GMAT prep question
This topic has expert replies
-
- Master | Next Rank: 500 Posts
- Posts: 340
- Joined: Thu Jun 12, 2008 8:09 am
- Location: India
- Thanked: 6 times
I could not think of any algebraic solution for this one. Plugged in some numbers. Hope I got it correct. If not then please help.
Stmt1: x^2 + y^2 > z^2
Stmt2: x + y > z
Let us look at Stmt2 first.
x = 3, y = 4, z = 6
x + y = 7 which is greater than z = 6 but x^4 + y^4 = 81 + 256 = 337
and z^4 = 1296. So the answer to the question is No.
But we could have x = 3, y = 4 and z = 1. In this case the asnwer would be Yes.
So Stmt 2 is insufficient. Left with A, C and E.
For plugging in the values into stmt1, we could use the sqrt of the values (as x, y, and z need not be integers) used for stmt 2 to arrive at the same conclusion that its insufficient.
Combining the 2 also we cannot conclusively say whether x^4 + y^4 > z^4.
Hence E.
Please comment and correct me if I am wrong.
Stmt1: x^2 + y^2 > z^2
Stmt2: x + y > z
Let us look at Stmt2 first.
x = 3, y = 4, z = 6
x + y = 7 which is greater than z = 6 but x^4 + y^4 = 81 + 256 = 337
and z^4 = 1296. So the answer to the question is No.
But we could have x = 3, y = 4 and z = 1. In this case the asnwer would be Yes.
So Stmt 2 is insufficient. Left with A, C and E.
For plugging in the values into stmt1, we could use the sqrt of the values (as x, y, and z need not be integers) used for stmt 2 to arrive at the same conclusion that its insufficient.
Combining the 2 also we cannot conclusively say whether x^4 + y^4 > z^4.
Hence E.
Please comment and correct me if I am wrong.
-
- Legendary Member
- Posts: 1153
- Joined: Wed Jun 20, 2007 6:21 am
- Thanked: 146 times
- Followed by:2 members
I think the answer should be E.
question stem: x^4 + y^4 > z^4 ?
Statement I
x^2 + y^2 > z^2
if you use integers x^4 + y^4 > z^4 yes.
if you use fractions x^4 + y^4 > z^4 no.
Rule: when fractions are squared or increased with positive exponents the value of fraction decreases.
Insufficient.
Statement II
x+y>z
if you use integers x^4 + y^4 > z^4 yes.
if you use fractions x^4 + y^4 > z^4 no.
same reasoning as above.
Insufficient.
Combining I & II
if you use integers x^4 + y^4 > z^4 yes.
if you use fractions x^4 + y^4 > z^4 no.
x=0.5, y=0.7, z=0.8
x+y>z
0.5+0.7>0.8
1.2>0.8
x+y>z
x^2 + y^2 > z^2
0.25 + 0.49 > 0.64
0.74>0.64
x^2 + y^2 > z^2
x^4 + y^4 > z^4
0.0625 + 0.2401 < 0.4096
0.3026 < 0.4096
Hence E is the answer.
question stem: x^4 + y^4 > z^4 ?
Statement I
x^2 + y^2 > z^2
if you use integers x^4 + y^4 > z^4 yes.
if you use fractions x^4 + y^4 > z^4 no.
Rule: when fractions are squared or increased with positive exponents the value of fraction decreases.
Insufficient.
Statement II
x+y>z
if you use integers x^4 + y^4 > z^4 yes.
if you use fractions x^4 + y^4 > z^4 no.
same reasoning as above.
Insufficient.
Combining I & II
if you use integers x^4 + y^4 > z^4 yes.
if you use fractions x^4 + y^4 > z^4 no.
x=0.5, y=0.7, z=0.8
x+y>z
0.5+0.7>0.8
1.2>0.8
x+y>z
x^2 + y^2 > z^2
0.25 + 0.49 > 0.64
0.74>0.64
x^2 + y^2 > z^2
x^4 + y^4 > z^4
0.0625 + 0.2401 < 0.4096
0.3026 < 0.4096
Hence E is the answer.