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?

A. 10 min 48 sec
B. 14 min 52 sec
C. 14 min 58 sec
D. 16 min 6 sec
E. 16 min 12 sec

We are given that Dara completed 10% of her exercise session when the readout indicated 24 min and 18 seconds as her time remaining. In other words she had 90% left of her workout at that time. We need to determine the readout after she has completed 40% of her exercise, or when she has 60% left.

We can create a proportion to determine the time when Dara has 60% left. First, let's convert 24 min 18 sec to minutes.

24 min 18 sec = (24 + 18/60) min = (24 + 3/10) min = 24.3 min

We can also express 90 percent as 90/100 = 0.9 and 60 percent as 60/100 = 0.6. We define x as the number of minutes remaining in her workout when she has 60%, or 0.6, of her workout left to do.

Our proportion is as follows:

0.9/24.3 = 0.6/x

9/243 = 0.6/x

9x = 145.8

x = 145.8/9 = 16.2 min

Thus, x = (16 + 2/10) min = (16 + 12/60) min = 16 min 12 sec.

Answer: E

Hi lucas211,

While this question is a bit quirky, once you figure out the total time when the clock STARTED, then the rest of the work should be pretty easy. Since none of the answer choices include fractions, it's likely that the TOTAL time is an integer. You know that when 10% of the time is passed, the clock says 24 min 18 seconds.... It's helpful to remember that 10% of 1 minute = 6 seconds.

Could the total time be 25 minutes?
10% of 25 minutes = (6)(25) = 150 seconds = 2.5 minutes
25 minutes - 2.5 minutes = 22.5 minutes

This does NOT match what we were told though (there's supposed to be 24 min. 18 secs left), so clearly the TOTAL time has to be GREATER than 25 minutes.

Could the total time be 27 minutes?
10% of 25 minutes = (6)(27) = 162 seconds = 2 minutes 42 seconds
27 minutes - (2 minutes 42 seconds) = 24 minutes 18 seconds

This IS a match for what we were told, so the starting time must have been 27 minutes. From here, we can determine 40% of 27 minutes....
(4)(6)(27) = 648 seconds = 10 minutes 48 seconds
Thus, the remaining time was: 27 minutes - (10 minutes 48 seconds) = 16 minutes 12 seconds.

Final Answer: E

GMAT assassins aren't born, they're made,
Rich