Problem Solving

swerve wrote: ↑

Wed Feb 24, 2021 4:40 pm

BTGmoderatorDC wrote: ↑

Tue Feb 23, 2021 6:41 pm

If x < 0, which of the following represents a positive number?

A) x/|x|
B) |x|/x
C) x|x|
D) -x|x|
E) x|-x|


OA D

As every option has \(|x|,\) which is always positive or non negative, and \(x\) is negative (Given \(x < 0\)), only answer choice with \(-x\) can yield the positive result \((-x\cdot-x).\)

Only option D has "\(- x\)".

Solution:

Let’s say x = -2 and analyze each answer choice:

A) -2/|2| = -2/2 = -1

B) |-2|/-2 = 2/-2 = -1

C) -2|-2| = -2 x 2 = -4

D) -(-2)|-2| = 2 x 2 = 4

Alternate Solution:

We know that |x| is positive. Therefore, we can ignore the |x| part of the answer choices (because that part is already positive). We know that x itself is negative. Scanning the answer choices, we see that the only choice that negates the already negative value of x is choice D, which makes the value of –x|x| positive.


Answer: D