Question : Directions: Which of the following numbers will replace the question mark (?) in the given series?
$\left [ \frac{1}{176} \right ],\left [ \frac{1}{88} \right ],?,\left [ \frac{1}{22} \right ],\left [ \frac{1}{11} \right ]$
Option 1: $\left[\frac{1}{32}\right]$
Option 2: $\left\lceil\frac{1}{44}\right]$
Option 3: $\left\lceil\frac{1}{48}\right]$
Option 4: $\left\lceil\frac{1}{42}\right]$
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Correct Answer: $\left\lceil\frac{1}{44}\right]$
Solution :
Given:
$\left[\frac{1}{176}\right],\left[\frac{1}{88}\right], ?,\left[\frac{1}{22}\right],\left[\frac{1}{11}\right]$
In the above-given series, the numerator will remain the same and the denominator will be divided by 2.
$\left[\frac{1}{176}\right]$; 176 ÷ 2 = 88; $\left[\frac{1}{88}\right]$
$\left[\frac{1}{88}\right]$; 88 ÷ 2 = 44; $\left[\frac{1}{44}\right]$
$\left[\frac{1}{44}\right]$; 44 ÷ 2 = 22; $\left[\frac{1}{22}\right]$
$\left[\frac{1}{22}\right]$; 22 ÷ 2 = 11; $\left[\frac{1}{11}\right]$
So, $\left[\frac{1}{44}\right]$ is the missing number of the series. Hence, the second option is correct.
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