GMAT Practice Question: Dara ran on a treadmill that had a readout indicating the time remaining in her exercise...
Question
Dara ran on a treadmill that had a readout indicating the time remaining in her exercise session. When the readout indicated 24 min 18 sec , she had completed 10 \% of her exercise session. The readout indicated which of the following when she had completed 40 \% of her exercise session?
- 10 min 48 sec
- 14 min 52 sec
- 14 min 58 sec
- 16 min 6 sec
- 16 min 12 sec
Topics: word problems, percentages, conversions
Solution
Step 1
At \textbf{\text{10\% completion}}, the remaining time displayed is \textbf{\text{90\% of the total exercise duration}}.
0.9T = 24 \times 60 + 18
Step 2
Convert the remaining time of \textbf{\text{24 minutes 18 seconds}} to total seconds.
24 \times 60 + 18 = 1458
Step 3
Solve for the total time by dividing both sides by 0.9, rewriting as a fraction and canceling common factors.
T = \frac{1458}{0.9} = \frac{1458}{\frac{9}{10}} = 1458 \times \frac{10}{9} 1458 = 9 \times 162 \frac{1458}{9} = \frac{\cancel{9} \times 162}{\cancel{9}} = 162 T = 162 \times 10 = 1620
Step 4
At \textbf{\text{40\% completion}}, \textbf{\text{60\% of the total time}} remains. This uses the **Percents of** method to calculate 60\% of 1620.
0.6 \times 1620 = 972
Step 5
Convert 972 seconds back into minutes and seconds.
972 \div 60 = 16 \text{ remainder }12[[LB]]=16 \text{ min }12 \text{ sec}
Answer
E
