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

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Math Expert
Joined: 02 Sep 2009
Posts: 55277
Is the area of circle X larger than the area of square Y? (1) The di  [#permalink]

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14 Sep 2018, 01:58
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Difficulty:

65% (hard)

Question Stats:

45% (02:32) correct 55% (02:00) wrong based on 21 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, 23:37
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   [#permalink] 14 Sep 2018, 23:37
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