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

 

51 + 52 + 53 + ...........+ 100

 = (1 + 2 + 3 + .... + 100) - (1 + 2 + 3 + ...... + 50)

 = It is in the form of n(n+1)2 series summation

= n1 = 100 , n2 = 50

=100100+12 - 5050+12

 =  (5050 - 1275) = 3775

Divisor = 

           = 

$$\begin{gathered} 2211 x 75 x 112 \\ => 222 x 75 x 112 \end{gathered}$$

 Total number of prime factors is (22+5+2) = 29

The sum of n natural numbers 

Step 1 :2x + 5y

Step 2 :3(2x + 5y) = 6x + 15y

Step 3 :(6x + 15y) - (x +y) = 6x + 15y - x - y (watch that last minus sign!)

This gives 5x + 14y

In case (A), x and y could, for example, both be equal fractions and x/y would be an integer.

The weight will be 250g plus (1.55 - 0.65)/0.10 units of 100g

250 + 900 = 1150

This is the maximum weight that can be sent at that price. But, weights exceeding

250 + 800 will also get charged this amount (that is what the ‘part thereof’ implies).

Hence a package weighing 1145 will be charged $1145

To solve a pair of simultaneous equations such as those given we can add or subtract them.

Adding we get 4x + 4y = 20

Therefore 2x + 2y = 10