Square C has side lengths that are 2.5 times the side lengths of square D. The area of square D is $m$ times the area of square C. What is the value of $m$?
The correct answer is .16 or $\nicefrac{4}{25}$.
current priority level - the Path to 600+ or higher
There are two ideas that we are going to discuss from the start here that could be considered rather foundational….
Following through with what’s above, our square D could have sides that are 2 by 2. This would mean that square C has sides of 5 by 5(since 2.5 x 2 is 5).
The area of square D is 4, and the area of square C is 25. Getting to this point is part of the foundation we are building.
If you finished things out by dividing 25 by 4, we understand. We did, like the test writers are certainly inclined to do, intentionally set things up here to be a bit counterintuitive. If the question had indicated that the area square C is $m$ times the area of square D, the correct answer would have been $\nicefrac{25}{4}$ or 6.25. But, given what we chose to ask here, we want things the other way around.
It could be contended that actually arriving at the correct answer here is more of a Path to 650+ kind of thing. But, we very much hold fast to the initial two ideas being foundational ideas, one that arguably are ones that we all want to have in place.