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# Is the area of circle X larger than the area of square Y? (1) The di

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Joined: 02 Sep 2009
Posts: 50580
Is the area of circle X larger than the area of square Y? (1) The di  [#permalink]

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14 Sep 2018, 00:58
00:00

Difficulty:

65% (hard)

Question Stats:

53% (02:17) correct 47% (02:03) wrong based on 19 sessions

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Is the area of circle X larger than the area of square Y?

(1) The diagonal of square Y is greater than the diameter of circle X.
(2) The perimeter of square Y is equal to the circumference of circle X.

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Re: Is the area of circle X larger than the area of square Y? (1) The di  [#permalink]

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14 Sep 2018, 22:37
1
Bunuel wrote:
Is the area of circle X larger than the area of square Y?

(1) The diagonal of square Y is greater than the diameter of circle X.
(2) The perimeter of square Y is equal to the circumference of circle X.

Area of the circle = $$πD^2/4$$
Area of square = $$s^2$$

Question: Is $$πD^2/4 > s^2$$ ?
Question: Is $$D^2/s^2 > 4/π$$ ?
Question: Is $$D/s > 2/√π$$ ?
Question: Is $$D/s > 1.13$$ ?

Statement 1: The diagonal of square Y is greater than the diameter of circle X.
i.e. $$s√2 > D$$
i.e. $$D/s < 1.4$$NOT SUFFICIENT

Statement 2: The perimeter of square Y is equal to the circumference of circle X
$$4s = πD$$
i.e. $$D/s = 1.27$$
SUFFICIENT

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Re: Is the area of circle X larger than the area of square Y? (1) The di &nbs [#permalink] 14 Sep 2018, 22:37
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