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CAT 2003 Slot 1 — QA Question 47

Inequality Maximization / MinimizationEasy
Passage / Data

Each question is followed by two statements, A and B. Answer each question using the following instructions

Choose 1 if the question can be answered by using one of the statements alone but not by using the other statement alone.
Choose 2 if the question can be answered by using either of the statements alone.
Choose 3 if the question can be answered by using both statements together but not by either statement alone.
Choose 4 if the question cannot be answered on the basis of the two statements.

If x, y, z are distinct positive real numbers, then x2(y+z)+y2(x+z)+z2(x+y)xyz would be

Answer & solution

  • A

    greater than 4

  • B

    greater than 5

  • greater than 6

  • D

    None of these

Solution

The given expression may be represented as

xy+xz+yx+yz+zx+zy

We know that, A.M. ≥ G.M.

∴(xy+xz+yx+yz+zx+zy)6≥xy×xz×yx×yz×zx×zy6

xy+xz+yx+yz+zx+zy≥6

∴ The given expression will have a minimum value of 6.

But x, y and z are distinct, so the value will always be greater than 6.

Hence, option (c).

CAT 2003 Slot 1 QA Q47: If x, y, z are distinct positive real numbers, then x 2 ( y + z ) + y 2 ( x + z ) + z 2 ( x + y ) x y z would — Solution | TheCATExam