CAT 1998 — DILR Question 44
Direction: Answer the question based on the following information.
The following operations are defined for real numbers.
a # b = a + b, if a and b both are positive else a # b = 1
a ∇ b = (a × b)a + b if a × b is positive else a ∇ b = 1.
then which of the following must be true?
Answer & solution
- A
X = 2, Y = 1
X > 0, Y < 0
- C
X, Y both positive
- D
X, Y both negative
The best possible way to solve this is to check each of the given answer choices. In options (a), (c) and (d), either both X and Y are positive or both X and Y are negative.
Since we have (–Y) in the numerator of our expression and (–X) in the denominator, X and Y will never be both positive and neither will XY be positive.
Hence, both the numerator and the denominator of our expression will be 1 and the value will always be 1.
Hence, the only possible answer choice is (b).