Study the following table and answer the question. Classification of 100…
2024
Study the following table and answer the question. Classification of 100 Students Based on the Marks Obtained by them in Physics and Chemistry in an Examination.
If it is known that at least 23 students were eligible for a Symposium on Chemistry, then the minimum qualifying marks in Chemistry for eligibility to the Symposium would lie in the range?
- A.
40-45
- B.
30-40
- C.
20-30
- D.
Below 20
Show answer & explanation
Correct answer: C
Concept: In a data-interpretation table, the "X and above" row is a cumulative frequency distribution — it can only stay the same or increase as the cutoff mark falls. The minimum qualifying mark for at least N students to be eligible is the highest cutoff at which this cumulative count first reaches (or exceeds) N.
Application: From the table, the Chemistry cumulative counts by cutoff are:
Marks Cutoff | Students Scoring at or Above (Chemistry) |
|---|---|
40 and above | 4 |
30 and above | 21 |
20 and above | 66 |
10 and above | 81 |
0 and above | 100 |
At least 23 students must be eligible.
At a cutoff of 40, only 4 students qualify — far short of 23.
At a cutoff of 30, only 21 students qualify — still 2 short of 23.
At a cutoff of 20, 66 students qualify — well past 23.
Because the count rises from 21 to 66 as the cutoff falls from 30 to 20, the 23rd qualifying student is reached at some mark strictly between 20 and 30 — not at 30 itself, since only 21 students qualify there. So the minimum qualifying mark in Chemistry lies in the range 20-30.
Cross-check: 66 - 21 = 45 students scored between 20 and 29 in Chemistry. Reaching 23 needs only 2 more students beyond the 21 who scored 30 and above, and the 20-29 band comfortably contains them. This rules out a cutoff as high as 30 (falls short by 2) and rules out going as low as 10 or 0 (which would overshoot 23 far more than necessary), confirming the 20-30 range.