Question : Study the given pie charts and answer the question that follows.
The number of students who passed the examination from Institute D exceeds the number of students who appeared from Institute A is $x$. The value of $x$ lies between:
Option 1: 11 and 14
Option 2: 5 and 8
Option 3: 14 and 17
Option 4: 8 and 11
Correct Answer: 11 and 14
Solution :
From the pie chart, the percentage of students who passed Institute D is 28%.
The number of students who passed Institute D is 28% of 900 = 252 students
The degree of the sector for Institute A in the pie chart representing students appeared is $72^\circ$.
The number of students who appeared from Institute A $=\frac{72^\circ}{360^\circ} \times 1200 = 240$ students
Therefore, the number of students who passed the examination from Institute D exceeds the number of students who appeared from Institute A $ = 252 - 240 = 12$, which is between 11 and 14
Hence, the correct answer is 11 and 14.
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