Q: If a – b > a + b, where a and b are integers, which of the following must be true?
I. a < 0
II. b < 0
III. ab < 0
Through inequality; I just derived that b is -ve
a – b > a + b
-b > b --> subtracting 'a' from both sides
-2b > 0 --> subtracting 'b' from both sides
-b > 0 --> dividing both sides by 2
b < 0 --> multiplying -ve sign on both sides
The rest two; I ruled out using numbers
Let b, as we know is -ve, to be equal to -1
a=+ve, say 100
a - b = 100 – (-1) = 101
a + b = 100 + (-1) = 99
a-b > a+b
a=-ve, say -100
a - b = -100 – (-1) = -100 + 1 = -99
a + b = -100 + (-1) = -100 - 1 = -101
So, a - b > a + b
Thus, a - b > a + b is true for both +ve and -ve 'a'
We just proved that a-b>a+b is true for both +ve and -ve values of a.
We can't conclusively say that a < 0. Statement I is ruled out.
for a=+ve; ab = +ve * -ve = -ve
for a=+ve; ab = -ve * -ve = +ve
So, we can't conclusively say ab < 0. Statement III is ruled out.
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