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# What is 1! + 2! + ... + 10! ?

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SVP
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What is 1! + 2! + ... + 10! ? [#permalink]

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14 May 2008, 02:16
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35% (medium)

Question Stats:

64% (02:11) correct 36% (00:56) wrong based on 543 sessions

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What is 1! + 2! + ... + 10! ?

A. 4,037,910
B. 4,037,913
C. 4,037,915
D. 4,037,916
E. 4,037,918
[Reveal] Spoiler: OA

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14 May 2008, 02:41
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sondenso wrote:
What is 1!+2!+...+10! ?

4,037,910
4,037,913
4,037,915
4,037,916
4,037,918

I think that if I meet this on the real Gmat, I must waste 10 minute, even 1 hour 15 minutes more!

There's a easier way to crack this...

1! = 1
2! = 2
3! = 6
4! = 24
5! = 120
Now, all figures after 5! will have 0 in their unit digit (720 on 6!, 5040 on 7! etc.) so, all that we have to look into is the unit's place in the answer!

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Is this okay?

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14 May 2008, 02:57
B.

1+2*1+3*2*1+..................
= 1+2[1+3[1+4[1+5[1+6[.................
unit's digit => 3
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14 May 2008, 05:31
1
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sondenso wrote:
What is 1!+2!+...+10! ?

4,037,910
4,037,913
4,037,915
4,037,916
4,037,918

I think that if I meet this on the real Gmat, I must waste 10 minute, even 1 hour 15 minutes more!

just look at the unit digit
1!=1
2!=2
3!=6
4!=4
5!=0..after this all numbers will have a 2 and 5..and thus unit digit for all of them is 0..

1+2+6+4=13..luckily 13, 3 is only one of the ans choices..
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01 Feb 2011, 08:09
hello, Can somebody explain /explain whats wrong with my method:

[(1+10!)/2] *10 ( average * number of terms)

i am getting 5 as last unit digit ???
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01 Feb 2011, 09:46
Expert's post
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tinki wrote:
hello, Can somebody explain /explain whats wrong with my method:

[(1+10!)/2] *10 ( average * number of terms)

i am getting 5 as last unit digit ???

You can apply the formula above: $$Sum=\frac{first+last}{2}*# \ of \ terms$$, the mean multiplied by the number of terms for evenly spaced set (aka arithmetic progression). But as in the sequence given (1!, 2!, 3!, ..., 10!) the difference between any two successive terms is not the same then we don't have evenly spaced set (arithmetic progression) and thus can not apply this formula.

As for the solution:
What is 1!+2!+...+10! ?
A. 4,037,910
B. 4,037,913
C. 4,037,915
D. 4,037,916
E. 4,037,918

For any integer $$n$$ more than or equal to 5 the units digit of $$n!$$ will be zero as $$n!$$, in this case, will contain at least one 2 and 5 which when multiplied will give a trailing zero. So terms from 5! to 10! will have zero as their units digit. 1!+2!+3!+4!=1+2+6+24=33 so the whole sum will have 3 as the units digit. Only option B offers a number with 3 as its units digit.

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01 Feb 2011, 10:12
got it. somehow thought factorials were evenly spaced. silly me ...

i saw the material. ARE you kind of magician ?

you are like : "you need help? Here i am" THANKS SOOOO MUCH, YOU ARE DEFINITELY GREAT !!!
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Re: What is 1! + 2! + ... + 10! ? [#permalink]

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03 Feb 2014, 06:27
Hello from the GMAT Club BumpBot!

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Re: What is 1! + 2! + ... + 10! ? [#permalink]

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03 Feb 2014, 08:53
1
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Taking units digits of 1! To 4! ie 1+2+6+4+0=13(Because only the units digits are diff in options).After that 0 will be at the unit's place for 5!,6!,7!,8!,9!,10!.Therefore,the last two digits will be 13.
Ans.B

(Is the logic above flawed?)

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Re: What is 1! + 2! + ... + 10! ? [#permalink]

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19 Apr 2015, 02:58
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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What is 1! + 2! + ... + 10! ? [#permalink]

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23 Jan 2016, 01:24
1
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Bunuel wrote:
tinki wrote:
hello, Can somebody explain /explain whats wrong with my method:

[(1+10!)/2] *10 ( average * number of terms)

i am getting 5 as last unit digit ???

You can apply the formula above: $$Sum=\frac{first+last}{2}*# \ of \ terms$$, the mean multiplied by the number of terms for evenly spaced set (aka arithmetic progression). But as in the sequence given (1!, 2!, 3!, ..., 10!) the difference between any two successive terms is not the same then we don't have evenly spaced set (arithmetic progression) and thus can not apply this formula.

As for the solution:
What is 1!+2!+...+10! ?
A. 4,037,910
B. 4,037,913
C. 4,037,915
D. 4,037,916
E. 4,037,918

For any integer $$n$$ more than or equal to 5 the units digit of $$n!$$ will be zero as $$n!$$, in this case, will contain at least one 2 and 5 which when multiplied will give a trailing zero. So terms from 5! to 10! will have zero as their units digit. 1!+2!+3!+4!=1+2+6+24=33 so the whole sum will have 3 as the units digit. Only option B offers a number with 3 as its units digit.

Hello Bunuel,

so in that case, 1!+2!.....1500! will also have the unit digit as 3 only.....

I can remember this concept and apply to any similar questions

Thanks,
Arun
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Re: What is 1! + 2! + ... + 10! ? [#permalink]

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05 Feb 2016, 01:34
can reduce to B and C because sum of numbers is odd. I took C and made mistake
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Re: What is 1! + 2! + ... + 10! ? [#permalink]

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05 Feb 2016, 07:40
Expert's post
sondenso wrote:
What is 1! + 2! + ... + 10! ?

A. 4,037,910
B. 4,037,913
C. 4,037,915
D. 4,037,916
E. 4,037,918

CRITICAL OBSERVATION : All options have different Unit digit so calculating unit digit of the sum above will suffice

Unit digit of (1! + 2! + 3! + 4! + 5! + 6!+... + 10!) = 1 + 2+ 6 + 4 + 0 + 0 + 0 + 0+ 0 + 0 = Unit digit 3, Hence

every Factorial of an integer greater than 4 will have Unit digit 0 as it will be a multiple of 10

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Re: What is 1! + 2! + ... + 10! ?   [#permalink] 05 Feb 2016, 07:40
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