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• ### $450 Tuition Credit & Official CAT Packs FREE January 15, 2019 January 15, 2019 10:00 PM PST 11:00 PM PST EMPOWERgmat is giving away the complete Official GMAT Exam Pack collection worth$100 with the 3 Month Pack ($299) • ### The winning strategy for a high GRE score January 17, 2019 January 17, 2019 08:00 AM PST 09:00 AM PST Learn the winning strategy for a high GRE score — what do people who reach a high score do differently? We're going to share insights, tips and strategies from data we've collected from over 50,000 students who used examPAL. # In the figure above every square is contained (inscribed)  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics Author Message TAGS: ### Hide Tags SVP Status: The Best Or Nothing Joined: 27 Dec 2012 Posts: 1823 Location: India Concentration: General Management, Technology WE: Information Technology (Computer Software) In the figure above every square is contained (inscribed) [#permalink] ### Show Tags 08 Jan 2015, 00:12 1 00:00 Difficulty: 35% (medium) Question Stats: 70% (01:28) correct 30% (01:12) wrong based on 109 sessions ### HideShow timer Statistics Attachment: 2015-01-07_1840.png [ 1.63 KiB | Viewed 1571 times ] In the figure above every square is contained (inscribed) within a square as shown. What is the length of the side of the smallest square, if the largest square has an area of 16? A. 4 B. $$2\sqrt{2}$$ C. 2 D. $$\sqrt{2}$$ E. 1 _________________ Kindly press "+1 Kudos" to appreciate SVP Status: The Best Or Nothing Joined: 27 Dec 2012 Posts: 1823 Location: India Concentration: General Management, Technology WE: Information Technology (Computer Software) Re: In the figure above every square is contained (inscribed) [#permalink] ### Show Tags 08 Jan 2015, 01:57 1 2 Answer = C = 2 Area of largest square = 16 So, area of the square inscribed $$= \frac{16}{2} = 8$$ (This is by property of the inscribed square. Can be calculated theoretically) So, area of the smallest square $$= \frac{8}{2} = 4$$ Side of the smallest square $$= \sqrt{4} = 2$$ _________________ Kindly press "+1 Kudos" to appreciate EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 13325 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: In the figure above every square is contained (inscribed) [#permalink] ### Show Tags 08 Jan 2015, 13:26 Hi All, This is a great "concept" question and can be solved without a lot of complex math. You do need to understand how the squares relate to one another though.... **Note: For organizational purposes, I'm going to refer to the 3 squares as the 'large', 'medium' and 'small' squares.** To start, we know that the area of the large square is 16, so each of its sides = 4. If you take the 4 corners of the large square and "fold them in" so that they meet at the center, you will end up with a square with the same size as the medium square. This means that the medium square has the same area as the sum of the 4 white-corner triangles: medium square = 4 white triangles medium square + 4 white triangles = large square = area of 16 medium square = 4 white triangles = area of 8 This medium square has an area of 8, so its sides are each 2(root2). Now we can do the same "math moves" (as above) with the medium square and the small square... Fold the 4 black triangles of the medium square towards the center and you get a square with the same size as the small square. small square = 4 black triangles small square + 4 black triangles = medium triangle = area of 8 small square = 4 black triangles = area of 4 So, the small square has an area of 4, so its sides are each 2. Final Answer: GMAT assassins aren't born, they're made, Rich _________________ 760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com # Rich Cohen Co-Founder & GMAT Assassin Special Offer: Save$75 + GMAT Club Tests Free
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Joined: 23 Jan 2013
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Re: In the figure above every square is contained (inscribed)  [#permalink]

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11 Nov 2015, 03:36
Smallest square's side is about half of the largest one, so 4/2=2

Paresh, thanks for concept

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Re: In the figure above every square is contained (inscribed)  [#permalink]

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11 Mar 2017, 05:03
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: In the figure above every square is contained (inscribed) &nbs [#permalink] 11 Mar 2017, 05:03
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