Let x, y and z be distinct integers, that are odd and positive. Which one of the following statements cannot be true?
Explanation:
Option 1: Product of odd numbers is always odd.
∴ x × y × z × z is always odd
Option 2: (x − y) is even.
∴ (x − y)2z is even.
Option 3: (x + y) is always even.
∴ (x + y − z)2(x + y) is even.
Option 4: (x − y) is even, (y + z) is even, and (x + y − z) is odd.
∴ (x − y) (y + z) (x + y − z) is even.
Hence, option (d).
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