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#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here. # If the diameter (d ) of a circle is an integer and 6 cm ≤ d  Question banks Downloads My Bookmarks Reviews Important topics
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If the diameter (d ) of a circle is an integer and 6 cm ≤ d [#permalink]
Expert's post 00:00

Question Stats: 87% (00:55) correct 12% (00:16) wrong based on 8 sessions

If the diameter (d) of a circle is an integer and $$6 cm$$ $$\leq$$ $$d$$ $$\leq$$ $$10 cm$$, which could be the area of the circle?

A. $$36\pi cm^2$$

B. $$25\pi cm^2$$

C. $$14\pi cm^2$$

D. $$6\pi cm^2$$

E. $$3\pi cm^2$$

Kudo for the right solution and explanation
[Reveal] Spoiler: OA

_________________ Manager  Joined: 15 Jan 2018
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Re: If the diameter (d ) of a circle is an integer and 6 cm ≤ d [#permalink]
1
KUDOS
Firstly, let me just remark that problems by McGraw-Hill are generally terrible. So don't take them as a very accurate gauge of how the GRE works.

This one is not too bad though. When we find the area of circles, we don't really care about diameters; we care about radii. We could quickly eliminate 3 answer choices by thinking along these lines: If the diameter is an integer, then the radius must also be an integer, or end in .5. For example, if the diameter was 10, the radius must be 5, but if the diameter was 9, the radius would be 4.5. So the area, which is πr^2, should either be a perfect square (if the radius was an integer) or end in .25 (if the radius ended in .5). C, D, and E fulfill neither of those categories. So it's either A or B.

We've also been told that 6 ≤ d ≤ 10. We still don't care about d, so I'd replace it with 2r and we'd get 6 ≤ 2r ≤ 10. Dividing all three parts gets us 3 ≤ r ≤ 5. So the radius must be 3, 4, or 5, and the areas could be 9π, 16π, or 25π. So it's B.
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Need help with GRE math? Check out our ground-breaking books and app. Re: If the diameter (d ) of a circle is an integer and 6 cm ≤ d   [#permalink] 04 Feb 2018, 19:14
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