Question 32

Select the number that can replace the question mark (?) in the following series.

19, 20, 24, 51, 67, ?

Solution

In the given series,

20 - 19 = 1 = 1$$^3$$

24 - 20 = 4 = 2$$^2$$

51 - 24 = 27 = 3$$^3$$

67 - 51 = 16 = 4$$^2$$

The difference between numbers of the series are square and cubes of natural numbers alternatively.

The next difference should be 5$$^3$$

Let the required number be 'a'

$$\Rightarrow$$  a - 67 = 5$$^3$$

$$\Rightarrow$$  a = 125 + 67

$$\Rightarrow$$  a = 192

$$\therefore\ $$Required number = 192

Hence, the correct answer is Option B


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