Tag: maths

The difference between $88.888$ and $100$ is,

In the given sequence there are 3 such combinations where an even number is immediately preceded by an odd number and immediately followed by even number.

Let the required number be $n$
Then, $3n+9=45$
$\Rightarrow$  $3n=45-9$
$\Rightarrow$  $3n=36$
$\Rightarrow$  $n=\cfrac{36}{3}=12$
Hence the required number is $12$

Place value of $5$ in
$91,25,678 = 5000$
Face value of $5$ in
$91,25,678 = 5$
$\displaystyle \therefore $ difference  $= 5000 - 5
= 4995$

Sum of face values of all the digits of 
$749205=7+4+9+2+0+5=27$

Lets take an example : $245$- place value for Hundred's place digit is $200$ and face value is $2$.

$2015! + 3^{7886}$

$2015! \Rightarrow$ Unit digit $\Rightarrow \underline { 0 }$

$3^{7886}=3^{4n+2}$, So unit digit $\Rightarrow 9$

$\therefore 0+9 \Rightarrow \underline{9}$.

$\therefore$ Digit at unit place $\Rightarrow 9$ 

The face value of a digit is the digit itself, regardless of its position in the number. Therefore, the sum of the face values of 4 and 8 is 4 + 8 = 12.

Using Euler's totient theorem, phi(100) = 40. Since 3 and 100 are coprime, 3^40 is congruent to 1 mod 100. Thus, 3^400 = (3^40)^10 is congruent to 1^10 = 1 mod 100. The last two digits are 01.

Let the numbers Of all kind is $x$