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#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # In the figure above a > b. Is the area of the shaded region greater th

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Manager  G
Joined: 31 May 2020
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In the figure above a > b. Is the area of the shaded region greater th  [#permalink]

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Difficulty:   75% (hard)

Question Stats: 50% (03:04) correct 50% (02:44) wrong based on 22 sessions

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In the figure above a > b. Is the area of the shaded region greater than half the area of square WXYZ?

(1) $$a^2 + b^2 > 6ab$$

(2) $$a > 6b$$
Manager  G
Joined: 31 May 2020
Posts: 204
Re: In the figure above a > b. Is the area of the shaded region greater th  [#permalink]

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Area of square WXYZ = $$(a+b)^2$$
Area of shaded regiion = $$(a-b)^2$$

To find: $$(a-b)^2>\frac{1}{2}*(a+b)^2?= a^2+b^2>6ab?$$

Statement 1: Tells us that a^2+b^2 is greater than 6ab. Sufficient.

Statement 2: a>6b.. Assume a=7b.
Thus, $$(7b-b)^2>\frac{1}{2}(7b+b)^2? --> 72b^2>64b^2--> b^2>0?$$
Since, b>0 in the square given, b^2>0.... Sufficient.

Option (D) Re: In the figure above a > b. Is the area of the shaded region greater th   [#permalink] 11 Jul 2020, 10:22

# In the figure above a > b. Is the area of the shaded region greater th  