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

Case I

a=+ve, say 100

a - b = 100 – (-1) = 101

a + b = 100 + (-1) = 99

a-b > a+b

Case II

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

and

for a=+ve; ab = -ve * -ve = +ve

So, we can't conclusively say ab < 0. Statement III is ruled out.

Ans: B

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~fluke

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