Last visit was: 04 Apr 2025, 07:54 It is currently 04 Apr 2025, 07:54
Decision Tracker
My Rewards
New comers' posts
New posts
Unanswered

Close

GRE Prep 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 GRE 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.

Go to My Error Log Learn more
Close

Request Expert Reply

Confirm Cancel
PREVIOUS TOPIC
NEXT TOPIC

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

Tags :
Find Similar Topics  About  Add a Tag

Show Tags
Hide Tags

User avatar
D
Carcass
Verbal Expert
Joined: 18 Apr 2015
Posts: 31444
Own Kudos [?]: 37660 [29]
Given Kudos: 26233
Send PM
A certain right triangle has sides of length x, y, and z, wh [#permalink] New post   10 Jun 2020, 10:08
2
1
Expert Reply
26
Bookmarks
00:00
A
B
C
D
E

Question Stats:

51% (02:25) correct 48% (02:59) wrong based on 187 sessions

Show timer Statistics

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>√2

B. √32<y<√2

C. √23<y<√32

D. √34<y<√23

E. y<√34
ShowHide Answer
Official Answer
A
Most Helpful Community Reply
avatar
B
grenico
Manager
Manager
Joined: 05 Aug 2020
Posts: 101
Own Kudos [?]: 249 [18]
Given Kudos: 14
Send PM
Re: A certain right triangle has sides of length x, y, and z, wh [#permalink] New post   17 Aug 2020, 15:24
11
7
Bookmarks
Carcass 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>√2

B. √32<y<√2

C. √23<y<√32

D. √34<y<√23

E. y<√34



So we have a right triangle, with a hypotenuse of z, the long leg as y, and the short leg as x.

This has to satisfy xy2=1, or

xy=2

Notice that if x=y, making the triangle an isosceles triangle, then x=√2=y.

But we know this can't be true. y is the longer leg.

This means we need to make x smaller than √2 and y bigger than √2. The only answer that gives us y>√2 is A
General Discussion
User avatar
D
Carcass
Verbal Expert
Joined: 18 Apr 2015
Posts: 31444
Own Kudos [?]: 37660 [0]
Given Kudos: 26233
Send PM
Re: A certain right triangle has sides of length x, y, and z, wh [#permalink] New post   10 Jun 2020, 10:08
Expert Reply
Post A Detailed Correct Solution For The Above Questions And Get A Kudos.
Question From Our New Project: GRE Quant Challenge Questions Daily - NEW EDITION!
User avatar
P
GreenlightTestPrep
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Own Kudos [?]: 12345 [4]
Given Kudos: 136
Send PM

Top Member of the Month
Re: A certain right triangle has sides of length x, y, and z, wh [#permalink] New post   10 Jun 2020, 10:22
4
Carcass 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>√2

B. √32<y<√2

C. √23<y<√32

D. √34<y<√23

E. y<√34


There are infinitely many right triangles that have an area of 1.
So, one approach is to find a triangle that meets the given conditions, and see what conclusions we can draw.

Here's one such right triangle:
Image

This meets the conditions that the area is 1 AND x < y < z
With this triangle, y = 4

When we check the answer choices, only one (answer choice A) allows for y to equal 4

Answer: A

Cheers,
Brent
avatar
B
computerbot
Intern
Intern
Joined: 03 Feb 2016
Posts: 42
Own Kudos [?]: 29 [0]
Given Kudos: 6
Send PM
Re: A certain right triangle has sides of length x, y, and z, wh [#permalink] New post   12 Sep 2022, 21:01
Carcass 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>√2

B. √32<y<√2

C. √23<y<√32

D. √34<y<√23

E. y<√34


Can we approach the solution using a different manner besides the one shared by grenico?
User avatar
D
Carcass
Verbal Expert
Joined: 18 Apr 2015
Posts: 31444
Own Kudos [?]: 37660 [0]
Given Kudos: 26233
Send PM
Re: A certain right triangle has sides of length x, y, and z, wh [#permalink] New post   13 Sep 2022, 01:41
Expert Reply
The explanation by brent I believe is the fastest approach sir
avatar
S
YB114
Manager
Manager
Joined: 11 Oct 2023
Posts: 69
Own Kudos [?]: 46 [1]
Given Kudos: 25
Send PM
Re: A certain right triangle has sides of length x, y, and z, wh [#permalink] New post   06 Dec 2023, 01:09
1
Area = 1/2 * x * y

we know x < y thus Area = 1/2 * (<y) * y

Area = 1 , thus 1 = (< y^2/2)

2 < y^2

as both are positives we can take square root without changing sign of inequality.

y > sqrt 2
User avatar
bumpbot
GRE Prep Club Legend
GRE Prep Club Legend
Joined: 07 Jan 2021
Posts: 5224
Own Kudos [?]: 77 [0]
Given Kudos: 0
Send PM
Re: A certain right triangle has sides of length x, y, and z, wh [#permalink] New post   24 Mar 2025, 22:54
Hello from the GRE Prep Club BumpBot!

Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
Prep Club for GRE Bot
gmatclubot
Re: A certain right triangle has sides of length x, y, and z, wh [#permalink]
24 Mar 2025, 22:54
Moderators:
adewale223
GRE Instructor
108 posts
bronaugust
GRE Forum Moderator
37 posts
BrushMyQuant
Moderator
1131 posts
VibhuAnurag
GRE Instructor
234 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Main navigation

Partners

GRE Resources

www.ets.org/gre | About | Terms and Conditions and Privacy Policy | Prep Club for GRE Rules | Contact