GATE EE 2021 Set 1 — Question 9
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General Aptitude → Quantitative Aptitude → Data Interpretation (Bar, Pie, Graphs, Tables)
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Question
The number of students who took the exam for the first time in the year 2 and the year 3 respectively, are
Correct answer
(D) 55 and 48
Solution
Let's extract the data from the bar chart:Year 1:
Students Passed = 50
Students Failed = 10
Total Students in Year 1 = 50 + 10 = 60Year 2:
Students Passed = 60
Students Failed = 5
Total Students in Year 2 = 60 + 5 = 65Year 3:
Students Passed = 50
Students Failed = 3
Total Students in Year 3 = 50 + 3 = 53Now, let's apply the given conditions:
Total students who appeared in Year 2 = 65.
From condition 2, students who failed in Year 1 (10 students) must reappear in Year 2. From condition 3, they will pass in Year 2.
So, the 10 students who failed in Year 1 are part of the 65 students in Year 2, and they are not taking the exam for the first time.
Number of students who took the exam for the first time in Year 2 = (Total students in Year 2) - (Students who failed in Year 1 and reappeared)
= 65 - 10 = 55.Calculate students who took the exam for the first time in Year 3:
Total students who appeared in Year 3 = 53.
From condition 2, students who failed in Year 2 (5 students) must reappear in Year 3. From condition 3, they will pass in Year 3.
So, the 5 students who failed in Year 2 are part of the 53 students in Year 3, and they are not taking the exam for the first time.
Number of students who took the exam for the first time in Year 3 = (Total students in Year 3) - (Students who failed in Year 2 and reappeared)
= 53 - 5 = 48.Therefore, the number of students who took the exam for the first time in Year 2 and Year 3 respectively are 55 and 48.The final answer is .
Students Passed = 50
Students Failed = 10
Total Students in Year 1 = 50 + 10 = 60Year 2:
Students Passed = 60
Students Failed = 5
Total Students in Year 2 = 60 + 5 = 65Year 3:
Students Passed = 50
Students Failed = 3
Total Students in Year 3 = 50 + 3 = 53Now, let's apply the given conditions:
1."Students who pass the exam cannot appear for the exam again."
2."Students who fail the exam in the first attempt must appear for the exam in the following year."
3."Students always pass the exam in their second attempt."
Calculate students who took the exam for the first time in Year 2:Total students who appeared in Year 2 = 65.
From condition 2, students who failed in Year 1 (10 students) must reappear in Year 2. From condition 3, they will pass in Year 2.
So, the 10 students who failed in Year 1 are part of the 65 students in Year 2, and they are not taking the exam for the first time.
Number of students who took the exam for the first time in Year 2 = (Total students in Year 2) - (Students who failed in Year 1 and reappeared)
= 65 - 10 = 55.Calculate students who took the exam for the first time in Year 3:
Total students who appeared in Year 3 = 53.
From condition 2, students who failed in Year 2 (5 students) must reappear in Year 3. From condition 3, they will pass in Year 3.
So, the 5 students who failed in Year 2 are part of the 53 students in Year 3, and they are not taking the exam for the first time.
Number of students who took the exam for the first time in Year 3 = (Total students in Year 3) - (Students who failed in Year 2 and reappeared)
= 53 - 5 = 48.Therefore, the number of students who took the exam for the first time in Year 2 and Year 3 respectively are 55 and 48.The final answer is .
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