Quant Fundamentals: Signs and the Number Line
Which of the following is NOT always true?
Eliminate this answer choice because the square of any number is always non-negative. It's either positive or zero (if $$x=0$$).
Eliminate this answer choice because a positive times 0 is 0 (non-negative), 0 times 0 is 0 (non-negative), and a positive times a positive is positive (non-negative).
Keep in mind that we're looking for an answer choice that is NOT always true. According to answer choice C, The sum of two distinct non-negative numbers is positive. In other words, the sum of any two different numbers which are either positive or zero is always positive.
When adding two positive numbers, the result is always positive. Even if one of the two numbers is zero, the result will still be positive, since adding a positive number and 0 always results in a positive number. Also, keep in mind that the two numbers need to be different, so they can't both be 0. Seeing as the statement is always true, this answer choice is incorrect.
This is the correct answer because a negative times 0 is 0. For example: $$-3 \times 0 = 0$$. Therefore, the product of two distinct non-positive numbers is NOT always positive.
Eliminate this answer choice because a negative plus a negative is negative and a negative plus 0 is negative. For example:
> $$(-1) + (-4) = -5$$
> $$(-3) + 0 = -3$$
The sum of two *distinct* non-positive numbers is negative.
The product of two *distinct* non-positive numbers is positive.
The sum of two *distinct* non-negative numbers is positive.
The product of two non-negative numbers is non-negative.
$$x^2$$ is non-negative for any value of $$x$$.