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mxs2009
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Post subject: Oodles of 0's  Posted: Sat Jul 18, 2009 5:28 pm |
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If 60! is written out as an integer, with how many consecutive 0’s will that integer end?
A. 6
B. 12
C. 14
D. 42
E. 56
I calculated this in excel and the answer came out to 67 0's at the end. what am I missing?
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susan.meng
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Post subject: Re: Oodles of 0's Posted: Tue Jul 21, 2009 4:49 pm |
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Another way to write 60! = k *10^p where k is some constant
For a number to end in 0, it must be divisible by 10
10^p = 2^p * 5^p
We are looking for the number of 5's in 60!.
5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60
There are 14 5's (two in 25 and 2 in 50 and 1 in each of the other numbers).
Answer is C.
Last edited by susan.meng on Tue Jul 21, 2009 9:28 pm, edited 1 time in total.
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mxs2009
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Post subject: Re: Oodles of 0's Posted: Tue Jul 21, 2009 4:55 pm |
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Thanks. I realized that excel rounds the calculation
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deepak1982
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Post subject: Re: Oodles of 0's Posted: Tue Jul 28, 2009 9:57 am |
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This can also be done by
Successively divide 60 by 5 till u get a quotient which is less than 5.
24/5 = 12
12/5 = 2
So the total no.of Zeros = 12+2 = 14
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mxs2009
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Post subject: Re: Oodles of 0's Posted: Wed Jul 29, 2009 2:04 am |
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I don't think that shortcut works. try it with 30!. the answer is 7 and your method results in an answer of six.
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RonPurewal
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Post subject: Re: Oodles of 0's Posted: Thu Aug 13, 2009 5:38 am |
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| ManhattanGMAT Staff |
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Posts: 7146
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hi -
just checking - do you have a question about the actual problem or its solution, or are you just wondering about the excel discrepancy?
thanks
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girl.jobless
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Post subject: Re: Oodles of 0's Posted: Sat Oct 03, 2009 3:45 pm |
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The value of 60! = 8.32098711 × 10^81 as per google. So that would mean that there are 73 0's following the integer 832098711. So how is 14 as the answer correct?
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vishalsahdev03
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Post subject: Re: Oodles of 0's Posted: Sun Oct 04, 2009 11:09 am |
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I calculated 14 0s, i wonder what is google saying.
Answer is C.
Any reviews on this?
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RonPurewal
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Post subject: Re: Oodles of 0's Posted: Mon Nov 02, 2009 9:48 pm |
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Quote: I calculated this in excel and the answer came out to 67 0's at the end. what am I missing? Quote: The value of 60! = 8.32098711 × 10^81 as per google. whoa people. these are rounded values; google and excel are not going to give you ALL the digits of such a huge number. first, to write all eighty digits of such a number on the screen would be, to say the least, unsightly. second, it would be terrible for comprehension. (quick, which is bigger: 48372938478394095827393827840293 or 443222334688970552213733257840677? now, which is bigger: 3.83 x 10^21, or 2.63 x 10^22?) if you want proof that the values are rounded, type in something like 5^90 into either google or excel. ALL exact powers of 5 end with 5, but your answer most likely won't. this indicates rounding.
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RonPurewal
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Post subject: Re: Oodles of 0's Posted: Mon Nov 02, 2009 9:50 pm |
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| ManhattanGMAT Staff |
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mxs2009 wrote: If 60! is written out as an integer, with how many consecutive 0’s will that integer end?
A. 6
B. 12
C. 14
D. 42
E. 56
I calculated this in excel and the answer came out to 67 0's at the end. what am I missing? exact solution: each "0" comes from the presence of a 10 in the number; each 10 will come from a 2 and a 5. the limiting factor is whichever of these are fewer. it should be clear that there will be WAY more 2's than 5's, so we only have to figure how many 5's are in the product. you get ONE "5" each from the following numbers: 5, 10, 15, 20, 30, 35, 40, 45, 55, 60 you get TWO "5"s from: 25, 50 so that's fourteen 5's total.
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dul_hadita
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Post subject: Re: Oodles of 0's Posted: Fri May 28, 2010 9:51 am |
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RonPurewal wrote:
you get ONE "5" each from the following numbers:
5, 10, 15, 20, 30, 35, 40, 45, 55, 60 there are 10 5s here
you get TWO "5"s from:
25, 50 additional 2 s's here
so that's fourteen 5's total.
that is 12 5's in total. 2x5, 10,12x15, 20, 22x25, 30, 32x35, 40, 42x45, 50, 52x55, 60 25 and 50 will each get you an adiitional 5. so 10+2=12
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RonPurewal
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Post subject: Re: Oodles of 0's Posted: Wed Jun 23, 2010 9:20 am |
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dul_hadita wrote: that is 12 5's in total. nope -- see your own work: Quote: 2x5, 10,12x15, 20, 22x25, 30, 32x35, 40, 42x45, 50, 52x55, 60 this is already twelve 5's. i'm not sure why you are introducing all of the extra multiples of 2 -- we know that we have an excess of 2's, so we really don't have to bother thinking about multiples of 2. Quote: 25 and 50 will each get you an adiitional 5. so 10+2=12 ...so the addition of these two extra 5's brings the total to fourteen.
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mirzank
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Post subject: Re: Oodles of 0's Posted: Wed Dec 07, 2011 5:31 pm |
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I'm going to re open an old questions, i got this question wrong and just wanted to show my methodology. Maybe I missed something in my method, or maybe tottaly wrong if someone can enlighten me would appreciate it. The way I looked at it was to say that the 0's in 60! will either come from the multiples of 10, i.e. 10, 20, 30, 40, 50, 60, which is 6 0's. Plus another set of zero's will come from 2 and 5 being multipled from units digits. This way i get another 6 0's. 2 and 5, 12 and 15, 22 and 25, 32 and 35, 42 and 45, & 52 and 55. This way I only get 12 0's. Is this totally the wrong way to think about this? If not, then what can i add to this method to get the 2 extra 0's. RonPurewal wrote: dul_hadita wrote: that is 12 5's in total. nope -- see your own work: Quote: 2x5, 10,12x15, 20, 22x25, 30, 32x35, 40, 42x45, 50, 52x55, 60 this is already twelve 5's. i'm not sure why you are introducing all of the extra multiples of 2 -- we know that we have an excess of 2's, so we really don't have to bother thinking about multiples of 2. Quote: 25 and 50 will each get you an adiitional 5. so 10+2=12 ...so the addition of these two extra 5's brings the total to fourteen.
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tim
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Post subject: Re: Oodles of 0's Posted: Tue Dec 13, 2011 2:49 am |
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Location: Southwest Airlines, seat 21C
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You missed the same two 0’s that have been discussed extensively in this thread – the extra 0’s that derive from 25 and 50. Please re-read the discussion above so you can see where the extra two 0’s come from ..
_________________
Tim Sanders
Manhattan GMAT Instructor
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iconstudent475
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Post subject: Re: Oodles of 0's Posted: Mon Jan 30, 2012 12:08 am |
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Sorry for reopening this, but Excel give me this number when i calculate 60! :
8320987112741390000000000000000000000000000000000000000000000000000000000000000000.00
Much more than 14 zeros...
Did i miss anything ?
Pierre
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