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

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Manager
Joined: 01 Apr 2006
Posts: 180
Is x^4 + y^4 > z^4? 1) x^2 + y^2 >z^2 2) x +y >z [#permalink]

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02 Sep 2006, 18:46
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Is x^4 + y^4 > z^4?

1) x^2 + y^2 >z^2
2) x +y >z
Manager
Joined: 30 Jan 2006
Posts: 62

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02 Sep 2006, 19:57
It is A

S1) x^2+y^2>z^2

if x =1 and y =2 and z =1

or any fraction also x = 0.5 y = 0.2 z = 0.4

also which satisifies it.

For S2)if x = 1 and y =2 and z = 2 which satisfies x^4+y^4>z^4

if x = 1 y = 1 and z = -4

which doesn't satisfy the equation above.

So A.
Manager
Joined: 01 Apr 2006
Posts: 180

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02 Sep 2006, 20:30
smily_buddy,

For statement1, what if x=1/2; y=1/2; z=2/3 --> does not satify the original inequality.

jjhko
Senior Manager
Joined: 14 Jul 2005
Posts: 402
Re: DS: x^4+y^4 > z^4? [#permalink]

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02 Sep 2006, 22:53
It is E

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

1) x^2 + y^2 >z^2
If x^2=2, y^2=3 and z=2
Then x^4 + y^4 > z^4 is FALSE
If x,y,z = 1
Then x^4 + y^4 > z^4 is TRUE
INSUFF

2) x +y >z

e.g. 2 + 3 > 5
But x^4 + y^4 > z^4 FALSE
when 1 + 1 > 1
Then x^4 + y^4 > z^4 is TRUE
INSUFF

Combined is also INSUFF as shown above
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Joined: 28 Dec 2004
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Location: New York City
Schools: Wharton'11 HBS'12

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03 Sep 2006, 10:01
this should be A...

stem X^4+y^4>z^4?

st1) x^2+y^2>z^2

lets say if x and y are integers...x=1, y=2, then 1+4=5; we are told is greater than z, z^2 can be 4 or 3...

if X and y were fractions, we are told that sume X^2+y^2 is greater than z^2..

if z^2 is a fraction or not, it is still less than x^2 + y^2...same should hold for z^4+y^4...
Manager
Joined: 01 Apr 2006
Posts: 180

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03 Sep 2006, 10:37
OA is E.

I'm not sure if there is a sure way of working out this problem... the only way that could was to try out various sample values... which has the down side of being time consuming.

jjhko
Manager
Joined: 04 Feb 2004
Posts: 70
Location: India

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04 Sep 2006, 21:53
Problems like these can ruin my PS score ...
Senior Manager
Joined: 14 Jul 2006
Posts: 326

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06 Sep 2006, 00:55
ok here goes my explantion

x^2 + y^2 > z^2

since left side is positive and right side is postive
the inequality can be squared
therfore,x^4 + y^4 + 2x^4 y^4 > z^4

therfore not necessary that x^4 + y^4 > z^4

Also x+y > z
x+y and z might be negative in which case the fourth power would not hold.combining both also nnothing can be said of x and y
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06 Sep 2006, 00:55
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