Question

If a, b, c are three consecutive natural numbers, then the expression (a + b - c) (a + c - b) (b + c - a) is:

• A. positive
• B. negative
• C. non - positive
• D. non - negative

Answer 1

The correct option is D

non - negative

Take any three consecutive natural numbers as: n-1, n, n + 1
Now add any two and subtract third from the sum.
n - 1 + n - (n + 1) = n - 2; n + n + 1 - (n - 1) = n + 2; n - 1 + n + 1 - n = n
So you will get either n - 2 or n + 2 or n. As you are considering natural numbers, smallest natural number is 1 $⟹$ n -1 = 1 or n = 2. (So that n - 1 is a natural number)
So n - 2, n, n + 2 all three will be non - negative. So the given expression is also non - negative.