Question 45

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

213, 217, 233, 269, ?

Solution

217 - 213 = 4 = 2$$^2$$

233 - 217 = 16 = 4$$^2$$

269 - 233 = 36 = 6$$^2$$

The difference between the consecutive numbers of the series are squares of even numbers.

The next difference is 8$$^2$$ = 64

Let the required number = a

$$\Rightarrow$$ a - 269 = 64

$$\Rightarrow$$ a = 333

$$\therefore\ $$The required number = 333

Hence, the correct answer is Option B

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