Question: The digit in the unit place of the number represented by `(7^95 - 3^58)` is :
A
7
B
0
C
6
D
4
Note: Unit digit in `7^4` is 1.
So, unit digit in `7^92` is 1.`:.` Unit digit in `7^95` is 3. [`:.` Unit digit in `1xx7xx7xx7` is 3]
Unit digit in `3^4` is 1.
`:.` Unit digit in `3^56` is 1.Unit digit in 3^58 is 9 [`:.` Unit digit in `1xx3xx3` is 9]
`:.` Unit digit in `(7^95 - 3^58)` is 4.
[Subtracting unit digit 9 from unit digit 3 ]
Question: If `a^3b` = abc = 180 and a, b, c are positive integers, then the value of c is :
A
110
B
25
C
15
D
None
Note: Since a , b, c are positive integer and 180 is not divisible by any of `2^3 , 3^3, 4^5` and `5^3`.
So , `a^3b ` = 180 is possible only when `a^3` = 1 and b = 180.
`:.`a = 1 and b = 180.
Now `a^3b ` = abc =>c = `a^2` = 1.