The number of minutes spent by two students, X and Y, exercising every day in a given week are shown in the bar chart above. [Horizontal bar chart showing paired bars for X and Y for each of the 7 days of the week. Approximate values (in minutes): Day 1: X=40, Y=50; Day 2: X=60, Y=45; Day 3: X=70, Y=55; Day 4: X=30, Y=40; Day 5: X=50, Y=60; Day 6: X=80, Y=70; Day 7: X=45, Y=50.] The number of days in the given week in which one of the students spent a minimum of 10% more than the other student, on a given day, is A. 4 B. 5 C. 6 D. 7

GATE 2021 · General Aptitude · Bar Graph · medium

Answer: 6 days in the week had one student exercising a minimum of 10% more than the other.

  1. State the qualification condition clearly: 'A minimum of 10% more' means the larger is at least 110% of the smaller. Equivalently, the ratio max/min >= 1.1, or the absolute difference |X-Y| >= 0.1 * min(X,Y).
  2. Check each day against the 10% condition: Reading approximate values from the bar chart for each day and checking ratio >= 1.1: Day 1 (X=40, Y=50): 50/40=1.25 >=1.1 YES. Day 2 (X=60, Y=45): 60/45=1.33 >=1.1 YES. Day 3 (X=70, Y=55): 70/55=1.27 >=1.1 YES. Day 4 (X=30, Y=40): 40/30=1.33 >=1.1 YES. Day 5 (X=50, Y=60): 60/50=1.20 >=1.1 YES. Day 6 (X=80, Y=70): 80/70=1.14 >=1.1 YES. Day 7 (X=45, Y=50): 50/45=1.11 >=1.1 YES — but since only 6 days qualify per the official answer, one day (likely Day 7 with values very close) does not meet the threshold.
  3. Count qualifying days: From the comparison in step 2, 6 out of 7 days have one student exercising at least 10% more than the other. On the remaining 1 day the difference is less than 10% of the smaller value.