Which of the following can be used to illustrate that not all prime numbers are odd? 

 

On dividing we get

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

87)13601(156
       87
       -----
       490
       435
        -----
        551
        522
         -----
         29
         -----
Required number is 29.

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.

Let the number  be 476ab0 

476ab0 is divisible by 3 

=> 4 + 7 + 6 + a + b + 0 is divisible by 3

=> 17 + a + b is divisible by 3 ------------------------(i)

476ab0 is divisible by 11

[(4 + 6 + b) -(7 + a + 0)] is 0 or divisible by 11

=> [3 + (b - a)] is 0 or divisible by 11  --------------(ii)

Substitute the values of a and b with the values given in the choices and select the values which satisfies both Equation 1 and Equation 2.

if a=6 and b=2, 

17 + a + b = 17 + 6 + 2 = 25 which is not divisible by 3 --- Does not meet equation(i).Hence this is not the answer

if a=8 and b=2, 

17 + a + b = 17 + 8 + 2 = 27 which is divisible by 3 --- Meet equation(i)

[3 + (b - a)] = [3 + (2 - 8)] = -3 which is neither 0 nor divisible by 11---Does not meet equation(ii).Hence this is not the answer

if a=6 and b=5, 

17 + a + b = 17 + 6 + 5 = 28 which is not divisible by 3 --- Does not meet equation (i) .Hence this is not the answer

if a=8 and b=5, 

17 + a + b = 17 + 8 + 5 = 30 which is divisible by 3 --- Meet equation 1

[3 + (b - a)] = [3 + (5 - 8)] = 0 ---Meet equation 2

Since these values satisfies both equation 1 and equation 2, this is the answer

Clearly 4864 is divisible by 4
So, 9 P 2 must be divisible by 3. So (9+P+2) must be divisible by 3.
So P=1.

Given exp . is like this 854*854*854-276*276*276854*854+854*276+276*276=?

so ans = 854 - 276 = 578

given sum =9+34+7+217-9+115

9+7+9+34+217-115

=> 7+765+120-681020=>7+8171020 

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