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What is the tens digit of 7^381?

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by Max@Math Revolution » Thu Aug 04, 2016 6:25 pm
What is the tens digit of 7^381?
A. 0
B. 3
C. 5
D. 7
E. 9

*An answer will be posted in 2 days
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by Manonamission » Mon Aug 08, 2016 12:32 pm
Hello,

Have given it a try. Please see if this is correct?

7 * 1 = 07
7*7 = 49
7*7*7 = 343
7*7*7*7 = 2401
7*7*7*7*7 = 16807

Hence, cyclicity of 7 is 4.
Tens digit of an odd number - Number form when it ends with 1. (7*7*7*7 = 2401)

So, it can be re-written as (7^4)^95.25 [ 381/4 = 95.25]

The units digit is always equal to 1.The tens digit of a number that ends with 1 is equal to
the last digit of the power multiplied by the d tens digit of the number.

last digit of power = 5
Tens digit of number = 7*7*7*7 = 2401 = 0

Hence, required value 7^381 is 5 *0 = 0

Regards,
MoM
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by Max@Math Revolution » Mon Aug 08, 2016 5:18 pm
From ~7^1=~07, ~7^2=~49, ~7^3=~43, ~7^4=~01, the tens digit repeats 0-->4-->4-->0-->0. Then, from 7^381=7^(4(95)+1), the tens digit is same as ~7^1. Hence, it is 0.
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by Manonamission » Tue Aug 09, 2016 4:53 am
Max@Math Revolution wrote:From ~7^1=~07, ~7^2=~49, ~7^3=~43, ~7^4=~01, the tens digit repeats 0-->4-->4-->0-->0. Then, from 7^381=7^(4(95)+1), the tens digit is same as ~7^1. Hence, it is 0.
Hello Max,
What's the difference between (7^4)^95.25 AND 7^(4(95)+1)?

This is to find the ten's digit of an odd number.

Regards,
MoM
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