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

It is currently 18 Dec 2018, 07:17

Expecting Soon:

R1 Admission Decisions from McCombs - Join Chat Room for Latest Updates


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 December
PrevNext
SuMoTuWeThFrSa
2526272829301
2345678
9101112131415
16171819202122
23242526272829
303112345
Open Detailed Calendar
  • Happy Christmas 20% Sale! Math Revolution All-In-One Products!

     December 20, 2018

     December 20, 2018

     10:00 PM PST

     11:00 PM PST

    This is the most inexpensive and attractive price in the market. Get the course now!
  • Key Strategies to Master GMAT SC

     December 22, 2018

     December 22, 2018

     07:00 AM PST

     09:00 AM PST

    Attend this webinar to learn how to leverage Meaning and Logic to solve the most challenging Sentence Correction Questions.

2 equilateral triangles XYZ and ABC are shown as above figure. If YX =

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

Hide Tags

Senior DS Moderator
User avatar
V
Joined: 27 Oct 2017
Posts: 1143
Location: India
Concentration: International Business, General Management
GPA: 3.64
WE: Business Development (Energy and Utilities)
Premium Member CAT Tests
2 equilateral triangles XYZ and ABC are shown as above figure. If YX =  [#permalink]

Show Tags

New post Updated on: 16 Oct 2018, 00:52
4
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

50% (02:19) correct 50% (02:17) wrong based on 42 sessions

HideShow timer Statistics

Image
2 equilateral triangles XYZ and ABC are shown as above figure. If YX = XA=m and AB=n, what is the area of a square CKHZ, in terms of m and n?


A. \(\sqrt{3m^2+n^2}\)

B. \(3m^2+n^2\)

C. \(\sqrt{3}m^2+n^2\)

D. \(\sqrt{m^2+3n^2}\)

E. \(m^2+3n^2\)


Weekly Quant Quiz #3 Question No 9



Attachment:
PS Question 9.jpg
PS Question 9.jpg [ 16.87 KiB | Viewed 831 times ]

_________________

Win GMAT CLUB Test- Weekly Quant Quiz Contest
Weekly Quant Quiz Questions- Direct Download
SC: Confusable words

All you need for Quant, GMAT PS Question Directory,GMAT DS Question Directory
Error log/Key Concepts
Combination Concept: Division into groups
Question of the Day (QOTD)
Free GMAT CATS


Originally posted by gmatbusters on 06 Oct 2018, 09:37.
Last edited by Bunuel on 16 Oct 2018, 00:52, edited 3 times in total.
Renamed the topic and edited the question.
Senior DS Moderator
User avatar
V
Joined: 27 Oct 2017
Posts: 1143
Location: India
Concentration: International Business, General Management
GPA: 3.64
WE: Business Development (Energy and Utilities)
Premium Member CAT Tests
Re: 2 equilateral triangles XYZ and ABC are shown as above figure. If YX =  [#permalink]

Show Tags

New post 06 Oct 2018, 09:38

Official Explanation


If you enlarge the diagram above, we get below figure
Attachment:
Q1.jpg
Q1.jpg [ 20.65 KiB | Viewed 605 times ]


Here, the angles of the triangle is 90deg:60deg:30deg, so the corresponding ratio of the side lengths is 1:√3:2, as shown below.
Attachment:
Q2.jpg
Q2.jpg [ 9.76 KiB | Viewed 605 times ]

Then, you get ZA= 2TA = 2((√3 m)/2)=√3m. Since ∠ZAC=90deg, according to the Pythagorean Theorem,
We get \(ZC^2 =ZA^2 + CA^2\) = \((√3m)^2+n^2=3m^2+n^2\), and the area of the square CKHZ = \(ZC^2 = 3m^2+n^2\). Therefore, the answer is B.
_________________

Win GMAT CLUB Test- Weekly Quant Quiz Contest
Weekly Quant Quiz Questions- Direct Download
SC: Confusable words

All you need for Quant, GMAT PS Question Directory,GMAT DS Question Directory
Error log/Key Concepts
Combination Concept: Division into groups
Question of the Day (QOTD)
Free GMAT CATS

Manager
Manager
avatar
B
Joined: 16 Sep 2011
Posts: 92
GMAT ToolKit User Reviews Badge CAT Tests
Re: 2 equilateral triangles XYZ and ABC are shown as above figure. If YX =  [#permalink]

Show Tags

New post 06 Oct 2018, 09:52
triangle AZC is a right angled triangle

and AC= n

XZ= n ,AX=n
so in AZ = ?

sin 120/ AZ = sin 30/n

so sqrt 3/2AZ = 1/2n

so AZ= n sqrt 3

so CZ ^2= sqrt (AZ^2 + AC^2) = 3n^2 + m^2= area of square

E is the answer
PS Forum Moderator
User avatar
P
Status: It always seems impossible until it's done.
Joined: 16 Sep 2016
Posts: 441
GMAT ToolKit User Premium Member Reviews Badge CAT Tests
Re: 2 equilateral triangles XYZ and ABC are shown as above figure. If YX =  [#permalink]

Show Tags

New post 06 Oct 2018, 10:03
In my opinion (B) is the answer. I have made some constructions and the solution is in image.

Best Regards,
G
Attachments

Q9.jpeg
Q9.jpeg [ 98.41 KiB | Viewed 755 times ]

Intern
Intern
avatar
B
Joined: 17 Dec 2016
Posts: 20
CAT Tests
Re: 2 equilateral triangles XYZ and ABC are shown as above figure. If YX =  [#permalink]

Show Tags

New post 06 Oct 2018, 10:09
Draw a line to connect Z and A

Angle ZXA = 180∘ - angle ZXY = 90∘

Triangle ZXA is isoceles --> Angle XAZ = 30∘, ZA = 2 x (m\sqrt{3}/2) = m\sqrt{3}

Angle ZAC = 180∘ - Angle XAZ - Angle CAB = 180∘ - 30∘ - 60∘ = 90∘

--> ZC = \sqrt{\(ZA^{2}\) + \(AC^{2}\)} = \sqrt{\((m[square_root]3})^{2}\) + \(n^{2}\)[/square_root]

--> Area of square CKHZ = \((m\sqrt{3})^{2}\) + \(n^{2}\)

--> Option B
Intern
Intern
avatar
B
Joined: 06 Feb 2018
Posts: 16
Re: 2 equilateral triangles XYZ and ABC are shown as above figure. If YX =  [#permalink]

Show Tags

New post Updated on: 11 Oct 2018, 03:42
Use Pythagoras theorem

How?

Find the base and height of the triangle formed whose side is the side of square

Height(the horizontal part) comes out (after a few calculations) as (3n+m)/2 and base(upright( as root(3)/2(m-n)

Use Pythagoras theorem (result turns out nicely as 3m^2+n^2

B

Originally posted by hargun3045 on 06 Oct 2018, 10:20.
Last edited by hargun3045 on 11 Oct 2018, 03:42, edited 1 time in total.
RC Moderator
User avatar
D
Joined: 24 Aug 2016
Posts: 576
Location: Canada
Concentration: Entrepreneurship, Operations
GMAT 1: 630 Q48 V28
GMAT 2: 540 Q49 V16
GMAT ToolKit User Premium Member Reviews Badge CAT Tests
Re: 2 equilateral triangles XYZ and ABC are shown as above figure. If YX =  [#permalink]

Show Tags

New post 06 Oct 2018, 12:07
I am glad that finally I could solve it.......... nice one. Worth the time.
But if this shows up in the exam ........
( :-) I hope I can figure out the effort required in 1 min and move on
(unless I can borrow some gray matter from the amazing Quant minds of the GC Community))

........... Thanks again .
Attachments

Quiz_3 Question No 9_Oct 06  2018.jpg
Quiz_3 Question No 9_Oct 06 2018.jpg [ 1.63 MiB | Viewed 701 times ]


_________________

Please let me know if I am going in wrong direction.
Thanks in appreciation.

Intern
Intern
avatar
B
Joined: 17 Aug 2018
Posts: 6
Re: 2 equilateral triangles XYZ and ABC are shown as above figure. If YX =  [#permalink]

Show Tags

New post 07 Oct 2018, 17:49
Hi..Congrats for getting it right.Could u please elaborate ur explanation? I am not clear with the image that u hve uploaded.

Thanks & Regards,

Gladiator59 wrote:
In my opinion (B) is the answer. I have made some constructions and the solution is in image.

Best Regards,
G


Posted from my mobile device
Director
Director
User avatar
D
Joined: 27 May 2012
Posts: 637
Premium Member
Re: 2 equilateral triangles XYZ and ABC are shown as above figure. If YX =  [#permalink]

Show Tags

New post 16 Oct 2018, 00:49
gmatbusters wrote:
2 equilateral triangles XYZ and ABC are shown as above figure. If YX = XA=m and AB=n, what is the area of a square CKHZ, in terms of m and n?


A. \(\sqrt{3m^2+n^2}\)

B. \(3m^2+n^2\)

C. \(\sqrt{3}m^2+n^2\)

D. \(\sqrt{m^2+3n^2}\)

E. \(m^2+3n^2\)


Weekly Quant Quiz #3 Question No 9



Attachment:
PS Question 9.jpg


Hi gmatbusters,

The figure is not visible in the question , kindly look into this. Thank you.
_________________

- Stne

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 51280
Re: 2 equilateral triangles XYZ and ABC are shown as above figure. If YX =  [#permalink]

Show Tags

New post 16 Oct 2018, 00:53
stne wrote:
gmatbusters wrote:
2 equilateral triangles XYZ and ABC are shown as above figure. If YX = XA=m and AB=n, what is the area of a square CKHZ, in terms of m and n?


A. \(\sqrt{3m^2+n^2}\)

B. \(3m^2+n^2\)

C. \(\sqrt{3}m^2+n^2\)

D. \(\sqrt{m^2+3n^2}\)

E. \(m^2+3n^2\)


Weekly Quant Quiz #3 Question No 9



Attachment:
PS Question 9.jpg


Hi gmatbusters,

The figure is not visible in the question , kindly look into this. Thank you.

__________________
Fixed that. Thank you.
_________________

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

Manager
Manager
User avatar
G
Joined: 07 Aug 2018
Posts: 110
Location: United States (MA)
GMAT 1: 560 Q39 V28
CAT Tests
Re: 2 equilateral triangles XYZ and ABC are shown as above figure. If YX =  [#permalink]

Show Tags

New post 25 Oct 2018, 06:19
gmatbusters wrote:

Official Explanation


If you enlarge the diagram above, we get below figure
Attachment:
Q1.jpg


Here, the angles of the triangle is 90deg:60deg:30deg, so the corresponding ratio of the side lengths is 1:√3:2, as shown below.
Attachment:
Q2.jpg

Then, you get ZA= 2TA = 2((√3 m)/2)=√3m. Since ∠ZAC=90deg, according to the Pythagorean Theorem,
We get \(ZC^2 =ZA^2 + CA^2\) = \((√3m)^2+n^2=3m^2+n^2\), and the area of the square CKHZ = \(ZC^2 = 3m^2+n^2\). Therefore, the answer is B.


gmatbusters,

how do I know that the bisector of line \(ZA\) will divide \(∠ZXA\)into two eual angles? I somehow cannot get into my head how we can be sure of that... Do you mind explaining it in more detail?

Thanks you in advance!
_________________

Quantitative Megathread:https://gmatclub.com/forum/ultimate-gmat-quantitative-megathread-244512.html
Verbal Megathread:https://gmatclub.com/forum/all-you-need-for-gmat-verbal-164070.html
Flashcards Quant + Verbal:https://gmatclub.com/forum/gmat-flashcards-108651.html
Thursdays with Ron:https://gmatclub.com/forum/manhattan-s-thursdays-with-ron-consolidated-video-index-223612.html#p2138753

Senior DS Moderator
User avatar
V
Joined: 27 Oct 2017
Posts: 1143
Location: India
Concentration: International Business, General Management
GPA: 3.64
WE: Business Development (Energy and Utilities)
Premium Member CAT Tests
Re: 2 equilateral triangles XYZ and ABC are shown as above figure. If YX =  [#permalink]

Show Tags

New post 25 Oct 2018, 06:29
1
Hi T1101
Please note that since YX = XA

hence triangle ZXA is an isosceles triangle, hence the altitude XT is also the angle bisector. ( Geometric property)
I hope it is clear now.
Attachment:
Q1.jpg
Q1.jpg [ 15.29 KiB | Viewed 282 times ]


In an isosceles triangle (where base is the side which is not equal to any other side):

– the altitude drawn to the base is the median and the angle bisector;

– the median drawn to the base is the altitude and the angle bisector;

– the bisector of the angle opposite to the base is the altitude and the median.



https://www.veritasprep.com/blog/2014/05/medians-altitudes-and-angle-bisectors-in-special-triangles-on-the-gmat/


T1101 wrote:
gmatbusters wrote:

Official Explanation


If you enlarge the diagram above, we get below figure
Attachment:
The attachment Q1.jpg is no longer available


Here, the angles of the triangle is 90deg:60deg:30deg, so the corresponding ratio of the side lengths is 1:√3:2, as shown below.
Attachment:
The attachment Q2.jpg is no longer available

Then, you get ZA= 2TA = 2((√3 m)/2)=√3m. Since ∠ZAC=90deg, according to the Pythagorean Theorem,
We get \(ZC^2 =ZA^2 + CA^2\) = \((√3m)^2+n^2=3m^2+n^2\), and the area of the square CKHZ = \(ZC^2 = 3m^2+n^2\). Therefore, the answer is B.


gmatbusters,

how do I know that the bisector of line \(ZA\) will divide \(∠ZXA\)into two eual angles? I somehow cannot get into my head how we can be sure of that... Do you mind explaining it in more detail?

Thanks you in advance!

_________________

Win GMAT CLUB Test- Weekly Quant Quiz Contest
Weekly Quant Quiz Questions- Direct Download
SC: Confusable words

All you need for Quant, GMAT PS Question Directory,GMAT DS Question Directory
Error log/Key Concepts
Combination Concept: Division into groups
Question of the Day (QOTD)
Free GMAT CATS

GMAT Club Bot
Re: 2 equilateral triangles XYZ and ABC are shown as above figure. If YX = &nbs [#permalink] 25 Oct 2018, 06:29
Display posts from previous: Sort by

2 equilateral triangles XYZ and ABC are shown as above figure. If YX =

  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®.