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Kinshook
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What are the last 2 digits of 7^49*143^5? 24 Aug 2019, 03:12
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A
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95% (hard)

Question Stats:

47% (02:25) correct 53% (02:25) wrong based on 165 sessions

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

A. 01
B. 07
C. 79
D. 41
E. 91
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A
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Archit3110
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What are the last 2 digits of 7^49*143^5? 03 Sep 2019, 22:55
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jfranciscocuencag
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Kinshook
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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jfranciscocuencag i actually learned the following method in of the posts on the gmatclub

7^4= 2401 infact 7^4x where x is an + integer will always give tens place as 0 you may check for 7^8 , 7^12 and so on..
so for 7^49 we can write it as 7^4*12+1 ; or say 7^4*12 * 7^1 ; placement of digit will be respective place ; 07
hope this helps
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What are the last 2 digits of 7^49*143^5? 24 Aug 2019, 03:33
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Kinshook
What are the last 2 digits of 7^49*143^5?

A. 01
B. 07
C. 79
D. 41
E. 91
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7^49 = 7^44 * 7^5*143^5 = 7^44 * 1001^5

Last 2 digits of 7^49*143^5 = Last 2 digits of 7^44 * 1001^5 = Last 2 digits of 7^44 = Last 2 digits of 2401^11 = 01

IMO A
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What are the last 2 digits of 7^49*143^5? 24 Aug 2019, 03:45
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Kinshook
What are the last 2 digits of 7^49*143^5?

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

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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What are the last 2 digits of 7^49*143^5? 03 Sep 2019, 14:49
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Archit3110
Kinshook
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
Show more

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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What are the last 2 digits of 7^49*143^5? 01 Jul 2024, 01:41
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Kinshook
What are the last 2 digits of 7^49*143^5?

A. 01
B. 07
C. 79
D. 41
E. 91
Show more
­
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.
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What are the last 2 digits of 7^49*143^5? 28 Aug 2024, 02:40
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stalinjacob

Kinshook
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.
Show more
Let me try and explain:

For 7^49:
7^1 = 07
7^2 = 49
7^3 = 343
7^4 = 2401
7^5 = 168'07'
7^6 = 1176'49'
7^7 = 8235'43'
7^8 = 57648'01'
As you can see from above, the last two digits are also cyclical for powers of 7 (07, 49, 43, 01.....)
Hence, last two digits for 7^49 (49 will be same as power of 1 for cyclicity) = 07

For 143^5:
3^1 = 03
3^2 = 09
3^3 = 27
3^4 = 81
3^5 = 2'43'
So the last two digits of 143^5 = Last two digits of 3^5 = 43

Using the two together:
Last two digits of 7^49 * 143^5 = 07 * 43 = 3'01'

Hence, Ans - (A) 01­

- Cheers
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