BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Factorial!!

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Master | Next Rank: 500 Posts
Posts: 118
Joined: Wed Mar 16, 2011 12:51 am
Location: New Delhi, India
Thanked: 12 times
Followed by:1 members

Factorial!!

by pankajks2010 » Sat May 14, 2011 9:37 pm
If N is a positive integer, what is the last digit of the result for 1!+2!+...N!?

a) N is divisible by 4
b) (N^2+1)/5 is an odd integer

Courtesy: 800score.com
Not sure, if this question is already discussed on the forum or not.
Top
Source: — Data Sufficiency |
User avatar
Legendary Member
Posts: 516
Joined: Fri Jul 31, 2009 3:22 pm
Thanked: 112 times
Followed by:13 members

by smackmartine » Sat May 14, 2011 10:03 pm
IMO D

1) N is divisible by 4

If N=4 , 1!+2!+3!+4! = 1+2+6+24 =33, so Last digit is 3
If N=8 , 1!+2!+3!+4!+......+ 8! =??

Now we know 5!= 120 and further multiplication with any integer (6,7,8 etc) will result in 0 as its unit's digit.
so 1!+2!+3!+4!+......+ 8! = 33+ 120+ ..0+...0+ ....0 = ......3

So last digit is 3 , Sufficient

2) (N^2+1)/5 is an odd integer

Both N= 8 and N= 18 satisfy statement 2 .

Now substituting each values in 1!+2!+3!+4!...+ N! will give the last digits as 3 in both the cases (same logic as mentioned above).

So last digit is 3 , Sufficient
Last edited by smackmartine on Sun May 15, 2011 9:14 am, edited 2 times in total.
Top
User avatar
Master | Next Rank: 500 Posts
Posts: 436
Joined: Tue Feb 08, 2011 3:07 am
Thanked: 72 times
Followed by:6 members

by manpsingh87 » Sun May 15, 2011 12:13 am
pankajks2010 wrote:If N is a positive integer, what is the last digit of the result for 1!+2!+...N!?

a) N is divisible by 4
b) (N^2+1)/5 is an odd integer

Courtesy: 800score.com
Not sure, if this question is already discussed on the forum or not.
1!+2!+......N!

1) N is divisible by 4;
N=4k; if N=4; 1+2!+3!+4!=1+2+6+24=33; last digit is 3;
now consider analyze this, 5! onwards every factorial is going to end with 0, because it contains 5, hence 1+2!+3!+4!+5!+6!+7!+8!; will also have 3 as its last digit, hence 1 alone is sufficient to answer the question.

2)(N^2+1)/5 is an odd integer;
i.e. last digit of N^2+1 must be 5 hence last digit of N^2 must be 4; now possible no. here would be 8!,12!,18!,22!,28!.....;

again by same reasoning, when we add these no. they will always have 3 as its last digit; hence 2 alone is also sufficient to answer the question, hence answer should be D
O Excellence... my search for you is on... you can be far.. but not beyond my reach!
Top
Legendary Member
Posts: 1084
Joined: Fri Apr 15, 2011 2:33 pm
Thanked: 158 times
Followed by:21 members

by pemdas » Sun May 15, 2011 12:29 am
why should we make assumption of consecutive integers (sequence) when it says
If N is a positive integer, what is the last digit of the result for 1!+2!+...N!?
it wouldn't mention N as +ve in case of consecutive no-s

isn't it c

what's OA? (explanation after)
Success doesn't come overnight!
Top
Master | Next Rank: 500 Posts
Posts: 118
Joined: Wed Mar 16, 2011 12:51 am
Location: New Delhi, India
Thanked: 12 times
Followed by:1 members

by pankajks2010 » Sun May 15, 2011 12:31 am
Manpsingh got it spot on!!..The OA is D.
Top
Legendary Member
Posts: 1084
Joined: Fri Apr 15, 2011 2:33 pm
Thanked: 158 times
Followed by:21 members

by pemdas » Sun May 15, 2011 12:36 am
800score.com is an awesome source, but sometimes their wording is guess-through unlike that of GMAT official source
Success doesn't come overnight!
Top
User avatar
Legendary Member
Posts: 516
Joined: Fri Jul 31, 2009 3:22 pm
Thanked: 112 times
Followed by:13 members

by smackmartine » Sun May 15, 2011 8:58 am
manpsingh87: again by same reasoning, when we add these no. they will always have 3 as its last digit; hence 2 alone is also sufficient to answer the question, hence answer should be D
Thanks manpsingh87

I forgot to apply values of N(8,18) to.. 1!+2!+....N! to get the last digits :(
(These are some of the common silly mistakes I have been doing now and then. I hope my mind functions right in the real exam! )

Definitely D is the answer.
Top
User avatar
Legendary Member
Posts: 934
Joined: Tue Nov 09, 2010 5:16 am
Location: AAMCHI MUMBAI LOCAL
Thanked: 63 times
Followed by:14 members

by [email protected] » Fri Mar 16, 2012 10:56 am
If N is a positive integer, what is the last digit of the result for 1!+2!+...N!?

a) N is divisible by 4
b) (N^2+1)/5 is an odd integer


This question is such that even if you do not give any of the statements, and only say that N is a positive integer (which is given), still the last digit would end in 3.

Thats the best part of this question...
IT IS TIME TO BEAT THE GMAT

LEARNING, APPLICATION AND TIMING IS THE FACT OF GMAT AND LIFE AS WELL... KEEP PLAYING!!!

Whenever you feel that my post really helped you to learn something new, please press on the 'THANK' button.
Top
Post new topic Post Reply
• Page 1 of 1