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

 It is currently 21 May 2019, 20:42 ### 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. ### Request Expert Reply # It is given that x^2 + y^2 = z + 1, y^2 + z^2 = x + 1 and z^2 +x^2=y+1

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

### Hide Tags

Senior Manager  G
Joined: 19 Oct 2018
Posts: 261
Location: India
It is given that x^2 + y^2 = z + 1, y^2 + z^2 = x + 1 and z^2 +x^2=y+1  [#permalink]

### Show Tags

1 00:00

Difficulty:   95% (hard)

Question Stats: 28% (02:52) correct 72% (02:25) wrong based on 29 sessions

### HideShow timer Statistics

It is given that $$x^2+y^2=z+1$$, $$y^2+z^2=x+1$$ and $$z^2+x^2=y+1$$. Find the value of x*y*z?

A. 1
B. -1/8
C. 1 or 1/8
D. 1 or -(1/8)
E. 1/3

Originally posted by nick1816 on 21 Apr 2019, 22:52.
Last edited by Bunuel on 22 Apr 2019, 00:38, edited 1 time in total.
Renamed the topic.
Manager  B
Joined: 05 Oct 2017
Posts: 64
Re: It is given that x^2 + y^2 = z + 1, y^2 + z^2 = x + 1 and z^2 +x^2=y+1  [#permalink]

### Show Tags

This seems like a formula based question. Could someone post a solution on how to approach it?
_________________
Press Kudos if you liked my response!!!
Senior Manager  G
Joined: 19 Oct 2018
Posts: 261
Location: India
Re: It is given that x^2 + y^2 = z + 1, y^2 +z^2 = x + 1  [#permalink]

### Show Tags

3
$$x^2 + y^2$$ = z + 1 and $$y^2 + z^2$$ = x + 1
subtracting these equations, we get $$x^2 - z^2$$=z-x
or (x+z )(x-z) + (x-z) =0
or (x-z) (x+z+1 ) =0
Hence either x=z or x+z=-1
Similarly you can prove either y=z or y+z=-1
Either way we will get x=y=z

Now we have $$x^2 + y^$$2 = z + 1 or $$x^2 + x^2$$ = x + 1
2$$x^2 - x$$ - 1=0
x= 1 or -(1/2)

Whenever you see these symmetrical equations in a particular question, mostly you have to either subtract them or add them. Then factorize the resulting equation.
neha283 wrote:
This seems like a formula based question. Could someone post a solution on how to approach it?
Manager  B
Joined: 27 Oct 2017
Posts: 61
Re: It is given that x^2 + y^2 = z + 1, y^2 + z^2 = x + 1 and z^2 +x^2=y+1  [#permalink]

### Show Tags

Can someone please help with this? Re: It is given that x^2 + y^2 = z + 1, y^2 + z^2 = x + 1 and z^2 +x^2=y+1   [#permalink] 23 Apr 2019, 08:13
Display posts from previous: Sort by

# It is given that x^2 + y^2 = z + 1, y^2 + z^2 = x + 1 and z^2 +x^2=y+1

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics 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®.

#### MBA Resources  