Carcass wrote:
\(x^2=|y|\)
Quantity A |
Quantity B |
\(|x|\) |
\(y\) |
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
Kudos for the right answer and explanation
We know that: \(x^2 = |y|\)
\(=> |x|^2 = |y|\)
\(=> |x| = \sqrt{|y|}\)
Thus, we need to compare:
Quantity A: \(|x| = \sqrt{|y|}\)
Quantity B: \(y\)
The various possibilities are:
#1. If \(y < 0\): Quantity A will be greater since it is positive while Quantity B is negative
#2. If \(y = 1\) or \(y = 0\): Quantity A will be equal to Quantity B, both being zero
#3. If \(0 < y < 1\): Quantity A will be greater than Quantity B since square root of a fraction is greater than the fraction itself (ex. \(\sqrt{0.49} = 0.7 > 0.49\))
#4. If \(y > 1\): Quantity B will be greater than Quantity A
Thus, there is no relation
Answer DWould like to point out. when square is removed from x, it becomes +sqrt(|y|) or - sqrt(|y|). not just the positive sqrt(|y|), but it can be negative also. that much information is enough to tell that the answer is D.
So in case #1 as you point out, it can actually be either greater or lesser than B