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# What are the last 2 digits of 7^49*143^5?

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GMAT Club Legend
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GMAT 1: 690 Q50 V34
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545 Q79 V79 DI73
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General Discussion
GMAT Club Legend
Joined: 03 Jun 2019
Posts: 5307
Own Kudos [?]: 4220 [3]
Given Kudos: 161
Location: India
GMAT 1: 690 Q50 V34
WE:Engineering (Transportation)
GMAT Club Legend
Joined: 18 Aug 2017
Status:You learn more from failure than from success.
Posts: 7998
Own Kudos [?]: 4236 [1]
Given Kudos: 243
Location: India
Concentration: Sustainability, Marketing
GMAT Focus 1:
545 Q79 V79 DI73
GPA: 4
WE:Marketing (Energy and Utilities)
Re: What are the last 2 digits of 7^49*11^5*13^5? [#permalink]
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Kinshook wrote:
What are the last 2 digits of 7^49*143^5?

A. 01
B. 07
C. 79
D. 41
E. 91

7^49*143^5

we can solve using 7 cyclicity ; 7,9,3,1 for 7^49 last two digits ; 07
143^5 ; 11^5; 13^5 ;
we get last two digits of 11^5 ; ~ 51 and 13^5 ; 93 or say 143^5; ~43 last two
so 07*43 ; 01
IMO A
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Re: What are the last 2 digits of 7^49*143^5? [#permalink]
Archit3110 wrote:
Kinshook wrote:
What are the last 2 digits of 7^49*143^5?

A. 01
B. 07
C. 79
D. 41
E. 91

7^49*143^5

we can solve using 7 cyclicity ; 7,9,3,1 for 7^49 last two digits ; 07
143^5 ; 11^5; 13^5 ;
we get last two digits of 11^5 ; ~ 51 and 13^5 ; 93 or say 143^5; ~43 last two
so 07*43 ; 01
IMO A

Hello Archit3110

How do we know that the last two digits of 7^49 are 07?, I mean, I understant why is 7 but how do we discovery the 0?

Kind regards!
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Re: What are the last 2 digits of 7^49*143^5? [#permalink]
Kinshook wrote:
What are the last 2 digits of 7^49*143^5?

A. 01
B. 07
C. 79
D. 41
E. 91

­
Can anyone please share a detailed step on how to find last two digits in these cases? I am seeing very breif explanations and I am not able to really comprehend the logic well.
Re: What are the last 2 digits of 7^49*143^5? [#permalink]
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