The mean of 5 consecutive odd numbers of set A is 37. What will be the average of set B containing four consecutive even numbers if the smallest number of set B is 13 more than the greatest number of set A?

1. 53

2. 55

3. 57

4. 59

Five consecutive odd numbers = x - 4, x - 2, x, x + 2, x + 4.

By formula,

$\Rightarrow \text{Mean} = \dfrac{\sum x_i}{n} \\[1em] \Rightarrow 37 = \dfrac{(x - 4) + (x - 2) + x + (x + 2) + (x + 4)}{5} \\[1em] \Rightarrow 37 \times 5 = 5x \\[1em] \Rightarrow x = 37.$

Set A = 33, 35, 37, 39, 41

Smallest number of Set B = 41 + 13 = 54

Set B = 54, 56, 58, 60

$\text{Average} = \dfrac{\text{ Sum of all observations}}{\text{ Number of observations}} \\[1em] = \dfrac{54 + 56 + 58 + 60}{4} \\[1em] = \dfrac{228}{4} \\[1em] = 57.$

Hence, option 3 is the correct option.