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If 10! - 2*(5!)^2 is divisible by 10^n, what is the greatest

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Re: If 10! - 2*(5!)^2 is divisible by 10^n, what is the greatest  [#permalink]

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New post 05 Nov 2015, 00:10
can this sort of question come up in exam, realisitically speaking, or is it out of scope? I get the basic trailing zero stuff, but I really doubt I could do this on the fly during an exam.
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Re: If 10! - 2*(5!)^2 is divisible by 10^n, what is the greatest  [#permalink]

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New post 28 Nov 2015, 02:47
Are there more questions similar to this one?
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Re: If 10! - 2*(5!)^2 is divisible by 10^n, what is the greatest  [#permalink]

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New post 28 Nov 2015, 08:25
srinjayc wrote:
Are there more questions similar to this one?


Check Trailing Zeros Questions and Power of a number in a factorial questions in our Special Questions Directory.



Hope it helps.
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Re: If 10! - 2*(5!)^2 is divisible by 10^n, what is the greatest  [#permalink]

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New post 24 Jan 2017, 18:59
1) We need to figure out how many 10 multipliers the numerator consists of.
2) 10!-2*5!*5!=5!(10*9*8*7*6-2*5*4*3*2)=5!*10*3*2*4(9*2*7-1)=5*4*3*2*10*3*2*4*125
3) Since there are plenty of 2's (7), we need to calculate the number of 5's to see how many of them will be in the numerator: 5 (5*1 - one 5), 10 (5*2 - one 5), 125 (5*5*5 - three 5's). This adds up to five 5's.

The correct answer is E
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Re: If 10! - 2*(5!)^2 is divisible by 10^n, what is the greatest  [#permalink]

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New post 12 Jul 2017, 07:52
10! = 10 * 9 * 8 * 7 * 6 * 5!
10! = 30240 * 5!

5!^2 = 120 * 5!

So now we can do the math

(30240 - 2*120) * 5! = 30,000 * 5! => we get 4 zeros from 30,000 + 1 zero from 5!, leading to 5 zeros, so the answer is E
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Re: If 10! - 2*(5!)^2 is divisible by 10^n, what is the greatest  [#permalink]

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New post 15 Jul 2018, 08:31
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: If 10! - 2*(5!)^2 is divisible by 10^n, what is the greatest &nbs [#permalink] 15 Jul 2018, 08:31

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