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

 It is currently 18 Sep 2018, 16:27

### 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

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

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

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 49206
A certain right triangle has sides of length x, y, and z, wh  [#permalink]

### Show Tags

13 Mar 2014, 02:22
3
51
00:00

Difficulty:

85% (hard)

Question Stats:

60% (02:00) correct 40% (02:20) wrong based on 828 sessions

### HideShow timer Statistics

The Official Guide For GMAT® Quantitative Review, 2ND Edition

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) $$y<\frac{\sqrt{3}}{4}$$

Problem Solving
Question: 157
Category: Geometry; Algebra Triangles; Area; Inequalities
Page: 83
Difficulty: 600

GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition - Quantitative Questions Project

Each week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.

We'll be glad if you participate in development of this project:
2. Please vote for the best solutions by pressing Kudos button;
3. Please vote for the questions themselves by pressing Kudos button;
4. Please share your views on difficulty level of the questions, so that we have most precise evaluation.

Thank you!

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 49206
Re: A certain right triangle has sides of length x, y, and z, wh  [#permalink]

### Show Tags

15 Mar 2014, 10:46
9
18
SOLUTION

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) $$y<\frac{\sqrt{3}}{4}$$

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 $$\frac{xy}{2}=\frac{x*1,000,000}{2}=1$$ --> $$x=\frac{2}{1,000,000}$$.
_________________
##### General Discussion
Director
Joined: 10 Mar 2013
Posts: 550
Location: Germany
Concentration: Finance, Entrepreneurship
GMAT 1: 580 Q46 V24
GPA: 3.88
WE: Information Technology (Consulting)
A certain right triangle has sides of length x, y, and z, wh  [#permalink]

### Show Tags

20 Nov 2015, 14:11
Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

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) $$y<\frac{\sqrt{3}}{4}$$

This was a tough problem for me, to be honest I couldn't find a solution like Bunuel did, but I have tested aswer choices to derive at the correct answer.

We know that $$x*y=2$$ actually let's square this expression $$x^2*y^2=4$$ so let's test the values given in the answer choices with Min/Max approach (we ca also square values in the answer choices, as sides of a triangle can not be -ve)

(B) so $$y^2$$ can be max 2 and $$x^2$$= max $$\frac{3}{4}$$--> multiply $$x^2*y^2$$=1,5. So B is out because we need a 4 when $$x^2 and y^2$$ are multiplied
(C) $$y^2$$ max = $$\frac{3}{4}$$, $$x^2$$ max=2/9 --> $$\frac{2}{9}*\frac{3}{4} < 4$$ , C is out
(D) $$\frac{2}{9}*\frac{3}{16} < 4$$
(E) $$y^2$$ < $$\frac{3}{16}$$, so we know that y > x, thus when y < $$\frac{3}{16}$$ $$x^2$$ is also < $$\frac{3}{16}$$ and their product is < 4, E is also out and we are left with Answer Choice A
(A)
_________________

When you’re up, your friends know who you are. When you’re down, you know who your friends are.

800Score ONLY QUANT CAT1 51, CAT2 50, CAT3 50
GMAT PREP 670
MGMAT CAT 630
KAPLAN CAT 660

Intern
Joined: 10 Aug 2015
Posts: 33
Location: India
GMAT 1: 700 Q48 V38
GPA: 3.5
WE: Consulting (Computer Software)
Re: A certain right triangle has sides of length x, y, and z, wh  [#permalink]

### Show Tags

27 Apr 2016, 17:59
Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

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) $$y<\frac{\sqrt{3}}{4}$$

Thank you![/textarea]

Hi,
from the area of triangle we know x*y = 2.
So there is one possibility that x could be 1 and y could be 2, but none of the answer choices ,except A confirms to y =2 possibility.

Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8278
Location: Pune, India
A certain right triangle has sides of length x, y, and z, wh  [#permalink]

### Show Tags

27 Apr 2016, 20:00
5
3
Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

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) $$y<\frac{\sqrt{3}}{4}$$

You can think about it in terms of transition points too.

x < y< z so this means that x and y are the legs of the right triangle and z is the hypotenuse.
The area of the triangle will be (1/2)*xy = 1
xy = 2

Now, if x = y, then both x and y would be equal to $$\sqrt{2}$$.
But y is greater than x, so y would be at least a slight bit greater than $$\sqrt{2}$$ and x would be a slight bit less than $$\sqrt{2}$$. In all options other than (A), y takes values less than 1.414.
_________________

Karishma
Veritas Prep GMAT Instructor

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

Current Student
Joined: 20 Mar 2014
Posts: 2639
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
A certain right triangle has sides of length x, y, and z, wh  [#permalink]

### Show Tags

27 Apr 2016, 20:12
1
1
Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

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) $$y<\frac{\sqrt{3}}{4}$$

First step will be to breakdown the options into recognizable decimal representations (assuming $$\sqrt{2} \approx 1.4$$, $$\sqrt{3} \approx 1.7$$)

A) y>1.4
B) 0.8<y<1.4
C) 0.5<y<0.8
D) 0.4<y<0.5
E) y<0.4

We are given that x<y<z and that 0.5*x*y=1 --> x*y=2

Now from the relation xy=2 --> go back to the options and test for y=1. You get x=2 but we are given that x<y ---> y MUST be > $$\approx$$1.4 such that x < y

For any value of y < 1.4 , you will end up getting x>y (try with y=0.5 or 0.75 etc).

Only A satisfies this condition and is hence the correct answer.

Hope this helps.
Intern
Joined: 03 Aug 2017
Posts: 27
A certain right triangle has sides of length x, y, and z, wh  [#permalink]

### Show Tags

29 Apr 2018, 01:25
VeritasPrepKarishma wrote:
Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

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) $$y<\frac{\sqrt{3}}{4}$$

You can think about it in terms of transition points too.

x < y< z so this means that x and y are the legs of the right triangle and z is the hypotenuse.
The area of the triangle will be (1/2)*xy = 1
xy = 2

Now, if x = y, then both x and y would be equal to $$\sqrt{2}$$.
But y is greater than x, so y would be at least a slight bit greater than $$\sqrt{2}$$ and x would be a slight bit less than $$\sqrt{2}$$. In all options other than (A), y takes values less than 1.414.

Hi can you Please help me understand why have you assumed if x= y then the value for both is equal to root 2 ?
I understood that x < y< z and if z is the Hypotenuese and therefore in case its a 30 60 90 triangle then hypotenuse coud hold the value of root 2
But how Y could hold the value higher than root 2 and x an even smaller value than root 2 ? also in the equation above we dervided xy=2 don't we use this finding ?
A certain right triangle has sides of length x, y, and z, wh &nbs [#permalink] 29 Apr 2018, 01:25
Display posts from previous: Sort by

# Events & Promotions

 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®.