Is x^4 + y^4 > z^4?
(1) x^2 + y^2 > z^2
(2) x + y > z
Can anyone please provide an explanation? Thanks!!
(1) x^2 + y^2 > z^2
(2) x + y > z
Can anyone please provide an explanation? Thanks!!
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Inequality Problem
Source: Beat The GMAT — Data Sufficiency |
answer is e. There's a nice solution posted at: https://www.manhattangmat.com/forums/is- ... t4655.html
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I believe that this exercise is more about picking numbers... (In case you don't trust your logic...)
IMO [spoiler](E)[/spoiler]
x^4 + y^4 > z^4 ?
1) x^2 + y^2 > z^2
This is similar to the Pythagorean theorem so it's easier to manipulate if you know the 3:4:5.
3^2 + 4.01^2 > 5^2 -> change power to 4 and we see that z would be greater
9999^2 + 9999^2 > 1^2 -> change power to 4 and x + y would be greater
So statement 1 is Insufficient
2) x + y > z
If x=99999, y=99999, z=1. Then x^4 + y^4 > z^4
If x=3, y=4, z=5. Then x^4 + y^4 < z^4
So statement 2 is insufficient
Combining 1 and 2
x^2 + y^2 > z^2
x + y > z
If x=3, y=4.01, z=5 THEN x^2+y^2 > z^2 BUT x^4 + y^4 < z^4
If x=99999, y=99999, z=1 THEN x^2+y^2 > z^2 AND x^4 + y^4 > z^4
So combined they are still insufficient
IMO [spoiler](E)[/spoiler]
x^4 + y^4 > z^4 ?
1) x^2 + y^2 > z^2
This is similar to the Pythagorean theorem so it's easier to manipulate if you know the 3:4:5.
3^2 + 4.01^2 > 5^2 -> change power to 4 and we see that z would be greater
9999^2 + 9999^2 > 1^2 -> change power to 4 and x + y would be greater
So statement 1 is Insufficient
2) x + y > z
If x=99999, y=99999, z=1. Then x^4 + y^4 > z^4
If x=3, y=4, z=5. Then x^4 + y^4 < z^4
So statement 2 is insufficient
Combining 1 and 2
x^2 + y^2 > z^2
x + y > z
If x=3, y=4.01, z=5 THEN x^2+y^2 > z^2 BUT x^4 + y^4 < z^4
If x=99999, y=99999, z=1 THEN x^2+y^2 > z^2 AND x^4 + y^4 > z^4
So combined they are still insufficient
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