st =

st = Quantity A : Quantity B : Quantity A is greater., Quantity B is greater., The two quantities are equal., The relationship cannot be determined from the information given.

2 Explanations

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Philip Weslow

I acknowledge that your algebraic approach makes perfect sense. However, I am not understanding why the plug-and-chug approach I initially took is invalid. I decided to test two cases. In each I picked two values that were factors of radical 10.

In the first case I assumed s = 1 and t = [radical 10]. Plugging in these numbers results in (1 vs [radical 10]), so column "B" is bigger. In the second case I reversed the two values resulting in (10 vs 10), the two values are equal. Since I wound up with two different results I initially thought the answer was D.

May 1, 2019 • Comment

Adam

Hey Philip!
You won't be able to just plug in these two values to prove that for every single value of s and t, both quantities are equal. You'll have to do some logical and algebraic confirmation to make that deduction.
But for what it's worth, if s = 1, then quantity A = 1. And if t = √10, then quantity B = 10/(√10)² = 10/10 = 1. So the two quantities are equal in this case as well.
Hope that helps!

May 6, 2019 • Reply

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Chris Lele