Concentric Circles Problem

GRE Quant Problem Solving
1

For question 8 on the tickbox #10 quick the question reads: Concentric circles 𝐴 and 𝐡 have radii of π‘₯ and π‘₯-3, respectively. If the area of the larger circle that is not covered by the smaller circle is 27 πœ‹, what is π‘₯?

When I attempted to solve I first transformed the relationship between the radii into x and x+3 since I felt like those values would be easier to work with. Then going through and subtracting the areas the pis and the x^2 terms cancel out and you’re left with 6x+9=27 which gives 3

What is confusing me is that in Greg’s solution when keeping the relationship as x and x-3 the equation becomes 6x-9=27 which yields 6.

I would have thought that transforming the relationship between the radii would not affect the answer but it appears as if either it does or I am missing something glaring when solving with x and x+3

2

The problem is that when making the transformation, you’re doing something like

t = x + 3

You need to undo this in the end, or you’ll be solving the wrong problem essentially.

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