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

It is currently 23 Mar 2019, 06:06

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.

Close

Request Expert Reply

Confirm Cancel

If x^3(x^2+y^2)=z^2, is xyz=0?

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

Hide Tags

 
GMATH Teacher
User avatar
G
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 910
If x^3(x^2+y^2)=z^2, is xyz=0?  [#permalink]

Show Tags

New post 25 Feb 2019, 16:03
00:00
A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

36% (02:29) correct 64% (01:20) wrong based on 14 sessions

HideShow timer Statistics

GMATH practice exercise (Quant Class 14)

If \(\,{x^3}\left( {{x^2} + {y^2}} \right) = {z^2}\,\), is \(\,xyz = 0\,\) ?

\(\left( 1 \right)\,\,{y^3}\left( {{y^2} + {z^2}} \right) = {x^2}\,\,\)

\(\left( 2 \right)\,\,{z^3}\left( {{z^2} + {x^2}} \right) = {y^2}\)

_________________

Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net

GMATH Teacher
User avatar
G
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 910
If x^3(x^2+y^2)=z^2, is xyz=0?  [#permalink]

Show Tags

New post 25 Feb 2019, 17:51
fskilnik wrote:
GMATH practice exercise (Quant Class 14)

If \(\,{x^3}\left( {{x^2} + {y^2}} \right) = {z^2}\,\), is \(\,xyz = 0\,\) ?

\(\left( 1 \right)\,\,{y^3}\left( {{y^2} + {z^2}} \right) = {x^2}\,\,\)

\(\left( 2 \right)\,\,{z^3}\left( {{z^2} + {x^2}} \right) = {y^2}\)

\({x^3}\left( {{x^2} + {y^2}} \right) = {z^2}\,\,\,\,\,\left( * \right)\)

\(xyz\,\,\mathop = \limits^? \,\,0\)


\(\left( {1 + 2} \right)\,\,\left\{ \matrix{
\,{y^3}\left( {{y^2} + {z^2}} \right) = {x^2}\,\,\left( * \right) \hfill \cr
\,{z^3}\left( {{z^2} + {x^2}} \right) = {y^2}\,\,\left( * \right) \hfill \cr} \right.\,\,\)

\({\rm{Take}}\,\,\,\left\{ \matrix{
\,\left( {x;y;z} \right) = \left( {0;0;0} \right)\,\,\,\, \Rightarrow \,\,\,\,\left\langle {{\rm{YES}}} \right\rangle \hfill \cr
\,\left( {**} \right)\,\,\,\left( {x;y;z} \right) = \left( {{1 \over {\root 3 \of 2 }};{1 \over {\root 3 \of 2 }};{1 \over {\root 3 \of 2 }}} \right)\,\,\,\, \Rightarrow \,\,\,\,\left\langle {{\rm{NO}}} \right\rangle \hfill \cr} \right.\)

\(\left( {**} \right)\,\,{\rm{Explore}}\,\,{\rm{symmetries(!),}}\,\,\underline {{\rm{trying}}} \,\,\,\left( {x,y,z} \right) = \left( {k,k,k} \right)\,\,\,\,\,\,\mathop \Rightarrow \limits^{{\rm{any}}\,\,\left( * \right)} \,\,\,\,{k^3}\left( {2{k^2}} \right) = {k^2}\,\,\,\,\mathop \Rightarrow \limits^{k\, \ne \,0} \,\,\,2{k^3} = 1\,\,\,\,\, \Rightarrow \,\,\,\,k = {1 \over {\root 3 \of 2 }}\,\,\,\,{\rm{viable}}!\)


The correct answer is (E).


We follow the notations and rationale taught in the GMATH method.

Regards,
Fabio.
_________________

Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net

GMAT Club Bot
If x^3(x^2+y^2)=z^2, is xyz=0?   [#permalink] 25 Feb 2019, 17:51
Display posts from previous: Sort by

If x^3(x^2+y^2)=z^2, is xyz=0?

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


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

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®.