DS Question - 16

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

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

b) x + y > z

Answer - E

(1) x^2 + y^2 > z^2, when squared, gives the stated equation.

From this we cannot conclude definitively whether x^4 + y^4 > z^4 because the equation contains (2x^2 * y^2).

If this is removed, then x^4 + y^4 may or may not be > z^4.

Thus insufficient..

e.g - 2+3+4 > 5 --- if we remove 1 number from the left hand side of the inequality then the inequality may or may not hold true..

OR

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

Let x = {(2) ^ 1/2}, y = {(3) ^ 1/2}, z = {(4) ^1/2}

Hence 2+3>4 but at the same time 4+9<16

Let x = 2, y= 4, z=3
4+16>9
And 16 + 256 > 81

Thus (1) is insufficient.

Statement (2) ---- x+y> z
Let x=2, y=3, z=6
Hence 2+3<6

Now let x=2, y=6, z=3
Then 2+6>3

Both 1 and 2 together:insufficient

Hence answer E.