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GMAT Practice Exam 6 - Word problem

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by GMATGuruNY » Sun Jun 26, 2016 4:25 am
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
Test an EASY CASE.
Let the total exercise session = 10 minutes.

After 10% of the exercise session -- in other words, after Dara has run for 1 of the 10 minutes -- the time remaining = 9 minutes.
After 40% of the exercise session -- in other words, after Dara has run for 4 of the 10 minutes -- the time remaining = 6 minutes.
(remaining time after 40% )/(remaining time after 10%) = 6/9 = 2/3.

Implication:
At the 40% mark, the remaining time will be 2/3 of the remaining time at the 10% mark.
Thus:
Remaining time at the 40% mark = (2/3)(24 minutes and 18 seconds) = 16 minutes and 12 seconds.

The correct answer is E.
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by DavidG@VeritasPrep » Sun Jun 26, 2016 9:58 am
lucas211 wrote:Hello BTG

Would someone be kind to help with an approach to this question:

Thanks
If Dara has completed 10% of her workout, we know she has 90% of her workout remaining. So, that 24 min. 18 sec. presents 90% of her total workout. If we designate her total workout time as "t," we end up with the following equation:

24 min. 18 sec. = 0.90t

18 seconds is 18/60 minutes, which simplifies to 3/10 minutes. 0.9 is 9/10, so we can rewrite our equation as:

24 + 3/10 = (9/10)t
(243/10) = (9/10)t
(243/10)*(10/9) = t
27 = t

Dara's full workout is 27 minutes long.

We want to know how much time is remaining when Dara has completed 40% of her workout. Well, if she's completed 40% of her workout, we know she has 60% of her workout remaining. If her full workout is 27 minutes, then 60% of this value is 0.60*27 = (3/5)*27 = 81/5 = 16 + 1/5, or 16 minutes 12 seconds. And we've got our answer: E.
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by DavidG@VeritasPrep » Sun Jun 26, 2016 9:59 am
Or we can estimate.

Say, instead of 24 min 18 seconds remaining, Dara had 24 minutes remaining (so we know we're going to underestimate the answer). If that's 90% of her workout time, 24 = (9/10)t, or 240/9 = t.

We want 60% of this, so we want (240/9)*(3/5).

Because 240/5 = 48 and 9/3 = 3, (240/9)*(3/5) = 48/3 = 16.

We know that the correct answer is over 16 minutes and that we've significantly underestimated - makes sense to go with E.
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by OptimusPrep » Sun Jun 26, 2016 10:24 am
lucas211 wrote:Hello BTG

Would someone be kind to help with an approach to this 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?

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

Thanks
Time remaining when 10% of session completed = 24 mins and 18 seconds.
Let us covert everything in seconds to calculate the total time.

24 mins 18 seconds = 24*60 + 18 = 1440 + 18 = 1458
90% of time = 1458 seconds.

100% of time = 1458*10/9 = 1620 seconds
40% completed = 60% remaining.
Time remaining = 0.6*1620 = 972seconds = 960 + 12 seconds = 16 minutes 12 seconds.

Correct Option: E
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by Scott@TargetTestPrep » Wed Nov 29, 2017 5:16 pm
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

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by [email protected] » Wed Nov 29, 2017 6:41 pm
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

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