EXTREME Quant Problem of the Day May 3rd, 2021

GRE Quant Problem Solving
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I think its A. Where can i find the solution to check?

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Find area of the shared portion between 2 circle - 2(Area of Equilateral triangle)= Area of the borders. Half of that will be the answer(for our ease take pi= 3 and root 3 = 2)

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  1. We have radius = 6 and we have equilateral triangle with side = 6
  2. We find the area of the triangle = 9√3 or 15.58
  3. We find the area of the circle which is going to be 36π.
  4. We find the area of the segment which is 1/6 of the total area of the circle. We get 6π.
  5. We substract are of the triangle from the area of segment. 6π - 9√3 = 18.84 - 15.58 = 3.26
  6. As we have two such shaded regions 3.26 * 2 = 6.52
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Yes

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Can you always find the square root result of a number and keep it precisely to 2 decimals?

I’m not sure how did you get this number without using a calculator? 1.7*9=15.3,wherase 1.8*9 =16.2, the only way you had this 15.58 is you took \sqrt{3} as 1.73, but the problem is how did you know so precisely? What would u say the approximate decimal of \sqrt{7} , \sqrt{5} ? like how to manually get it into two decimals form？

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9√3 is the same as √ 81 * √3 which is √243. Taking the square root of √243, you will have 15.58

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Appreciate your reply but you are not answering my question. My question is, how do you manage to break down a root number into its 2 decimals form manually? Anything special with \sqrt{243} ? Don’t we still need to bring in our calculator?

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Sorry. I guess there is nothing special with taking approximate square root of any number. I would suggest you learn by heart “Square numbers” up to 40. The strategy that I use is for example in the case with √243. I know that √243 is between √225 (which is 15) and √256 (which is 16). But it lies a bit close to √256 and my guess would be something around 15.6 or 15.7.

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The calculator on the GRE does have a square root function

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@gregmat Are Extreme Quant problems of the day meant to be similar in difficulty to the “Hard” (as opposed to Easy or Medium) second section of GRE Quant?

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In some cases yes, but I think they’re sometimes even harder than what you’ll see