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The plot below shows the relationship between the mortality risk of cardiovascular disease and the number of steps a person walks per day. Based on the data, which one of the following options is true? A. The risk reduction on increasing the steps/day from 0 to 10000 is less than the risk reduction on increasing the steps/day from 10000 to 20000. B. The risk reduction on increasing the steps/day from 0 to 2000 is less than the risk reduction on increasing the steps/day from 10000 to 20000. C. For any 5000 increment in steps/day the largest risk reduction occurs on going from 0 to 5000. D. For any 5000 increment in steps/day the largest risk reduction occurs on going from 15000 to 20000.

GATE 2024 · General Aptitude · Line Graph · medium

Answer: Option C is the true statement: for any 5000-step increment, the largest risk reduction occurs when going from 0 to 5000 steps/day, because the curve is steepest (most concave) at the low end.

  1. Read the curve shape: The graph shows a strongly decreasing, concave curve. The steepest part is at very low step counts (0 to ~5000). Beyond 10000 steps the curve is nearly horizontal.
  2. Evaluate Option A: The curve drops dramatically from 0 to 10000 steps (most of the total fall). From 10000 to 20000 it barely moves. So risk drop[0,10000] >> risk drop[10000,20000]. Option A claims the opposite — FALSE.
  3. Evaluate Option B: Even the small 0 to 2000 segment at the steep part of the curve shows a visible drop. From 10000 to 20000 the curve is nearly flat. So risk_drop[0,2000] > risk_drop[10000,20000]. Option B claims the opposite — FALSE.
  4. Evaluate Option C: The 5000-step intervals to compare are [0,5000], [5000,10000], [10000,15000], [15000,20000]. The curve is steepest in [0,5000], giving the largest vertical drop. Each subsequent interval has a smaller drop. Option C states the largest risk reduction for any 5000-step increment occurs at [0,5000] — TRUE.
  5. Evaluate Option D: Option D claims the largest 5000-step risk reduction is from 15000 to 20000. This is the flattest part of the curve — the smallest, not the largest, reduction. Option D is FALSE.