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Last two digits of 21^(100) are...

Last two digits of `21^(100)` are

A

a) 0

B

b) 1

C

c) 11

D

d) 01

Text Solution

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The correct Answer is:
B
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Consider the number 2751. The sum of its digital is 2+7+5+1=15 . Adding the digits of 15 we get 1+5=6 . This number 6 is called the 'digital root' of the number 2751. That is, to find the digital root of a number, find the sum of its digits (Don't forget to find the sum of the digits again, if the first sum has more than one digit) Let us see one more example. The sum of the digits of the numbe 679412 is 6+7+9+4+1+2=29 . Sum of digits of 29=2+9=11 . Sum of digits of 11=1+1=2 . Therefore the digital root of 679412 is 2 . Digital roots have an interesting property. To see this, consider the product 43times27=1161 . The digital roots of the numbers 43 and 27 are 4+3=7 and 2+7=9 . Product of the digital roots= 7times9=63 . Digital root of 63=6+3=9 . The Digital root of 1161 is also 9(1+1+6+1=9) that is the digital root of 1161 =The digital root of 63 , where 63 is the product of the digital roots of 43 and 27. This property is true for all other natural numbers. What is the digital root of 345times927 ?

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