Directions : Read the pie chart carefully and answer the following question.…
2023
Directions : Read the pie chart carefully and answer the following question.
Pie chart given below shows the percentage distribution of questions attempted by four different (A, B, C and D) students in an exam. Exam contains three subjects English, History and Mathematics which consist of 120, 60 and 100 questions respectively.
Maximum number of questions attempted by each student is 240 and total number of questions attempted by all the students is 800.
If C attempted 54 questions in History and questions attempted in English are more than that of history but less than that in Mathematics, then find possible number of questions attempted in Mathematics by C.
- A.
81
- B.
75
- C.
70
- D.
none of these
- E.
all of these
Show answer & explanation
Correct answer: E
Concept
In a pie chart, each sector's percentage of the whole gives that part's share of the grand total. To find one student's count, multiply the grand total by that student's percentage. When a quantity is split across categories with both upper limits and inequality conditions, list every integer split that satisfies all conditions simultaneously, then read off the possible values for the asked quantity.
Application
From the pie chart, student C's share is 24%, and the total questions attempted by all students is 800. So C's total attempted = 24% of 800 = 192.
Let English = E and Mathematics = M for C. With History = 54, the three subjects add to C's total: E + 54 + M = 192, so E + M = 138.
Apply the conditions. English is more than History: E > 54. English is less than Mathematics: E < M. Subject caps are English ≤ 120, History ≤ 60, Mathematics ≤ 100, and History = 54 already fits its cap of 60.
From E < M with E + M = 138, we get E < 69; combined with E > 54 this gives E ranging over 55 to 68. The matching M = 138 − E then ranges over 70 to 83, and every such M satisfies M ≤ 100.
So the possible Mathematics counts for C are every integer from 70 to 83 inclusive.
Cross-check
Check the three numeric choices against the 70–83 range. 70 comes from E = 68, M = 70 (68 > 54 and 68 < 70 ✓). 75 comes from E = 63, M = 75 (63 > 54 and 63 < 75 ✓). 81 comes from E = 57, M = 81 (57 > 54 and 57 < 81 ✓). All three values are attainable, so every listed numeric value is a valid answer.