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

It is currently 20 Aug 2014, 05:21

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

A certain right triangle has sides of length x, y, and z

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
2 KUDOS received
Manager
Manager
avatar
Joined: 26 Oct 2009
Posts: 54
Followers: 0

Kudos [?]: 7 [2] , given: 25

GMAT ToolKit User
A certain right triangle has sides of length x, y, and z [#permalink] New post 17 Jan 2010, 01:39
2
This post received
KUDOS
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

71% (02:10) correct 29% (01:22) wrong based on 67 sessions
A certain right triangle has sides of length x, y, and z, where x < y < z. If the area of this triangular region is 1, which of the following indicates all of the possible values of y ?

A. y >\sqrt{2}
B. \frac{\sqrt{3}}{2}<y<\sqrt{2}
C. \frac{\sqrt{2}}{3}<y<\frac{\sqrt{3}}{2}
D. \frac{\sqrt{3}}{4} < y <\frac{\sqrt{2}}{3}
E. y<\frac{\sqrt{3}}{4}

OPEN DISCUSSION OF THIS QUESTION IS HERE: a-certain-right-triangle-has-sides-of-length-x-y-and-z-107872.html
[Reveal] Spoiler: OA
Kaplan Promo CodeKnewton GMAT Discount CodesManhattan GMAT Discount Codes
Senior Manager
Senior Manager
avatar
Joined: 25 Jun 2009
Posts: 313
Followers: 2

Kudos [?]: 70 [0], given: 6

GMAT Tests User
Re: Possible Values of side of Right Angle Triangle [#permalink] New post 17 Jan 2010, 01:55
vibhaj wrote:
A certain right triangle has sides of length x, y, and z, where x < y < z. If the area of this triangular region is 1, which of the following indicates all of the possible values of y ?
A. y > sqr root (2)
B. sqr root (3)/2 < y < sqr root (2)
C. sqr root (2)/3 < y < sqr root (3)/2
D. sqr root (3)/4 < y < sqr root (2)/3
E. y < sqr root (3)/4

OA after discussion.

--Edited to denote the square roots more clearly


IMO it should be A,

area of the triangle=1 = 1/2 X*Y

or X*Y = 2

Now , also X<Y , now we by using the POE, we can see that apart from 1 option rest all doesn't satisfy this equation.

Cheers,
Manager
Manager
avatar
Joined: 26 Oct 2009
Posts: 54
Followers: 0

Kudos [?]: 7 [0], given: 25

GMAT ToolKit User
Re: Possible Values of side of Right Angle Triangle [#permalink] New post 17 Jan 2010, 06:51
Thanks Nitish.is there a better way to solve this , without POE ..?
1 KUDOS received
Senior Manager
Senior Manager
avatar
Joined: 25 Jun 2009
Posts: 313
Followers: 2

Kudos [?]: 70 [1] , given: 6

GMAT Tests User
Re: Possible Values of side of Right Angle Triangle [#permalink] New post 17 Jan 2010, 07:06
1
This post received
KUDOS
vibhaj wrote:
Thanks Nitish.is there a better way to solve this , without POE ..?



I am not sure about that but I guess for the purpose of GMAT I found this one quickest.

Anyway, going back to the options if you see, the options are like sqr root of 3 or 2

and from the equation XY =2, we know Y can have a value of 2 ( X=1, Y=2)

So thats why eliminated the rest of the options.

Cheers
Expert Post
13 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 19027
Followers: 3360

Kudos [?]: 24353 [13] , given: 2677

Re: Possible Values of side of Right Angle Triangle [#permalink] New post 17 Jan 2010, 11:30
13
This post received
KUDOS
Expert's post
vibhaj wrote:
Thanks Nitish.is there a better way to solve this , without POE ..?


The area of the triangle is \frac{xy}{2}=1 (x<y<z means that hypotenuse is z) --> x=\frac{2}{y}. As x<y, then \frac{2}{y}<y --> 2<y^2 --> \sqrt{2}<y.

Also note that max value of y is not limited at all. For example y can be 1,000,000 and in this case \frac{xy}{2}=\frac{x*1,000,000}{2}=1 --> x=\frac{2}{1,000,000}.

Hope it helps.
_________________

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

Senior Manager
Senior Manager
avatar
Joined: 24 Jul 2009
Posts: 298
Followers: 2

Kudos [?]: 67 [0], given: 0

GMAT Tests User
Geometry..?? [#permalink] New post 29 Apr 2010, 15:28
A certain right triangle has sides of length x, y, and z, where x < y < z. If the area of this triangular region is 1, which of the following indicates all of the possible values of y ?
A. y > sqrt 2
B. (sqrt 3)/2 < y <sqrt 2
C. (sqrt 2)/3 < y < (sqrt 3)/2
D. (sqrt 3)/4 < y < (sqrt 2)/3
E. y < (sqrt 3)/4

I'M LOOKING FOR THE ALGEBRAIC SOLUTION, WITHOUT SUPPOSING (PLUGGING) THE VALUES OF X,Y AND Z..!!
CEO
CEO
User avatar
Status: Nothing comes easy: neither do I want.
Joined: 12 Oct 2009
Posts: 2793
Location: Malaysia
Concentration: Technology, Entrepreneurship
Schools: ISB '15 (M)
GMAT 1: 670 Q49 V31
GMAT 2: 710 Q50 V35
Followers: 178

Kudos [?]: 922 [0], given: 235

GMAT Tests User Reviews Badge
Re: Geometry..?? [#permalink] New post 29 Apr 2010, 16:07
nverma wrote:
A certain right triangle has sides of length x, y, and z, where x < y < z. If the area of this triangular region is 1, which of the following indicates all of the possible values of y ?
A. y > sqrt 2
B. (sqrt 3)/2 < y <sqrt 2
C. (sqrt 2)/3 < y < (sqrt 3)/2
D. (sqrt 3)/4 < y < (sqrt 2)/3
E. y < (sqrt 3)/4

I'M LOOKING FOR THE ALGEBRAIC SOLUTION, WITHOUT SUPPOSING (PLUGGING) THE VALUES OF X,Y AND Z..!!


area = 1/2 * x* y = 1 => xy=1

since y>x => y^2 > xy => y^2 > 2

=>y > \sqrt{2}

Hence A...whats OA?
_________________

Fight for your dreams :For all those who fear from Verbal- lets give it a fight

Money Saved is the Money Earned :)

Jo Bole So Nihaal , Sat Shri Akaal

:thanks Support GMAT Club by putting a GMAT Club badge on your blog/Facebook :thanks

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Gmat test review :
670-to-710-a-long-journey-without-destination-still-happy-141642.html

Manager
Manager
avatar
Joined: 14 Apr 2010
Posts: 230
Followers: 2

Kudos [?]: 20 [0], given: 1

GMAT Tests User
Some questions .... please help [#permalink] New post 07 May 2010, 21:05
1.A certain right triangle has sides of length x, y, and z, where x < y < z. If the area of this triangular region is 1, which of the following indicates all of the possible values of y ?
A. y > sqrt.2
B. sqrt.3/2 < y < sqrt. 2
C. sqrt.2/3 < y < sqrt.3/2
D. sqrt.3/4 < y < sqrt.2/3
E. y < sqrt.3/4

Thanks :-)
Manager
Manager
avatar
Joined: 09 Apr 2010
Posts: 80
Followers: 1

Kudos [?]: 5 [0], given: 3

Re: Some questions .... please help [#permalink] New post 07 May 2010, 22:42
ok question 1 doesnt seem GMATesque but i have come up with the solution ...let me know what the source is and what the OA is


1) we know that area of triangle is 2 so xy/2 = 1 so xy = 2 moreover x < y .....so think about the two graphs ...y =2/x and x=y ....there will be a point on x-axis beyond which y<x ...to find this point lets equate the two eqns

2/x = x --> x = sqrt(2)

beyond this point y<x ...so y > sqrt(2)

so answer should be A ...in all other choices the value of y is less than sqrt(2)
Manager
Manager
avatar
Joined: 09 Apr 2010
Posts: 80
Followers: 1

Kudos [?]: 5 [0], given: 3

Re: Some questions .... please help [#permalink] New post 07 May 2010, 22:45
can you please post each question as a separate thread ...it would help you and others to post answers to your questions easily
Senior Manager
Senior Manager
User avatar
Affiliations: SPG
Joined: 15 Nov 2006
Posts: 326
Followers: 11

Kudos [?]: 257 [0], given: 20

GMAT Tests User
A certain right triangle [#permalink] New post 21 May 2010, 02:17
A certain right triangle has sides of length x, y, and z, where x < y < z. If the area of this triangular region is 1, which of the following indicates all of the possible values of y ?
A. y > sqrt.2
B. sqrt.3/2 < y < sqrt. 2
C. sqrt.2/3 < y < sqrt.3/2
D. sqrt.3/4 < y < sqrt.2/3
E. y < sqrt.3/4
Senior Manager
Senior Manager
avatar
Joined: 25 Jun 2009
Posts: 313
Followers: 2

Kudos [?]: 70 [0], given: 6

GMAT Tests User
Re: A certain right triangle [#permalink] New post 21 May 2010, 02:24
dimitri92 wrote:
A certain right triangle has sides of length x, y, and z, where x < y < z. If the area of this triangular region is 1, which of the following indicates all of the possible values of y ?
A. y > sqrt.2
B. sqrt.3/2 < y < sqrt. 2
C. sqrt.2/3 < y < sqrt.3/2
D. sqrt.3/4 < y < sqrt.2/3
E. y < sqrt.3/4



This has already been discussed, please follow the link

possible-values-of-side-of-right-angle-triangle-89294.html
Manager
Manager
avatar
Joined: 16 Mar 2010
Posts: 191
Followers: 2

Kudos [?]: 38 [0], given: 9

GMAT Tests User
Re: Possible Values of side of Right Angle Triangle [#permalink] New post 22 May 2010, 07:27
After all this information and discussions.... I think this one is one of most simple questions.... it seems the answer is obvious....
Director
Director
User avatar
Status: GMAT Learner
Joined: 14 Jul 2010
Posts: 652
Followers: 34

Kudos [?]: 213 [0], given: 32

GMAT Tests User
Re: Possible Values of side of Right Angle Triangle [#permalink] New post 10 Mar 2011, 12:20
as x<y<z so z is the hypotenuse
so, 1/2*xy=1
=> xy=2
y>x
=> y^2>xy
=>y^2>2

so y>√2
Ans. A
_________________

I am student of everyone-baten
Collections:-
PSof OG solved by GC members: http://gmatclub.com/forum/collection-ps-with-solution-from-gmatclub-110005.html
DS of OG solved by GC members: http://gmatclub.com/forum/collection-ds-with-solution-from-gmatclub-110004.html
100 GMAT PREP Quantitative collection http://gmatclub.com/forum/gmat-prep-problem-collections-114358.html
Collections of work/rate problems with solutions http://gmatclub.com/forum/collections-of-work-rate-problem-with-solutions-118919.html
Mixture problems in a file with best solutions: http://gmatclub.com/forum/mixture-problems-with-best-and-easy-solutions-all-together-124644.html

Director
Director
avatar
Status: Matriculating
Affiliations: Chicago Booth Class of 2015
Joined: 03 Feb 2011
Posts: 932
Followers: 11

Kudos [?]: 190 [0], given: 123

Reviews Badge
Re: Possible Values of side of Right Angle Triangle [#permalink] New post 10 Mar 2011, 18:39
Solved this intuitively - pls verify this reasoning.
The above stem means that one angle > 45 and another angle is < 45

At x = y (hypothetically) i.e. Both angles equal.
x = z sin (45) = z/ sqrt(2)
y = z cos (45) = z/ sqrt(2)

1/2 x y = 1
Hence z = 2

x = sqrt(2)
y = sqrt(2)

If one angle > 45 and another angle is < 45, And knowing x < y < z
So 0 < x < sqrt(2)
and sqrt(2) < y < Infinity .i.e. when x -> 0 then y -> Infinity
Expert Post
2 KUDOS received
Veritas Prep GMAT Instructor
User avatar
Joined: 16 Oct 2010
Posts: 4665
Location: Pune, India
Followers: 1070

Kudos [?]: 4771 [2] , given: 163

Re: Possible Values of side of Right Angle Triangle [#permalink] New post 10 Mar 2011, 20:03
2
This post received
KUDOS
Expert's post
gmat1220 wrote:
Solved this intuitively - pls verify this reasoning.
The above stem means that one angle > 45 and another angle is < 45

At x = y (hypothetically) i.e. Both angles equal.
x = z sin (45) = z/ sqrt(2)
y = z cos (45) = z/ sqrt(2)

1/2 x y = 1
Hence z = 2

x = sqrt(2)
y = sqrt(2)

If one angle > 45 and another angle is < 45, And knowing x < y < z
So 0 < x < sqrt(2)
and sqrt(2) < y < Infinity


Yes, it can be solved intuitively. It is a very interesting way of thinking. There is one small thing: z may not be 2. e.g. When x = 1 and y = 2, z = sqrt(5)

Think this way:
We know x < y and (1/2)xy = 1 (z is the hypotenuse)
So xy = 2
If x = y, then x = y = sqrt(2)
But since x < y, x is less than sqrt(2) and y is greater than sqrt(2). Makes sense. Good thinking.
_________________

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

Re: Possible Values of side of Right Angle Triangle   [#permalink] 10 Mar 2011, 20:03
    Similar topics Author Replies Last post
Similar
Topics:
4 Experts publish their posts in the topic A certain right triangle has sides of length x, y, and z, wh Bunuel 1 13 Mar 2014, 01:22
8 Experts publish their posts in the topic If the sides of a triangle have lengths x, y, and z, x + y = gmat1220 10 04 May 2011, 18:35
19 Experts publish their posts in the topic A certain right triangle has sides of length x, y, and z tonebeeze 14 16 Jan 2011, 15:01
1 A certain right triangle has sides of length x, y, and z, vivektripathi 7 07 Sep 2008, 07:15
1) In a right triangle x,y and z represent lengths of the sushom101 6 09 Nov 2005, 13:22
Display posts from previous: Sort by

A certain right triangle has sides of length x, y, and z

  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®.