The following question was covered in the Quant Concept videos.

“How many powers of 900 are in 50! ?”

Based on the explanation of the solution, I could reverse engineer and guess what the question asked about, i.e. how many multiples of 900 is 50!. But I’m not sure. And I still don’t understand the original question. Those that understood the question immediately when they first saw the video, can you please explain how did you interpret the question?

I’ve always understood “powers” as the equivalent of exponents. I immediately thought of 900^x = 50! and solve for x. But it doesn’t seem to mean that. Consider this a “parsing a sentence” challenge for quant

So is this a typical GRE question wording style? Or just…GregMat style? Should I just let this go and move on?

In layman terms the question is asking : what is the maximum power of 900 that is within 50! or max_value of x for 900 raise to the power of x that is in 50!

\displaystyle900^{(\mathbb{x})} \leq 50!

Now, first thing that comes to mind is to break 900 to it’s prime factors!

we can re-write 900 = 9 \times 100 = 3^2 \times(5^2 \times 2^2) = 2^2 \times 3^2 \times 5^2

Then our question can be re-written as:

(2^2 \times 3^2 \times 5^2)^{(\mathbb{x})} \leq 50!

Now, if you go-in to find the number of 2’s in 50! then it will take a plenty of time and there will be many of them and same will be the issue be 3’s . So, we need to find a **limiting factor** and if you think logically then 5 is a perfect candidate as there are only **10 multiples** of 5 in 50! {5,10,15,20,25,30,35,40,45,50} but a thing to remember will be that we need just the number of 5’s thus, {25,50} both will contain 2 five each!. So, in total we will have 12 fives . Now, the max_number of 900 we can make is 12 at-moment because we’ll not be left be any five’s after that!

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Perfect. I’m that layman that needs to read this explanation.

Thanks.