The classification of 100 students based on the marks obtained by them in English and Mathematics in an examination is given in the table below. Study the table and answer the question that follows. MARKS OUT OF 50 SUBJECT 40 and above 30 and above 20 and above 10 and above 0 and above ENGLISH 10 31 80 92 100 MATHEMATICS 3 23 65 81 100 AGGREGATE 7 27 73 87 100 If at least 40% marks in Mathematics are required for pursuing higher studies in Mathematics, how many students will be eligible to pursue higher studies in Mathematics?
- (a)65
- (b)70
- (c)55
- (d)50
Answer
Why
Correct — A. The percentage has to become a mark before the table can be read.
Marks are out of 50, so the cut-off is 40% of 50 = 0.40 × 50 = 20 marks.
The rows are cumulative: each figure counts everyone at that mark and above, so no adding or subtracting of cells is needed.
Read across the MATHEMATICS row to the "20 and above" column: 65 students clear 20 marks → option (a).
Why the others are wrong
- (b)70 — 70 is printed nowhere in the Mathematics row, which reads 3, 23, 65, 81, 100. The nearby 73 belongs to the AGGREGATE row, and the question names Mathematics.
- (c)55 — 55 does not appear anywhere in the table. A cumulative row is read straight off; combining cells is only needed when a question asks for a band such as 20 to 29.
- (d)50 — 50 is the paper's maximum mark, not a count of students. The 50 in the stem fixes the denominator of the percentage; it never enters the answer.
Concept
This is a cumulative frequency table of the "and above" kind. Every cell counts all students at that mark or higher, so the figures fall as you move left to right across the headings and reach 100 under "0 and above".
Two readings follow from that. A single cut-off is one cell — here "20 and above" in the Mathematics row. A band between two marks is the difference of two adjacent cells.
The only extra step this question adds is converting the eligibility rule, 40% of a 50-mark paper, into the 20-mark column heading.
The AGGREGATE row is a third series in its own right, not the sum of the other two: English and Mathematics read 80 and 65 at "20 and above", which total 145, while the aggregate cell reads 73. Use the row the question names.
Key facts
- In an "and above" table, the "30 and above" figure already contains everyone counted under "40 and above".
- Each subject row reaches 100 under "0 and above", because 100 students were classified.
- 40% of a 50-mark paper is 20 marks, so the eligibility column is "20 and above".
- The Mathematics row reads 3, 23, 65, 81, 100 across the five headings.
Study next
Common traps
- Jumping to the "40 and above" column because the stem says 40%, which gives 3.
- Taking the AGGREGATE row when the question names Mathematics.
- Subtracting adjacent cells out of habit when a single cumulative cell is what was asked for.
A data-interpretation item turns on which row and which column you pick, and often on converting the stem's own wording — here a percentage — into the table's units before you read anything.
Also asked 18 Sep 2024, 16:00, Quant Q.9, where a table of company employee totals plus male and female percentages has to be combined across three companies.
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