Inequality Problem
This topic has expert replies
Source: Beat The GMAT — Data Sufficiency |
answer is e. There's a nice solution posted at: https://www.manhattangmat.com/forums/is- ... t4655.html
-
MAAJ
- Master | Next Rank: 500 Posts
- Posts: 243
- Joined: Sun Jul 12, 2009 7:12 am
- Location: Dominican Republic
- Thanked: 31 times
- Followed by:2 members
- GMAT Score:480
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
"There's a difference between interest and commitment. When you're interested in doing something, you do it only when circumstance permit. When you're committed to something, you accept no excuses, only results."
