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# PS

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Author Message
Joined: 31 Dec 1969
Location: Russian Federation
Concentration: Technology, Entrepreneurship
GMAT 1: 710 Q49 V0
GMAT 2: 700 Q V
GMAT 3: 740 Q40 V50
GMAT 4: 700 Q48 V38
GMAT 5: 710 Q45 V41
GMAT 6: 680 Q47 V36
GMAT 7: Q42 V44
GMAT 8: Q42 V44
GMAT 9: 740 Q49 V42
GMAT 10: 740 Q V
GMAT 11: 500 Q47 V33
GMAT 12: 670 Q V
WE: Engineering (Manufacturing)
Followers: 0

Kudos [?]: 202 [0], given: 102283

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02 Jun 2004, 10:47
00:00

Difficulty:

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0% (00:00) correct 0% (00:00) wrong based on 0 sessions

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does anyone know a trick on how to solve these types of problems?

what is the tens digit of 221^4? thanks
Manager
Joined: 07 May 2004
Posts: 183
Location: Ukraine, Russia(part-time)
Followers: 2

Kudos [?]: 15 [0], given: 0

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03 Jun 2004, 01:22
gmatgmatgmat wrote:
does anyone know a trick on how to solve these types of problems?

what is the tens digit of 221^4? thanks

That's really simple:

221 = 22*10 + 1. => 221^4 = (22*10 + 1)^4 = [(22*10)^4 + ... ]+ 4*22*10 + 1 => 8 is the tenth digit of this number, because 100 divides sum in [...].
Joined: 31 Dec 1969
Location: Russian Federation
Concentration: Technology, Entrepreneurship
GMAT 1: 710 Q49 V0
GMAT 2: 700 Q V
GMAT 3: 740 Q40 V50
GMAT 4: 700 Q48 V38
GMAT 5: 710 Q45 V41
GMAT 6: 680 Q47 V36
GMAT 7: Q42 V44
GMAT 8: Q42 V44
GMAT 9: 740 Q49 V42
GMAT 10: 740 Q V
GMAT 11: 500 Q47 V33
GMAT 12: 670 Q V
WE: Engineering (Manufacturing)
Followers: 0

Kudos [?]: 202 [0], given: 102283

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03 Jun 2004, 07:27
thanks emmanuel!
thank   [#permalink] 03 Jun 2004, 07:27
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# PS

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