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

 It is currently 18 Sep 2018, 20:25

### 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

# Is x^4 + y^4 > z^4? 1) x^2 + y^2 > z^2 2) x + y > z

Author Message
TAGS:

### Hide Tags

Manager
Joined: 26 Mar 2007
Posts: 71
Schools: Thunderbird '15
Is x^4 + y^4 > z^4? 1) x^2 + y^2 > z^2 2) x + y > z  [#permalink]

### Show Tags

24 Jul 2011, 10:25
2
00:00

Difficulty:

75% (hard)

Question Stats:

49% (00:56) correct 51% (01:22) wrong based on 67 sessions

### HideShow timer Statistics

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

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

OPEN DISCUSSION OF THIS QUESTION IS HERE: http://gmatclub.com/forum/is-x-4-y-4-z-101358.html
Manager
Joined: 23 Jan 2011
Posts: 124
Re: Is x^4 + y^4 > z^4? 1) x^2 + y^2 > z^2 2) x + y > z  [#permalink]

### Show Tags

24 Jul 2011, 10:34
kannn wrote:
Is x^4 + y^4 > z^4?

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

OA later.
Source GMATPrep

Should be E.

Square first statment and you get x^4+y^4+2x^2y^2>z^4. As 2x^2y^2 is missing, th quality may or may not hold.

Statement 2 is similar, so wont answer either.

gmatprep-ds-is-x-4-y-4-z-66899.html
Manager
Joined: 11 Jul 2009
Posts: 132
WE: Design (Computer Software)
Re: Is x^4 + y^4 > z^4? 1) x^2 + y^2 > z^2 2) x + y > z  [#permalink]

### Show Tags

26 Jul 2011, 08:59
E both are not sufficient
_________________

Kaustubh

Math Expert
Joined: 02 Sep 2009
Posts: 49208
Re: Is x^4 + y^4 > z^4? 1) x^2 + y^2 > z^2 2) x + y > z  [#permalink]

### Show Tags

27 Nov 2017, 04:09
Is $$x^4+y^4>z^4$$?

The best way to deal with this problem is plugging numbers. Remember on DS questions when plugging numbers, goal is to prove that the statement is not sufficient. So we should try to get a YES answer with one chosen number(s) and a NO with another.

(1) $$x^2+y^2>z^2$$
It's clear that we get YES answer very easily with big x and y (say 10 and 10), and small z (say 0).

For NO answer let's try numbers from Pythagorean triples:
$$x^2=3$$, $$y^2=4$$ and $$z^2=5$$ ($$x^2+y^2=7>5=z^2$$) --> $$x^4+y^4=9+16=25=z^4$$, so we have answer NO ($$x^4+y^4$$ is NOT more than $$z^4$$, it's equal to it).

Not sufficient.

(2) $$x+y>z$$. This one is even easier: again we can get YES answer with big x and y, and small z.

As for NO try to make z some big enough negative number: so if $$x=y=1$$ and $$z=-5$$, then $$x^4+y^4=1+1=2<25=z^4$$.

Not sufficient.

(1)+(2) As we concluded YES answer is easily achievable. For NO try the case of $$x^2=3$$, $$y^2=4$$ and $$z^2=5$$ again: $$x+y=\sqrt{3}+\sqrt{4}>\sqrt{5}$$ ($$\sqrt{3}+2$$ is more than 3 and $$\sqrt{5}$$ is less than 3), so statement (2) is satisfied, we know that statement (1) is also satisfied ($$x^2+y^2=7>5=z^2$$) and $$x^4+y^4=9+16=25=z^4$$. Not sufficient.

OPEN DISCUSSION OF THIS QUESTION IS HERE: http://gmatclub.com/forum/is-x-4-y-4-z-101358.html
_________________
Re: Is x^4 + y^4 > z^4? 1) x^2 + y^2 > z^2 2) x + y > z &nbs [#permalink] 27 Nov 2017, 04:09
Display posts from previous: Sort by

# Events & Promotions

 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®.