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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