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PS - sum of factorials

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Manager
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PS - sum of factorials [#permalink] New post 28 Apr 2007, 04:08
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Question Stats:

100% (01:03) correct 0% (00:00) wrong based on 1 sessions
What is 1!+2!+...+20! ?


Do you guys know any trick to make such a calculation?

Thanks!
Senior Manager
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Re: PS - sum of factorials [#permalink] New post 28 Apr 2007, 04:36
querio wrote:
What is 1!+2!+...+20! ?


Do you guys know any trick to make such a calculation?

Thanks!


i am not aware of any nice shortcut. however, sometime the answer choices help in that given these you can find the right answer quickly. for example the units digit of the answer can be quickly calculated (it is 3), so if you had 5 answer choices and only one of those had 3 in its unit digit - you could have your answer very quickly.
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Re: PS - sum of factorials [#permalink] New post 28 Apr 2007, 05:09
I would interested to see a shortcut too..

btw Hobbit, how did you figure unit digit was 3?

hobbit wrote:
querio wrote:
What is 1!+2!+...+20! ?


Do you guys know any trick to make such a calculation?

Thanks!


i am not aware of any nice shortcut. however, sometime the answer choices help in that given these you can find the right answer quickly. for example the units digit of the answer can be quickly calculated (it is 3), so if you had 5 answer choices and only one of those had 3 in its unit digit - you could have your answer very quickly.
Manager
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 [#permalink] New post 28 Apr 2007, 05:30
1! = 1 (units digit 1)
2! = 2 (ud 2)
3! = 6 (ud 6)
4! = 24 (ud 4)
5!, 6!.... the units digit will be 0 because all the terms will include 5x2=10

units digit of 1!+2!+... will be 1+2+6+4+0+0+0.... = 3

No shortcut to make the calculation then?
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 [#permalink] New post 28 Apr 2007, 05:32
from 5! (i.e. 5!, 6!, 7! ...) the units digits is 0
so the units digit of the sum 1!+...+20! depends only on the units digits of 1!+2!+3!+4! = 1+2+6+24 = 33
hence the units digits of the complete sum is 3
similarly you can relatively easily compute the tens digit of the sum (you need to check only 1!...9!) and it will be inevitably and odd digit (or more specifically 1 if i'm not wrong with my quick no-paper calculations)

this would probably suffice to choose the right answer from a reasonable set of choices...
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Re: PS - sum of factorials [#permalink] New post 28 Apr 2007, 05:37
querio wrote:
What is 1!+2!+...+20! ?


Do you guys know any trick to make such a calculation?

Thanks!


although no shortcut .... it seems that this sum may be part of a "bigger picture" question - maybe related to counting/combinatorics....
if so, it might be that the wider context situation has a shortcut that bypasses the sum of factorial altogether.
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 [#permalink] New post 28 Apr 2007, 06:15
Hobbit, and querio..nice work on getting the unit digit..totally bummed on this one..

weird usually my mind works better in the morning..but somehow today totally stumbled ...
Manager
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Re: PS - sum of factorials [#permalink] New post 28 Apr 2007, 06:30
[quote="hobbit"][quote="querio"]What is 1!+2!+...+20! ?


Do you guys know any trick to make such a calculation?

Thanks![/quote]

although no shortcut .... it seems that this sum may be part of a "bigger picture" question - maybe related to counting/combinatorics....
if so, it might be that the wider context situation has a shortcut that bypasses the sum of factorial altogether.[/quote]

Yeah, you're right... I don't think Gmat will ask to make the calculation just to get the final number, but it will somehow hide the answer among the answer choices. Thanks!
Re: PS - sum of factorials   [#permalink] 28 Apr 2007, 06:30
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PS - sum of factorials

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