Is x^4 + y^4 > z^4 ?

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nikhilkatira: Master | Next Rank: 500 Posts; Posts: 318; Joined: Mon Jul 13, 2009 3:55 am; Thanked: 12 times

by nikhilkatira » Tue Jun 29, 2010 10:30 pm

Is x^4 + y^4 > z^4 ?

(1) x^2 + y^2 > z^2

(2) x+y > z

Please answer with explanation and time consumed.

Best,
Nikhil H. Katira

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Source: Beat The GMAT — Data Sufficiency | Tue Jun 29, 2010 10:30 pm

albatross86: Master | Next Rank: 500 Posts; Posts: 392; Joined: Sun May 16, 2010 2:42 amFollowed by: 10 members; Location: Bangalore, India; Thanked: 116 times; GMAT Score:770

by albatross86 » Tue Jun 29, 2010 11:12 pm

Hey Nikhil, this is a GMATPrep problem so I suggest that you post the source next time, since some people do not want to solve GMATPrep problems before they try them on the CAT. Thanks

Coming to your problem, I used about 2 minutes and arrived at the WRONG Answer, the first time I did this. It is one of the toughest DS questions I know of.

I cannot explain this better than a certain Ron Purewal, who many BTG members swear by. Here is a link to an EXCELLENT explanation by him, and in fact you will get a LOT of takeaways.

https://www.beatthegmat.com/post98539.html#98539

~Abhay

Believe those who are seeking the truth. Doubt those who find it. -- Andre Gide

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kvcpk: Legendary Member; Posts: 1893; Joined: Sun May 30, 2010 11:48 pmFollowed by: 7 members; Thanked: 215 times

by kvcpk » Tue Jun 29, 2010 11:30 pm

Good question to clarify my doubt.

Experts - please tell me if I can assume x,y to be complex numbers, since there is nothing specified about them. Or, In GMAT, I am not supposed to do that?

in this case, I was tempted to plugin, root(-10) for z^2 ans 1,1 for x^2 and Y^2 respectively.

This will serve the purpose. But, want to crosscheck on my method.

Praveen

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albatross86: Master | Next Rank: 500 Posts; Posts: 392; Joined: Sun May 16, 2010 2:42 amFollowed by: 10 members; Location: Bangalore, India; Thanked: 116 times; GMAT Score:770

by albatross86 » Tue Jun 29, 2010 11:35 pm

kvcpk wrote:Good question to clarify my doubt.

Experts - please tell me if I can assume x,y to be complex numbers, since there is nothing specified about them. Or, In GMAT, I am not supposed to do that?

in this case, I was tempted to plugin, root(-10) for z^2 ans 1,1 for x^2 and Y^2 respectively.

This will serve the purpose. But, want to crosscheck on my method.

Praveen

Hey Praveen, I'm no expert, but I guarantee you that complex numbers are out of scope of the GMAT.

If you notice right in the beginning of the Quantitative section, you will see the following disclaimer:

Numbers: All numbers used are real numbers

Please visit this thread for an excellent takeaway for this problem: https://www.manhattangmat.com/forums/is- ... t4655.html

~Abhay

Believe those who are seeking the truth. Doubt those who find it. -- Andre Gide

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kvcpk: Legendary Member; Posts: 1893; Joined: Sun May 30, 2010 11:48 pmFollowed by: 7 members; Thanked: 215 times

by kvcpk » Tue Jun 29, 2010 11:46 pm

Thanks Abhay for the confirmation!!

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nikhilkatira: Master | Next Rank: 500 Posts; Posts: 318; Joined: Mon Jul 13, 2009 3:55 am; Thanked: 12 times

by nikhilkatira » Wed Jun 30, 2010 12:43 am

albatross86 wrote:Hey Nikhil, this is a GMATPrep problem so I suggest that you post the source next time, since some people do not want to solve GMATPrep problems before they try them on the CAT. Thanks

Coming to your problem, I used about 2 minutes and arrived at the WRONG Answer, the first time I did this. It is one of the toughest DS questions I know of.

I cannot explain this better than a certain Ron Purewal, who many BTG members swear by. Here is a link to an EXCELLENT explanation by him, and in fact you will get a LOT of takeaways.

https://www.beatthegmat.com/post98539.html#98539

Thanks for the link..

I will surely write the source next time..

Btw is this question included in 198 question bank ?

Best,
Nikhil H. Katira

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albatross86: Master | Next Rank: 500 Posts; Posts: 392; Joined: Sun May 16, 2010 2:42 amFollowed by: 10 members; Location: Bangalore, India; Thanked: 116 times; GMAT Score:770

by albatross86 » Wed Jun 30, 2010 12:46 am

Funnily enough it doesn't seem to be there. Maybe the person who compiled the list missed it or found it easy,

~Abhay

Believe those who are seeking the truth. Doubt those who find it. -- Andre Gide

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kvcpk: Legendary Member; Posts: 1893; Joined: Sun May 30, 2010 11:48 pmFollowed by: 7 members; Thanked: 215 times

by kvcpk » Wed Jun 30, 2010 12:55 am

What is the 198 question bank? Can you please share it.

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albatross86: Master | Next Rank: 500 Posts; Posts: 392; Joined: Sun May 16, 2010 2:42 amFollowed by: 10 members; Location: Bangalore, India; Thanked: 116 times; GMAT Score:770

by albatross86 » Wed Jun 30, 2010 1:00 am

kvcpk wrote:What is the 198 question bank? Can you please share it.

Sure, BTG member Zuleron compiled it - https://www.beatthegmat.com/198-level-70 ... 43783.html

~Abhay

Believe those who are seeking the truth. Doubt those who find it. -- Andre Gide

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kvcpk: Legendary Member; Posts: 1893; Joined: Sun May 30, 2010 11:48 pmFollowed by: 7 members; Thanked: 215 times

by kvcpk » Wed Jun 30, 2010 2:49 am

albatross86 wrote:
kvcpk wrote:What is the 198 question bank? Can you please share it.
Sure, BTG member Zuleron compiled it - https://www.beatthegmat.com/198-level-70 ... 43783.html

Thanks Abhay!!

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Rich@VeritasPrep: GMAT Instructor; Posts: 147; Joined: Tue Aug 25, 2009 7:57 pmFollowed by: 17 members; Location: New York City; Thanked: 76 times; GMAT Score:770

by Rich@VeritasPrep » Wed Jun 30, 2010 3:05 am

This is indeed a tough TOUGH DS problem, and testing numbers is definitely a great way to go about it, considering you have an average of only 2 minutes a question on the Quant section.

I fooled around with the question a little bit more, though, and I think there's an interesting way you can arrive very quickly at answer E (although this would certainly be difficult to do in a time-pressure situation). Just for fun...

Is x^4 + y^4 > z^4 ?

(1) x^2 + y^2 > z^2

(2) x+y > z

This is a Yes/No DS question, meaning that we can if we can answer both Yes and No to the prompt with the information given, then that information is insufficient. One thing that's easy to forget is that showing x^4 + y^4 < z^4 is not the only way to answer No to the prompt. The answer would also be No if x^4 + y^4 were EQUAL to z^4.

Notice that this (along with Statement 1) bares an uncanny resemblance to the Pythagorean Theorem. That got me thinking about using Pythagorean triples.

There are no restrictions on x, y, or z, so use x = sqrt(3), y = sqrt(4), z = sqrt(5). These are values that satisfy both Statements (1) and (2), and thus they are legal.

In that case, x^4 + y^4 = z^4, and we would get a No.

Now, all we have to do is find a Yes, and that is very easy to do:

Choose ridiculously large values of x and y and a very small value for z. x = 100, y = 100, and z = 1 will work just fine.
Those values satisfy both Statements (1) and (2) and answer Yes to the prompt.

We are done! Answer: E

Rich Zwelling
GMAT Instructor, Veritas Prep

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albatross86: Master | Next Rank: 500 Posts; Posts: 392; Joined: Sun May 16, 2010 2:42 amFollowed by: 10 members; Location: Bangalore, India; Thanked: 116 times; GMAT Score:770

by albatross86 » Wed Jun 30, 2010 5:16 am

Nice one Rich - that is actually a great way to look at it - with the Pythagorean triangle in mind.

Thanks!

~Abhay

Believe those who are seeking the truth. Doubt those who find it. -- Andre Gide

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sumanr84: Legendary Member; Posts: 758; Joined: Sat Aug 29, 2009 9:32 pmFollowed by: 2 members; Location: Bangalore,India; Thanked: 67 times

by sumanr84 » Wed Jun 30, 2010 10:40 am

nikhilkatira wrote:Is x^4 + y^4 > z^4 ?

(1) x^2 + y^2 > z^2

(2) x+y > z

Please answer with explanation and time consumed.

I think these are the best questions when you should move on and buy yourself few extra mins (at least for me) :mrgreen:

I am on a break !!

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