last digits

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shashank.ism: Legendary Member; Posts: 1022; Joined: Mon Jul 20, 2009 11:49 pmFollowed by: 2 members; Location: Gandhinagar; Thanked: 41 times

by shashank.ism » Mon Feb 08, 2010 7:22 am

What are the last two digits of 7^2008?

a) 21
b) 61
c) 01
d) 41
e) 81

Last edited by shashank.ism on Mon Feb 08, 2010 11:19 am, edited 1 time in total.

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harsh.champ: Legendary Member; Posts: 1132; Joined: Mon Jul 20, 2009 3:38 amFollowed by: 6 members; Location: India; Thanked: 64 times; GMAT Score:760

by harsh.champ » Mon Feb 08, 2010 7:26 am

shashank.ism wrote:What are the last two digits of 72008?

a) 21
b) 61
c) 01
d) 41
e) 81

Apparently it is 08...

:)...Did you miss anything over here shashank??

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ajith: Legendary Member; Posts: 1275; Joined: Thu Sep 21, 2006 11:13 pmFollowed by: 2 members; Location: Arabian Sea; Thanked: 125 times

by ajith » Mon Feb 08, 2010 11:07 am

shashank.ism wrote:What are the last two digits of 72008?

a) 21
b) 61
c) 01
d) 41
e) 81

Thats not fun; what are the last two digits of 7^2008 would have been fun {which requires modulo operations and I think is out of scope again}

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harsh.champ: Legendary Member; Posts: 1132; Joined: Mon Jul 20, 2009 3:38 amFollowed by: 6 members; Location: India; Thanked: 64 times; GMAT Score:760

by harsh.champ » Mon Feb 08, 2010 11:19 am

ajith wrote:
shashank.ism wrote:What are the last two digits of 72008?

a) 21
b) 61
c) 01
d) 41
e) 81
Thats not fun; what are the last two digits of 7^2008 would have been fun {which requires modulo operations and I think is out of scope again}

Well,this is also okay.
Now,7^1 = 07 [ last 2 digits are written on the RHS of =]
7^2 = 49
7^3 = 43(343)
7^4= 01 (2401)
7^5 = 07
So,we see that after every 4 no.s the same last 2 digits are repeated.[spoiler]
As, 2008 is divisible by 4 so the abs. is 01. (C)[/spoiler]

Ajith,if you carefully note,rest of the 4 options are bogus.If any option would have been 49 or 43 or 07 then the question would have been difficult.

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ajith: Legendary Member; Posts: 1275; Joined: Thu Sep 21, 2006 11:13 pmFollowed by: 2 members; Location: Arabian Sea; Thanked: 125 times

by ajith » Mon Feb 08, 2010 11:55 am

harsh.champ wrote: Ajith,if you carefully note,rest of the 4 options are bogus.If any option would have been 49 or 43 or 07 then the question would have been difficult.

Well you cant say that, it is easily found out that last digit of 7^2008 is 1 so all the options have 1 as the last digit. It would have been easier had they kept the options as u have mentioned

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money9111: Legendary Member; Posts: 2109; Joined: Sun Apr 19, 2009 10:25 pmFollowed by: 79 members; Location: New Jersey; Thanked: 109 times; GMAT Score:640

by money9111 » Mon Feb 08, 2010 1:27 pm

harsh.champ i got as far as 7^4 then i'm like.. yeah i'm doing something wrong... not thinking to myself "just see if it begins repeating somewhere." i wouldn't have known to then divide 2008 by 4, to get to 01 being the answer. I will now in the future though

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