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# ABCD is a square. The dotted lines are the lines connecting two midpoi

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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GMAT 1: 760 Q51 V42
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ABCD is a square. The dotted lines are the lines connecting two midpoi  [#permalink]

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14 Nov 2019, 01:28
00:00

Difficulty:

25% (medium)

Question Stats:

74% (01:56) correct 26% (03:00) wrong based on 31 sessions

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[GMAT math practice question]

$$ABCD$$ is a square. The dotted lines are the lines connecting two midpoints of opposite lines. Moreover, $$E, F, G, H, I, J, K$$, and $$L$$ are midpoints between midpoints of sides and edges again in the following figure. What is the ratio of the area of the shaded region to the area of the unshaded region?

Attachment:

11.14ps.png [ 63.93 KiB | Viewed 418 times ]

A. $$1.5:1$$

B. $$1.3:1$$

C. $$1.1:1$$

D. $$1:1$$

E. $$1:1.1$$

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MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
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"Only $79 for 1 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Intern Joined: 16 Aug 2019 Posts: 11 Location: India Concentration: Human Resources, Real Estate GPA: 3.3 WE: Business Development (Human Resources) Re: ABCD is a square. The dotted lines are the lines connecting two midpoi [#permalink] ### Show Tags 14 Nov 2019, 04:59 area of square = AD * AD area of a triangle (shaded) = .5 * AD/2 * AD/2 total number of triangles =4 comparing the shaded and the unshaded areas of the square, we see that bot come out tp be equal. D Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 8235 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: ABCD is a square. The dotted lines are the lines connecting two midpoi [#permalink] ### Show Tags 17 Nov 2019, 18:42 => Assume $$MF = BF = BG = GN = x.$$ The area of the square of $$OGBF$$ is the sum of areas of triangles $$OGB$$ and $$OFB$$ , $$(\frac{1}{2})(x)(2x) + (\frac{1}{2})(x)(2x) = 2x^2$$ and the shaded area of the triangles $$OFM$$ and $$ONG$$ is $$(\frac{1}{2})(x)(2x) + (\frac{1}{2})(x)(2x) = 2x^2.$$ Attachment: 11.14ps(a).png [ 27.72 KiB | Viewed 185 times ] So, the ratio of the area of the shaded region to the area of the unshaded region is $$1:1$$. Therefore, D is the answer. Answer: D _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$79 for 1 month Online Course"
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Re: ABCD is a square. The dotted lines are the lines connecting two midpoi   [#permalink] 17 Nov 2019, 18:42
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