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

 It is currently 25 Sep 2016, 21:24

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

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

Author Message
TAGS:

### Hide Tags

Manager
Status: Current MBA Student
Joined: 19 Nov 2009
Posts: 127
Concentration: Finance, General Management
GMAT 1: 720 Q49 V40
Followers: 13

Kudos [?]: 299 [3] , given: 210

A certain right triangle has sides of length x, y, and z [#permalink]

### Show Tags

16 Jan 2011, 16:01
3
KUDOS
34
This post was
BOOKMARKED
00:00

Difficulty:

75% (hard)

Question Stats:

60% (02:35) correct 40% (02:18) wrong based on 507 sessions

### HideShow 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. $$y > \sqrt {2}$$

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. $$y < \frac {\sqrt {3}}{4}$$
[Reveal] Spoiler: OA
Math Expert
Joined: 02 Sep 2009
Posts: 34830
Followers: 6482

Kudos [?]: 82622 [20] , given: 10108

Re: Tricky Triangle Inequalities. QR #157 PS [#permalink]

### Show Tags

16 Jan 2011, 16:12
20
KUDOS
Expert's post
13
This post was
BOOKMARKED
tonebeeze 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. $$\frac {\sqrt {3}} {2} < y < \sqrt {2}$$

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 $$\frac{xy}{2}=\frac{x*1,000,000}{2}=1$$ --> $$x=\frac{2}{1,000,000}$$.

Hope it helps.
_________________
Intern
Joined: 14 Sep 2013
Posts: 1
Followers: 0

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

Re: A certain right triangle has sides of length x, y, and z [#permalink]

### Show Tags

05 Nov 2013, 11:04
1
KUDOS
tanviet wrote:
it is simple but hard enough to kill us

this is NOT og questions.

It is the Quant Review 2nd Ed. #157
Intern
Status: Focus is the Key
Joined: 07 Feb 2011
Posts: 9
Concentration: Strategy, Technology
Schools: ISB
GMAT 1: 710 Q49 V38
GPA: 3.35
WE: Consulting (Telecommunications)
Followers: 0

Kudos [?]: 6 [0], given: 26

Re: Tricky Triangle Inequalities. QR #157 PS [#permalink]

### Show Tags

06 Aug 2011, 04:41
Bunuel wrote:
tonebeeze 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. $$\frac {\sqrt {3}} {2} < y < \sqrt {2}$$

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 $$\frac{xy}{2}=\frac{x*1,000,000}{2}=1$$ --> $$x=\frac{2}{1,000,000}$$.

Hope it helps.

Dear Bunuel,

While solving the question ,I assumed it to be the special 90,60,30 triangle.
Am I wrong in following that approach ?
Math Expert
Joined: 02 Sep 2009
Posts: 34830
Followers: 6482

Kudos [?]: 82622 [0], given: 10108

Re: Tricky Triangle Inequalities. QR #157 PS [#permalink]

### Show Tags

09 Feb 2012, 04:42
rohansharma wrote:
While solving the question ,I assumed it to be the special 90,60,30 triangle.
Am I wrong in following that approach ?

We are just told that the triangle is right, not that it's a special kind like 30-60-90 or 45-45-90.
_________________
Manager
Status: MBA Aspirant
Joined: 12 Jun 2010
Posts: 178
Location: India
WE: Information Technology (Investment Banking)
Followers: 3

Kudos [?]: 70 [0], given: 1

Re: A certain right triangle has sides of length x, y, and z [#permalink]

### Show Tags

09 Feb 2012, 06:54
OA is A
since this is a rt angled triangle so z is th hypotnuse
and given xy = 2
so as x decreased y increases. Now if x is 1 then y is 2, when x is 1/2 y is 4.
Only option A supports this result.
Current Student
Joined: 27 Feb 2012
Posts: 94
Concentration: General Management, Nonprofit
GMAT 1: 700 Q47 V39
Followers: 0

Kudos [?]: 25 [0], given: 42

Re: A certain right triangle has sides of length x, y, and z [#permalink]

### Show Tags

13 Mar 2012, 15:11
Is there a reason we can completely ignore z in the inequality while solving for y? That is the only part I don't understand. (im rusty)
Intern
Joined: 31 Dec 2012
Posts: 11
GMAT 1: 700 Q44 V42
Followers: 0

Kudos [?]: 0 [0], given: 55

Re: Tricky Triangle Inequalities. QR #157 PS [#permalink]

### Show Tags

28 Feb 2013, 09:55
Bunuel wrote:
$$x=\frac{2}{y}$$. As $$x<y$$, then $$\frac{2}{y}<y$$

Could you explain why that is?
Math Expert
Joined: 02 Sep 2009
Posts: 34830
Followers: 6482

Kudos [?]: 82622 [0], given: 10108

Re: Tricky Triangle Inequalities. QR #157 PS [#permalink]

### Show Tags

28 Feb 2013, 10:01
2flY wrote:
Bunuel wrote:
$$x=\frac{2}{y}$$. As $$x<y$$, then $$\frac{2}{y}<y$$

Could you explain why that is?

Just substitute x with $$\frac{2}{y}$$ in $$x<y$$ to get $$\frac{2}{y}<y$$.
_________________
Moderator
Joined: 25 Apr 2012
Posts: 728
Location: India
GPA: 3.21
Followers: 43

Kudos [?]: 629 [0], given: 723

Re: Tricky Triangle Inequalities. QR #157 PS [#permalink]

### Show Tags

01 Mar 2013, 02:21
rohansharma wrote:
Bunuel wrote:
tonebeeze 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. $$\frac {\sqrt {3}} {2} < y < \sqrt {2}$$

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 $$\frac{xy}{2}=\frac{x*1,000,000}{2}=1$$ --> $$x=\frac{2}{1,000,000}$$.

Hope it helps.

Dear Bunuel,

While solving the question ,I assumed it to be the special 90,60,30 triangle.
Am I wrong in following that approach ?

Hi Bunuel,

The Q stem says that sides are x<y<z and it is a right angle triangle. So we can assume that it will be 30-60-90 triangle. Had it been 45-45-90 triangle then the 2 sides ie base and perpendicular would have been equal and therefore x=y and x,y<z

I guess it should be okay to assume that it is 30-60 -90 triangle.

_________________

“If you can't fly then run, if you can't run then walk, if you can't walk then crawl, but whatever you do you have to keep moving forward.”

Math Expert
Joined: 02 Sep 2009
Posts: 34830
Followers: 6482

Kudos [?]: 82622 [0], given: 10108

Re: Tricky Triangle Inequalities. QR #157 PS [#permalink]

### Show Tags

01 Mar 2013, 02:50
mridulparashar1 wrote:
rohansharma wrote:
Bunuel wrote:
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.

Dear Bunuel,

While solving the question ,I assumed it to be the special 90,60,30 triangle.
Am I wrong in following that approach ?

Hi Bunuel,

The Q stem says that sides are x<y<z and it is a right angle triangle. So we can assume that it will be 30-60-90 triangle. Had it been 45-45-90 triangle then the 2 sides ie base and perpendicular would have been equal and therefore x=y and x,y<z

I guess it should be okay to assume that it is 30-60 -90 triangle.

Yes, if it were 45-45-90, then we would have that x=y<z. BUT, knowing that it's not a 45-45-90 right triangle does NOT mean that it's necessarily 30-60-90 triangle: there are numerous other right triangles. For example, 10-80-90, 11-79-90, 25-65-90, ...

Hope it's clear.
_________________
VP
Joined: 09 Jun 2010
Posts: 1336
Followers: 3

Kudos [?]: 100 [0], given: 772

Re: A certain right triangle has sides of length x, y, and z [#permalink]

### Show Tags

04 Mar 2013, 03:20
it is simple but hard enough to kill us

this is NOT og questions.
Manager
Joined: 07 May 2013
Posts: 109
Followers: 0

Kudos [?]: 23 [0], given: 1

Re: A certain right triangle has sides of length x, y, and z [#permalink]

### Show Tags

10 Nov 2013, 19:20
Buneul has quite literally owned this problem. Great solution!
Intern
Joined: 12 Jun 2013
Posts: 3
Followers: 0

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

Re: A certain right triangle has sides of length x, y, and z [#permalink]

### Show Tags

15 Dec 2013, 08:04
i did some guesstimates to arrive at this choice

here we go -

if we assume this to be a isosceles right angled triangle then the area would be maximum.

and xy/2=1

y^2=1 (since it is an isosceles triangle)
y=Sq Root 2

now we know y>x and area =1; y has to be > sq root 2 and x < sq root 2

fortunately in this case, only one option had this range.
Senior Manager
Joined: 13 May 2013
Posts: 472
Followers: 3

Kudos [?]: 144 [0], given: 134

Re: A certain right triangle has sides of length x, y, and z [#permalink]

### Show Tags

16 Dec 2013, 14:17
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?

We are told that this is a right triangle which right off the bat tells me one of two things, either we need to solve with some variation of a^2 + b^2 = c^2 or that we can find the area with base*height.

Because this is a right triangle and x < y < z we know that z is the hypotenuse and that x is the shortest leg. The area = 1 so:

a=1/2 b*h
1=1/2 b*h
2=b*h.

Y is the second longest measurement in this right triangle which means it must be longer than x but shorter than z. If we run through a few possible combinations of a and b we see that there isn't a limit on the length of y so long as y*x = 2 and y<x. For example, x=1 and y = 4 and z can = 5. This means that there is no upward limit on the value of y so answer choice E is out. This also means that D, C and B are out as well because all contain upward limits on the value of y can be any number so long as y*x = 2 and y<x. Therefore, A is the only answer choice.

Answer: a. y > \sqrt {2}
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 11674
Followers: 527

Kudos [?]: 143 [0], given: 0

Re: A certain right triangle has sides of length x, y, and z [#permalink]

### Show Tags

31 Jan 2015, 09:25
Hello from the GMAT Club BumpBot!

Thanks to another GMAT 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.
_________________
Director
Joined: 10 Mar 2013
Posts: 608
Location: Germany
Concentration: Finance, Entrepreneurship
GMAT 1: 580 Q46 V24
GPA: 3.88
WE: Information Technology (Consulting)
Followers: 9

Kudos [?]: 198 [0], given: 200

Re: A certain right triangle has sides of length x, y, and z [#permalink]

### Show Tags

23 Aug 2015, 07:02
I think I've made it more comlicated then it is...
xy=2, z^2=x^2+y^2
(x+y)^2=z^2+4 and just stucked at this point ....
_________________

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

Manager
Joined: 13 Feb 2011
Posts: 104
Followers: 0

Kudos [?]: 24 [0], given: 3358

Re: A certain right triangle has sides of length x, y, and z [#permalink]

### Show Tags

12 Feb 2016, 19:34
One other way that I noticed to solve this problem is to check the length of $$y$$ when $$x=y$$, i.e. 45,45,90. In that case $$x=y=\sqrt{2}$$, however as $$y>x$$, it'd always need to be $$>\sqrt{2}$$.

HTH
Re: A certain right triangle has sides of length x, y, and z   [#permalink] 12 Feb 2016, 19:34
Similar topics Replies Last post
Similar
Topics:
Consider a right triangle ABC with length of sides being x,y and z whe 1 03 Apr 2016, 22:16
34 A certain right triangle has sides of length x, y, and z, wh 6 13 Mar 2014, 02:22
6 The sides of right triangle ABC are such that the length of 6 12 Mar 2013, 05:13
15 If the sides of a triangle have lengths x, y, and z, x + y = 13 04 May 2011, 19:35
36 A certain right triangle has sides of length x, y, and z 15 17 Jan 2010, 02:39
Display posts from previous: Sort by