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 degrees C) and a month in summer (average temperature 30 degrees C).
Consider the following statements based on the data shown above:
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 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?
A. Only i
B. Only ii
C. Both i and ii
D. Neither i nor ii
GATE 2017 · General Aptitude · Line Graph · medium
Answer: Only statement ii is correct. The ranges differ between seasons, but there are at least four days where the seasonal concentrations are within 1 ppm of each other.
Check statement i: compare range (max - min) for winter vs summer: From the graph, the winter curve ranges from approximately 8 ppm (min) to about 16 ppm (max), giving a range of ~8 ppm. The summer curve ranges from approximately 4 ppm (min) to about 14 ppm (max), giving a range of ~10 ppm. The ranges are NOT equal, so statement i is FALSE.
Check statement ii: count days where |winter - summer| <= 1 ppm: Reading the graph at corresponding day-positions: around days 11, 17, 19, and 25 the two curves nearly overlap or cross, meaning their concentrations are within 1 ppm. Counting these carefully gives at least 4 such days (the curves converge in the mid-to-late portion of the month). Statement ii is TRUE.
Select the correct option: Statement i is false; statement ii is true. The option 'Only ii' matches this conclusion.