Discussion
A school has 3 sections, A, B and C, of class VI students. The results of half-yearly and annual examinations are shown in the given table.
Answer the question based on this table.
| Result | Number of students | ||
|---|---|---|---|
| Section A | Section B | Section C | |
| Students who failed in both exams | 14 | 21 | 15 |
| Students who failed in the half-yearly but passed in the annual exams | 12 | 10 | 9 |
| Students who passed in the half-yearly but failed in the annual exams | 8 | 14 | 11 |
| Students who passed in both exams | 52 | 58 | 62 |
How many students are there in class VI in the school?
Answer: A
There are 286 students in class VI. Add the students in each row of the table across the three sections. Failed in both: 14 + 21 + 15 = 50. Failed in the half-yearly but passed in the annual: 12 + 10 + 9 = 31. Passed in the half-yearly but failed in the annual: 8 + 14 + 11 = 33. Passed in both: 52 + 58 + 62 = 172. The four groups cover every student exactly once, so the total is 50 + 31 + 33 + 172 = 286. The option 172 is only the number who passed both exams, and 276 and 196 do not match any sum of the groups.
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