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by dferm » Thu Aug 07, 2008 11:59 am
Did it take Pei more than 2 hours to walk a distance of 10 miles along a certain trail? (1mile=1.6 Kilometers, rounded to the nearest tenth)

(1) Pei walked this distance at an average rate of less than 6.4 kilometers per hour

(2) On average, it took Pei more than 9 minutes per Kilometers to walk this distance.

Can someone please shed some light on this Problem?

Thanks.

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by [email protected] » Thu Aug 07, 2008 12:49 pm
dferm wrote:Did it take Pei more than 2 hours to walk a distance of 10 miles along a certain trail? (1mile=1.6 Kilometers, rounded to the nearest tenth)

(1) Pei walked this distance at an average rate of less than 6.4 kilometers per hour

(2) On average, it took Pei more than 9 minutes per Kilometers to walk this distance.

Can someone please shed some light on this Problem?

Thanks.
Let's start by jotting down the relevant formula:

Distance = rate * time

We know that D=10 miles, which is 16km. Since the statements are all about kilometres, let's use that as our distance. So:

16 = r * t

and the question is: Is t > 2?

(1) r < 6.4

Let's think about the least amount of time it could take. To minimize time, we want to maximize rate, which in this case is 6.399999 km/h, or approx 6.4 km/h.

In that case, t = 16/6.4

Well, we know that 16/6.4 is greater than 2 (which is all that we care about). So, did it take Pei more than 2 hours? Definitely YES - sufficient.

(2) time per kilometre > 9 minutes.

So, the minimum possible time for the entire trip is 9 min * 16.4km, which is more than 120 minutes (again, the 2 hour mark is all we care about). Did it take Pei more than 2 hours? Definitely YES - sufficent.

(1) and (2) are each sufficient on their own: choose (D).

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by dferm » Fri Aug 08, 2008 5:38 am

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by GMAT dreamer » Mon Nov 17, 2008 10:03 am

It says that took Pei an avarage of 9 min per Km to walk the distance...
We know that in each 9 minutes he walked 1 Km; so to complete the entire journey ( 16 km), he needs to walk 16 km x 9 min = 144.
144 min> 2h, suffic.

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by cramya » Mon Nov 17, 2008 4:16 pm
Refer to

https://www.beatthegmat.com/gmat-prep-t15734.html

I have added my 2 cents worth also

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by Poisson » Mon Aug 29, 2016 6:01 am

It says that took Pei an avarage of 9 min per Km to walk the distance...
We know that in each 9 minutes he walked 1 Km; so to complete the entire journey ( 16 km), he needs to walk 16 km x 9 min = 144.
144 min> 2h, suffic.
I'm using the formula D = R*T

For Distance, I have 16 km. For Rate, I have 9 mins/ 1 km. Usually, I convert the units and divide distance by rate to get the time.

I'm trying to convert 9 mins/1 km to hours per km so that the units in the prompt (2 hours) matches the units in the rates. Could someone please show me the proper way to convert 9 mins/ km to hours?

I get (9 mins / 1 km) * ( 1 hr / 60 mins) = 9 hrs / 60 km. Is this correct? After I do the math I get 106 hours and this doesn't seem right.

Thanks so much.

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by [email protected] » Mon Aug 29, 2016 9:43 am
Hi Poisson,

Converting information into hours-per-km is not typical (km-per-hour is a measure that more people would likely be comfortable with). However, you can absolutely set up the calculation as you have - you just have to complete the calculation. Once you get to...

9 hrs / 60 km

You then have to divide 'top' and 'bottom' by 60....

(9/60 hrs) / 1 km

(3/20 hrs) / 1 km

.15 hrs / 1 km

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by [email protected] » Mon Aug 29, 2016 10:54 am
dferm wrote:Did it take Pei more than 2 hours to walk a distance of 10 miles along a certain trail? (1mile=1.6 Kilometers, rounded to the nearest tenth)

(1) Pei walked this distance at an average rate of less than 6.4 kilometers per hour

(2) On average, it took Pei more than 9 minutes per Kilometers to walk this distance.
Target question: Did it take Pei more than 2 hours to walk a distance of 10 miles?

This is a great candidate for rephrasing the target question.

Aside: We have a video with tips on rephrasing the target question: https://www.gmatprepnow.com/module/gmat- ... cy?id=1100

If Pei were able to walk 10 miles in EXACTLY 2 hours, then Pei's average speed would EQUAL 5 miles per hour.
So, if it were to take Pei MORE THAN 2 hours, then Pei's average speed would be LESS THAN 5 miles per hour.

This means we can rephrase the target question as...
REPHRASED target question: Is Pei's average speed less than 5 miles per hour?

Since the two statements are in terms of kilometers, let's rephrase the target question one more time...

5 miles = 8 kilometers, so 5 miles per hour = 8 kilometers per hour.
RE-REPHRASED target question: Is Pei's average speed less than 8 KILOMETERS per hour?

At this point, it will be relatively easy to handle the two statements.

Statement 1: Pei walked this distance at an average rate of less than 6.4 kilometer per hour.
If Pei walked slower than 6.4 kilometer per hour, we can be CERTAIN that Pei's average speed less is than 8 kilometers per hour
Since we can answer the RE-REPHRASED target question with certainty, statement 1 is SUFFICIENT

Statement 2: On average, it took Pei more than 9 minutes per kilometer to walk this distance.
Let's see what it means for Pei to walk 1 kilometer in EXACTLY 9 minutes.
This means Pei walks 7 kilometers in 63 minutes, which means he/she walks a little SLOWER than 7 kilometers per HOUR.
Since we're told that it took Pei MORE than 9 minutes per kilometer, we can be CERTAIN that Pei's average speed less is than 8 kilometers per hour
Since we can answer the RE-REPHRASED target question with certainty, statement 2 is SUFFICIENT

Cheers,
Brent

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by [email protected] » Mon Aug 29, 2016 3:44 pm
dferm wrote:Did it take Pei more than 2 hours to walk a distance of 10 miles along a certain trail? (1mile=1.6 Kilometers, rounded to the nearest tenth)

(1) Pei walked this distance at an average rate of less than 6.4 kilometers per hour

(2) On average, it took Pei more than 9 minutes per Kilometers to walk this distance.

Can someone please shed some light on this Problem?

Thanks.
We need to determine whether it took Pei more than 2 hours to walk a distance of 10 miles. Since our statements provide information about Pei's rate, let adjust the question to ask about rate.

Is t > 2 hr?

Is d/r > 2 hr?

Is 10 mi/r > 2 hr

Let's next convert 10 miles to kilometers. 10 miles = 1.6 x 10 = 16 kilometers

Is 16 km/r > 2 hr

Is 16km > (2 hr)r

Is 8 km/hr >r ?

Is r < 8 km/hr?

Statement One Alone:

Pei walked this distance at an average rate of less than 6.4 kilometers per hour.

Statement one tells us that Pei's rate was less than 8 km/hr. Thus statement one alone is sufficient to answer the question. We can eliminate answer choices, B, C, and E.

Statement Two Alone:

On average, it took Pei more than 9 minutes per kilometer to walk this distance.

Let's say it takes exactly 9 minutes to walk 1 kilometer, the question becomes: how many minutes will it take to walk 10 miles or 16 kilometers? If we let x be the number of minutes it takes to walk 16 kilometers, we can use a proportion to solve this question:

9 min/1 km = x min/16 km

9/1 = x/16

x = 144

Since the statement says it takes more than 9 min to walk 1 km, so it really takes more than 144 min to walk 16 km. Furthermore, since 2 hours = 120 minutes, so it definitely takes more than 2 hours to walk 16 kilometers or 10 miles. Statement two is sufficient to answer the question.