Numbers Questions

Let n=4*q + 3. Then, 2*n = 8*q + 6 = 4(2*q + 1) + 2.
Thus when 2*n is divided by 4, the reminder is 2.

The mutiplicative inverse of a number is nothing but a reciprocal of a number.

Now, the product of a number and its multiplicative inverse is always equal to 1.

For example :

Let the number be 15

Multiplicative inverse of 15 = 1/15

The product of a number and its multiplicative inverse is = 15 x 1/15 = 1.

Let a and b are the numbers.Then a+b is 12 and ab is 35.

a+b/ab = 12/35

1/b + 1/a = 12/35

2n+2n22x2n - 2n = 2n1 + 122n(2-1) = 32

On dividing we get

75)8485(113
     75
     ------
       98
       75
      ------
       235
       225
      ------
         10
      ------
Required number = (8485-10)=8475.

(kx22)/100 = 340 - 166.64 = 173.36
k = (173.36 x 100)/22
k = 788

By trial and error method, we get
2880/3 = 960 is not a perfect square
2880/4 = 720 is not a perfect square
2880/5 = 576 which is perfect square of 24
Hence, 5 is the least number by which 2880 must be divided in order to make it into a perfect square.

Let the numbers be x and (x-11)

   x = 28

 Another Number is (28 - 11) = 17