Square units of area in a circle

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I'm studying for the GRE and came across the practice question quoted below. I'm having a hard time understanding the meaning of the words they're using. Could someone help me parse their language?

"The number of square units in the area of a circle '$X$' is equal to $16$ times the number of units in its circumference. What are the diameters of circles that could fit completely inside circle $X$?"

For reference, the answer is $64$, and the "explanation" is based on $\pi r^2 = 16(2\pi r).$

Thanks!

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2 Answers

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Let the diameter be $d$. Then the number of square units in the area of the circle is $(\pi/4)d^2$. This is $16\pi d$. That forces $d=64$.

Remark: Silly problem: it is unreasonable to have a numerical equality between area and circumference. Units don't match, the result has no geometric significance. "The number of square units in the area of" is a fancy way of saying "the area of."

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I'm currently doing this, and how I see the problem is:

$πr^2 = (2πr) * 16 $

If you solve this, r gives $32$, and since diameter $d = 2*r$, $d = 64$.

So, any circle with a lesser diameter fits in this circle $(d<64)$

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