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13 Aug 2006, 19:15
Kudos
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N
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
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14 Aug 2006, 00:43
Kudos
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I think the answer should be A.
Let us take statement (2) first, x + y > z
Case I: if x = 3, y=-2, z=-10, then the statement is satisfied. But when we calculate x^4 + y^4 and z^4, the signs are removed and only the magnitudes remain. In this case, z^4 will be the greatest.
Case II: if x=3, y=2, z=4, x + y >z is true. But 3^4 + 2^4 (97) is not > 4^4 (256).
CASE III: if x=1, y=3,z=2, then 1 + 3 > 2 and 1^4 + 3^4 (82) > 2^4 (16).
As can be seen by the above 3 examples, we cannot say based on x + y >z if x^4 + y^4 is greater than z^4 or not.
Statement (1) says x^2 + y^2 > z^2.
in this case, the statement is dealing with squares. Therefore signs of x, y and z do not come into play. So we are dealing only with magnitude. Hence, the problem we were facing with case I above is eliminated.
Also, this statement ensures that z MUST lie between x and y. You can verify this for any value of x, y and z.
Since z lies between x and y, x^4 + y^4 will always be > z^4.
Hence IMO answer is (A).
Let us take statement (2) first, x + y > z
Case I: if x = 3, y=-2, z=-10, then the statement is satisfied. But when we calculate x^4 + y^4 and z^4, the signs are removed and only the magnitudes remain. In this case, z^4 will be the greatest.
Case II: if x=3, y=2, z=4, x + y >z is true. But 3^4 + 2^4 (97) is not > 4^4 (256).
CASE III: if x=1, y=3,z=2, then 1 + 3 > 2 and 1^4 + 3^4 (82) > 2^4 (16).
As can be seen by the above 3 examples, we cannot say based on x + y >z if x^4 + y^4 is greater than z^4 or not.
Statement (1) says x^2 + y^2 > z^2.
in this case, the statement is dealing with squares. Therefore signs of x, y and z do not come into play. So we are dealing only with magnitude. Hence, the problem we were facing with case I above is eliminated.
Also, this statement ensures that z MUST lie between x and y. You can verify this for any value of x, y and z.
Since z lies between x and y, x^4 + y^4 will always be > z^4.
Hence IMO answer is (A).
