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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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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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    @AndréNicolas: Of course, the phrasing "the number of square units in the area of" (and "the number of [linear] units") isn't just to be fancy; it's *specifically* to address your objection that units of length and area don't match, saying, in effect, "We know *that*. This isn't about units. Just make the *numbers* equal to each other." This is a *perfectly* reasonable algebraic exercise. Apples aren't oranges, either, but we can certainly compare *numbers* of each. – 2012-07-02