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# Which of the following could be the area of a regular hexagon in which

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 7603
GMAT 1: 760 Q51 V42
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Which of the following could be the area of a regular hexagon in which  [#permalink]

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02 Jan 2019, 01:47
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71% (01:36) correct 29% (01:38) wrong based on 44 sessions

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[Math Revolution GMAT math practice question]

Which of the following could be the area of a regular hexagon in which the length of the equal sides is an integer?

$$A. \frac{√3}{6}$$
$$B. \frac{√3}{5}$$
$$C. \frac{√3}{4}$$
$$D. 6√3$$
$$E. \frac{3√3}{4}$$

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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" General GMAT Forum Moderator Joined: 15 Jan 2018 Posts: 424 Concentration: General Management, Finance GMAT 1: 720 Q50 V37 Re: Which of the following could be the area of a regular hexagon in which [#permalink] ### Show Tags 02 Jan 2019, 01:59 1 Important Note: A regular hexagon has 6 equal equilateral triangles. We know the area of an equilateral triangles (√3/4)xa^2, where a is the length of the side Hence, Area of regular hexagon = 6x (√3/4)xa^2 = (3√3)/2 a^2 For a = 2, the above equation becomes 6√3. Hence, the Correct Answer is Option D.6√3 _________________ New to GMAT Club or overwhelmed with so many resources? Follow the GMAT Club Study Plan! Not happy with your GMAT score? Retaking GMAT Strategies! Game of Timers - Join the Competition to Win Prizes GMAT Club Legend Joined: 18 Aug 2017 Posts: 4242 Location: India Concentration: Sustainability, Marketing GPA: 4 WE: Marketing (Energy and Utilities) Re: Which of the following could be the area of a regular hexagon in which [#permalink] ### Show Tags 02 Jan 2019, 17:18 MathRevolution wrote: [Math Revolution GMAT math practice question] Which of the following could be the area of a regular hexagon in which the length of the equal sides is an integer? $$A. \frac{√3}{6}$$ $$B. \frac{√3}{5}$$ $$C. \frac{√3}{4}$$ $$D. 6√3$$ $$E. \frac{3√3}{4}$$ for a hexagon of equal sides the area can be calculated using formula sqrt3 * x^2/2 this has ben derieved from equilateral triangle formula (sqrt3*x^2/4) * 6 since given that x is an integer so only at x=2 we get option D 6 sqrt3 IMOD _________________ If you liked my solution then please give Kudos. Kudos encourage active discussions. Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 7603 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: Which of the following could be the area of a regular hexagon in which [#permalink] ### Show Tags 04 Jan 2019, 01:18 Attachment: 1.4.png [ 11.63 KiB | Viewed 253 times ] => Let $$n$$ be the side-length of a regular hexagon. Then the area of the shaded equilateral triangle is $$(\frac{√3}{4})n^2$$ and the area of the regular hexagon is $$(\frac{6√3}{4})n^2 = (\frac{3√3}{2})n^2$$ . If $$n = 2$$, then $$(\frac{3√3}{2})n^2 = (\frac{3√3}{2})2^2 =6√3$$. None of the other values are possible for integer values of $$n$$. Therefore, the answer is D. 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: Which of the following could be the area of a regular hexagon in which   [#permalink] 04 Jan 2019, 01:18
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