC^2 = 100 +x
4x^2 = 100 + x^2
3x^2 = 100
x = 10[square_root]3/3
AC = 2X = 20 [square_root]3/3


:banana
_________________

Thanks for Posting

LEARN TO ANALYSE

+1 kudos if you like

Senior Manager
Senior Manager
User avatar
Joined: 13 May 2013
Posts: 476
Followers: 1

Kudos [?]: 58 [0], given: 134

Re: BC=BD=DC=AD. If AB= 10, what is the length of AC? [#permalink] New post 12 Dec 2013, 12:12
Note: figure not drawn to scale

BC=BD=DC=AD. If AB= 10, what is the length of AC?

If BC=BD=DC then we know triangle DBC is an equilateral triangle. Furthermore, we know that ADC all lie on a line together which means angle ADB = 180-60 = 120. Because AD = DB we know that this triangle is isosceles and that the two other angle measures in this triangle are 30 each. Looking at both triangles together, we see that ABC is a 30:60:90 triangle. Knowing this, and one side length (the length opposite 60) we can solve for BC. Because BC = DC = AD we can find the length of AC (which is AD+DC)

The ratio of the sides in a 30:60:90 is (x/2) : (√3/2 x) : x
√3/2 x = 10
x = 20/√3
In a 30:60:90, the hypotenuse is twice the length of the shortest side. The shortest side is equal to x/2 or (20/√3)/2. Because the hypotenuse is twice that length, it is simply equal to 20/√3




Finally, to cancel out the root on the bottom multiply by (√3/√3) = 20√3/3
Re: BC=BD=DC=AD. If AB= 10, what is the length of AC?   [#permalink] 12 Dec 2013, 12:12
    Similar topics Author Replies Last post
Similar
Topics:
3 Experts publish their posts in the topic In figure above, the length of AC is 12 and the length of AB goodyear2013 3 21 Jan 2014, 10:10
5 Experts publish their posts in the topic The side lengths of triangle ABC are such that AC > BC > AB. swarman 8 11 Mar 2013, 14:13
9 Experts publish their posts in the topic In the diagram, what is the length of AB? enigma123 17 05 Feb 2012, 16:30
2 Experts publish their posts in the topic What is the length of the chord AB kenguva 7 29 Jan 2012, 22:52
1 Experts publish their posts in the topic If B is the midpoint of AC, what is the length of BE? shrive555 3 15 Nov 2010, 11:00
Display posts from previous: Sort by

BC=BD=DC=AD. If AB= 10, what is the length of AC?

  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®.