GordonFreeman wrote:
Bunuel wrote:
I had the solution to this problem in under a minute or so but couldn't actually compute the answer. Are we really supposed to be able to solve \(\sqrt{\frac{9,856}{\pi}}\) without a calculator? That seems like a stretch to me, but maybe I'm missing something... Is assuming \(\pi \approx \frac{22}{7}\) a standard assumption for this exam?
As I've written above this is not a proper GMAT question because we need to approximate \(\pi\) to get the answer, while the question does not ask about
approximate height. GMAT would never do that.
As for \(\pi \approx \frac{22}{7}\): this is a good/standard approximation for some problems asking for an approximate answer.
Are we expected to know the square root of 3,136 is 56 off the top of our heads as well? I'm just trying to get a sense for what I need to memorize.
No. There is very little memorization that is expected from you. But what is expected is that you will reduce the calculations you need to do using reasoning.
If such a question does come in GMAT, the number will be and easier than 9856. Also, you can easily solve with 9856 too.
\(r^2 = 9856/pi = 9856*7/22\)
r must be an integer otherwise this calculation will become far too cumbersome for GMAT. So 9856 will be completely divisible by 22.
Also, 9856 must have 7 as a factor since perfect squares have powers of prime factors in pairs.
So let's try to split 9856 into factors. We already know that it must have 7 as a factor and 11 as a factor (to be divisible by 22)
\(9856 = 7*1408 = 7*11*128 = 7*11*2^7\) (you must know that 2^7 = 128)
\(r^2 = \frac{7*11*2^7}{2*11} = 7*2^3 = 56\)
Again, \(H = \sqrt{65^2 - 56^2} = \sqrt{(65+56)(65 - 56)} = \sqrt{121*9} = 11*3 = 33\)
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