CAT 2000 — QA Question 10
Even OddEasy
Let x, y and z be distinct integers, that are odd and positive. Which one of the following statements cannot be true?
Answer & solution
- A
xyz2 is odd.
- B
(x − y)2 z is even.
- C
(x + y − z)2 (x + y) is even.
(x − y) (y + z) (x + y − z) is odd.
Solution
Option 1:
Product of odd numbers is always odd.
∴ x × y × z × z is always odd
Option 2:
(x − y) is even.
∴ (x − y)2 z 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).