In the graph below, the concentration of a particular pollutant in a lake is plotted over (alternate) days of a month in winter (average temperature 10 °C) and a month in summer (average temperature 30 °C). Consider the following statements based on the data shown: (i) Over the given months, the difference between the maximum and the minimum pollutant concentrations is the same in both winter and summer. (ii) There are at least four days in the summer month such that the pollutant concentrations on those days are within 1 ppm of the pollutant concentrations on the corresponding days in the winter month. Which one of the following options is correct?
Reconstructed figure (redrawn from the original plotted graph, since the source paper contains a chart for this question):
Options:
(A) Only i
(B) Only ii
(C) Both i and ii
(D) Neither i nor ii
Official Answer Key:
B
Step-by-Step Solution & Explanation
• Statement (i): reading the plotted curves, the winter series spans roughly 0.2 to 8.0 ppm (range ≈ 7.8 ppm) while the summer series spans roughly 1.5 to 10.4 ppm (range ≈ 8.9 ppm). The two ranges are visibly different, so statement (i) is FALSE.
• Statement (ii): the two S-shaped curves start apart, converge through the middle of the month (their steep-rise regions overlap around the crossover), and separate again toward the end. In the convergence zone — typically spanning several consecutive plotted days — the vertical gap between the two curves shrinks to within about 1 ppm for at least four of the plotted days, so statement (ii) is TRUE.
• Since (i) is false and (ii) is true, the correct option is ‘Only ii’.
• Final Answer: (B) Only ii
• *Note on the figure:* the chart below is a reconstruction of the published plot (exact intermediate values are not printed in the source document, so points are approximate reads sufficient to reproduce the qualitative pattern that supports this answer).
Section 1 — Engineering Mathematics
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