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# Did it take Pei more than 2 hours to walk a distance of 10

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Manager
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Did it take Pei more than 2 hours to walk a distance of 10  [#permalink]

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08 May 2008, 20:28
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Did it take Pei more than 2 hours to walk a distance of 10 miles along a certain trail ( i mile =1.6km rounded to nearest tenth)

(1) Pei walked the distance at an average rate of less than 6.4 km/hr.
(2) On average it took Pei more than 9 minutes per km to walk the distance .
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13 Feb 2011, 08:10
5
8
tinki wrote:
guy with 1st statement:

here is my calculation:
if it takes 1 hour to walk max 6.4 km
if will take max. 2.5 hours to walk 16 km.

since it says average rate less than 6.4 so time is less than 2.5 but it could be less than 2.
so im getting that A is not suff. whats wrong with my method ?
pls explain

distance=rate*time --> rate and time are inversely proportional, which means that if you increase the rate then you'll need less time to cover the same distance and if you decrease the rate you'll need more time to cover the same distance.

So, rate is less than 6.4 kilometers per hour means that time needed to cover 16 kilometers is more than 2.5 hours.

Alternate approach:

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)

Basically the question asks whether the rate was less than 10/2=5 miles per hour: is rate<5 miles per hour? Because if it is less than 5 miles per hour, then time needed to cover 10 miles would be more than 2 hours.

(1) Pei walked this distance at an average rate of less than 6.4 kilometers per hour --> rate<6.4 kilometers per hour --> 6.4 kilometer = 6.4/1.6 = 4 miles --> rate<4 miles per hour. Sufficient.

(2) On average, it took Pei more than 9 minutes per Kilometers to walk this distance --> more than 9/60 hours to cover 1 kilometer --> rate<60/9 kilometers per hour (time more - rate less) --> 60/9 kilometers = (60/9)/1.6 = ~4.2 miles --> rate<4.2 miles per hour. Sufficient.

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08 May 2008, 20:56
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neeraj.kaushal wrote:
A question from GMAT Prep I get wrong all the ways I did. Anybody knows how to do this

Did it take Pei more than 2 hours to walk a distance of 10 miles along a certain trail ( i mile =1.6km rounded to nearest tenth)

1 Pei walked the distance at an average rate of less than 6.4 km/hr.

2 On average it took Pei more than 9 minutes per km to walk the distance .

1. At most, Pei walked 12.8km in 2 hours. Since the trail is 16km long, then we know that Pei took more than 2 hours. Therefore, statement 1 is sufficient

2. At the fastest, Pei walked 1 km in 9 minutes. Then to walk 16km, the Pei needs 144 minutes, which is more than 2 hours. Therefore, statement 2 is sufficient.
##### General Discussion
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11 May 2008, 16:11
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neeraj.kaushal wrote:
A question from GMAT Prep I get wrong all the ways I did. Anybody knows how to do this

Did it take Pei more than 2 hours to walk a distance of 10 miles along a certain trail ( i mile =1.6km rounded to nearest tenth)

1 Pei walked the distance at an average rate of less than 6.4 km/hr.

2 On average it took Pei more than 9 minutes per km to walk the distance .

I say D.

first, conversions: 10 miles = 16 km

2 hours = 120 minutes

1) less than 6.4km/hr - you want to know if it took less than 2 hours. 6.4 x 2 = 12.8km in two hours, when she has to go 16. You can answer the question if it took more than 2 hours.

Sufficient, eliminate B, C, & E.

2) 9 minutes per km - you want to know if it took less than 2 hours. 16km x 9min = 144 minutes for 16 km, when 120 minutes = 2 hours. You can answer the question if it took longer than two hours.

Sufficient, eliminate A.

D.
Manager
Joined: 18 Aug 2010
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13 Feb 2011, 06:24
guy with 1st statement:

here is my calculation:
if it takes 1 hour to walk max 6.4 km
if will take max. 2.5 hours to walk 16 km.

since it says average rate less than 6.4 so time is less than 2.5 but it could be less than 2.
so im getting that A is not suff. whats wrong with my method ?
pls explain
Manager
Joined: 18 Aug 2010
Posts: 83

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13 Feb 2011, 08:58
Bunuel wrote:
tinki wrote:
guy with 1st statement:

here is my calculation:
if it takes 1 hour to walk max 6.4 km
if will take max. 2.5 hours to walk 16 km.

since it says average rate less than 6.4 so time is less than 2.5 but it could be less than 2.
so im getting that A is not suff. whats wrong with my method ?
pls explain

distance=rate*time --> rate and time are inversely proportional, which means that if you increase the rate then you'll need less time to cover the same distance and if you decrease the rate you'll need more time to cover the same distance.

So, rate is less than 6.4 kilometers per hour means that time needed to cover 16 kilometers is more than 2.5 hours.

Alternate approach:

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)

Basically the question asks whether the rate was less than 10/2=5 miles per hour: is rate<5 miles per hour? Because if it is less than 5 miles per hour, then time needed to cover 10 miles would be more than 2 hours.

(1) Pei walked this distance at an average rate of less than 6.4 kilometers per hour --> rate<6.4 kilometers per hour --> 6.4 kilometer = 6.4/1.6 = 4 miles --> rate<4 miles per hour. Sufficient.

(2) On average, it took Pei more than 9 minutes per Kilometers to walk this distance --> more than 9/60 hours to cover 1 kilometer --> rate<60/9 kilometers per hour (time more - rate less) --> 60/9 kilometers = (60/9)/1.6 = ~4.2 miles --> rate<4.2 miles per hour. Sufficient.

Thanks... got that
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Re: Did it take Pei more than 2 hours to walk a distance of 10  [#permalink]

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27 Jun 2013, 01:02
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE

All DS Distance/Rate Problems to practice: search.php?search_id=tag&tag_id=44
All PS Distance/Rate Problems to practice: search.php?search_id=tag&tag_id=64

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Re: Did it take Pei more than 2 hours to walk a distance of 10  [#permalink]

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27 Jun 2013, 12:53
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Bunuel wrote:
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE

Distance = Speed X Time

Speed = S mph
Distance = 10 miles
Ques = Was the time greater than 2 hours?

If S X 2 = 10, speed becomes 5 mph

when Distance is constant, speed decreases as the time increase. So for Time to be greater than 2 hours, speed should be less than 5 mph

So the question can be rephrased as "Was the speed less than 5mph?"

S1) Speed was less than 6.4 KMPH -----> Speed was less than 4 mph -----Sufficient

S2) Pie took more than 9 minutes per km to walk ------------> S X $$\frac{9}{60}$$ = 1 -----> S = 6.66 -------> Speed was less than 6.66 kmph -----------> Speed was less than 4.xxx mph --- Sufficient

Choice D.
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Re: Did it take Pei more than 2 hours to walk a distance of 10  [#permalink]

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28 Jul 2013, 10:42
1
Did it take Pei more than 2 hours to walk a distance of 10 miles along a certain trail ( i mile =1.6km rounded to nearest tenth)

Because both statements are in km, let's convert miles to km:

Did it take Pei more than 2 hours to walk a distance of 16km?

(1) Pei walked the distance at an average rate of less than 6.4 km/hr.

With #1, the fastest Pei could have walked in two hours was 12.8km which is far short of the 16km the question asks. Therefore, Pei took more than 2 hours to walk 16km.
SUFFICIENT

(2) On average it took Pei more than 9 minutes per km to walk the distance.
The stem tells us that Pei walked 16km. If his average was at a minimum, 9minutes/km then it would have taken him minimally 9minutes/16km = 151 minutes which is obviously greater than 120 minutes/2 hours.
SUFFICIENT

(D)
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Re: Did it take Pei more than 2 hours to walk a distance of 10  [#permalink]

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23 Oct 2013, 02:55
Statement 1 says R < 6.4

So in 2 hours the rate would be D < 6.4 ( rate) * 2 ( time)

So distance < 12.8 so it has to take more than 2 hours to complete 16 km

Sufficient

Statement 2 9 minutes for 1 km => for 16 km it will take 144 minutes which is more than 2 hours its sufficient!

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Re: Did it take Pei more than 2 hours to walk a distance of 10  [#permalink]

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23 Jul 2014, 14:35
9 min/km * 16 km = 144 minutes

120 min < 144 min (min duration)

so time is more than 2 hours
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Joined: 04 Jun 2015
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Did it take Pei more than 2 hours to walk a distance of 10  [#permalink]

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09 Jan 2016, 00:57
neeraj.kaushal wrote:
Did it take Pei more than 2 hours to walk a distance of 10 miles along a certain trail ( i mile =1.6km rounded to nearest tenth)

(1) Pei walked the distance at an average rate of less than 6.4 km/hr.
(2) On average it took Pei more than 9 minutes per km to walk the distance .

From (1) Rate< 6.4 kph
OR$$\frac{Dist.}{Time}$$< 6.4

===>$$\frac{16(km)}{Time}$$<6.4
===> Time>2.5 (Sufficient)

From (2) $$Avg =\frac{Sum}{#}$$
===> $$>$$ 9= Sum/16
===> Sum= $$>$$144 min or$$>$$2.4 hrs (Sufficient)
Hence, D
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Re: Did it take Pei more than 2 hours to walk a distance of 10  [#permalink]

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15 Jun 2018, 09:17
neeraj.kaushal wrote:
Did it take Pei more than 2 hours to walk a distance of 10 miles along a certain trail ( i mile =1.6km rounded to nearest tenth)

(1) Pei walked the distance at an average rate of less than 6.4 km/hr.
(2) On average it took Pei more than 9 minutes per km to walk the distance .

Given, Distance = 10 miles = 16 km
we are asked is the time taken, t > 2 hours

Statement 1:
Pei walked the distance at an average rate of less than 6.4 km/hr

Let s be the average rate, hence s < 6.4 km/hr

if s = 6.4 km/hr, then we have time taken t = 16/6.4 = 2.5 hours > 2 hours

Since time & speed are inversely proportional, if we reduce speed below 6.4 km/hr, the time will be above 2.5 hours.

Hence Statement 1 alone is Sufficient.

Statement 2:
On average it took Pei more than 9 minutes per km to walk the distance.

Hence Pei, to walk 16 kms took 144 mins > 120 mins = 2hours

Statement 2 alone is Sufficient.

Thanks,
GyM
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Re: Did it take Pei more than 2 hours to walk a distance of 10  [#permalink]

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15 Jun 2018, 09:32
(1) rate is less than 6.4 km/hr * 1/1.6 mile/km
rate is less than 4 mph
10 miles / less than 4 mph, is greater than or equal to 2.5 hours
Sufficient

(2) 10 miles * 1.6 km/mile = 16 km
Pei takes more than 9 min per km so Pei takes more than 9 * 16 = 145 min for 10 miles
Pei takes more than 145/60 hours for 10 miles, which is greater than 2 hours
Sufficient

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Posts: 1783
Re: Did it take Pei more than 2 hours to walk a distance of 10  [#permalink]

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02 Aug 2018, 20:27
Bunuel wrote:
tinki wrote:
guy with 1st statement:

here is my calculation:
if it takes 1 hour to walk max 6.4 km
if will take max. 2.5 hours to walk 16 km.

since it says average rate less than 6.4 so time is less than 2.5 but it could be less than 2.
so im getting that A is not suff. whats wrong with my method ?
pls explain

distance=rate*time --> rate and time are inversely proportional, which means that if you increase the rate then you'll need less time to cover the same distance and if you decrease the rate you'll need more time to cover the same distance.

So, rate is less than 6.4 kilometers per hour means that time needed to cover 16 kilometers is more than 2.5 hours.

Alternate approach:

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)

Basically the question asks whether the rate was less than 10/2=5 miles per hour: is rate<5 miles per hour? Because if it is less than 5 miles per hour, then time needed to cover 10 miles would be more than 2 hours.

(1) Pei walked this distance at an average rate of less than 6.4 kilometers per hour --> rate<6.4 kilometers per hour --> 6.4 kilometer = 6.4/1.6 = 4 miles --> rate<4 miles per hour. Sufficient.

(2) On average, it took Pei more than 9 minutes per Kilometers to walk this distance --> more than 9/60 hours to cover 1 kilometer --> rate<60/9 kilometers per hour (time more - rate less) --> 60/9 kilometers = (60/9)/1.6 = ~4.2 miles --> rate<4.2 miles per hour. Sufficient.

Dear Bunuel,

Does statement 2 means that average speed = 1/9 Km/min?

Can you please post similar problems?

Thanks
Math Expert
Joined: 02 Sep 2009
Posts: 47983
Did it take Pei more than 2 hours to walk a distance of 10  [#permalink]

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02 Aug 2018, 21:11
Mo2men wrote:
Bunuel wrote:
tinki wrote:
guy with 1st statement:

here is my calculation:
if it takes 1 hour to walk max 6.4 km
if will take max. 2.5 hours to walk 16 km.

since it says average rate less than 6.4 so time is less than 2.5 but it could be less than 2.
so im getting that A is not suff. whats wrong with my method ?
pls explain

distance=rate*time --> rate and time are inversely proportional, which means that if you increase the rate then you'll need less time to cover the same distance and if you decrease the rate you'll need more time to cover the same distance.

So, rate is less than 6.4 kilometers per hour means that time needed to cover 16 kilometers is more than 2.5 hours.

Alternate approach:

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)

Basically the question asks whether the rate was less than 10/2=5 miles per hour: is rate<5 miles per hour? Because if it is less than 5 miles per hour, then time needed to cover 10 miles would be more than 2 hours.

(1) Pei walked this distance at an average rate of less than 6.4 kilometers per hour --> rate<6.4 kilometers per hour --> 6.4 kilometer = 6.4/1.6 = 4 miles --> rate<4 miles per hour. Sufficient.

(2) On average, it took Pei more than 9 minutes per Kilometers to walk this distance --> more than 9/60 hours to cover 1 kilometer --> rate<60/9 kilometers per hour (time more - rate less) --> 60/9 kilometers = (60/9)/1.6 = ~4.2 miles --> rate<4.2 miles per hour. Sufficient.

Dear Bunuel,

Does statement 2 means that average speed = 1/9 Km/min?

Can you please post similar problems?

Thanks

(2) means that the average speed was LESS than 1/9 kilometres per minute (because time was MORE than 9 minutes per kilometre).

I could not recall very similar questions to this one but you can check distance/rate questions for the same concepts.
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Re: Did it take Pei more than 2 hours to walk a distance of 10  [#permalink]

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04 Aug 2018, 22:41
neeraj.kaushal wrote:
Did it take Pei more than 2 hours to walk a distance of 10 miles along a certain trail ( i mile =1.6km rounded to nearest tenth)

(1) Pei walked the distance at an average rate of less than 6.4 km/hr.
(2) On average it took Pei more than 9 minutes per km to walk the distance .

Iam unable to view the choices from question
Math Expert
Joined: 02 Sep 2009
Posts: 47983
Re: Did it take Pei more than 2 hours to walk a distance of 10  [#permalink]

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05 Aug 2018, 04:33
dhanush95 wrote:
neeraj.kaushal wrote:
Did it take Pei more than 2 hours to walk a distance of 10 miles along a certain trail ( i mile =1.6km rounded to nearest tenth)

(1) Pei walked the distance at an average rate of less than 6.4 km/hr.
(2) On average it took Pei more than 9 minutes per km to walk the distance .

Iam unable to view the choices from question

This is a data sufficiency question. Options for DS questions are always the same.

The data sufficiency problem consists of a question and two statements, labeled (1) and (2), in which certain data are given. You have to decide whether the data given in the statements are sufficient for answering the question. Using the data given in the statements, plus your knowledge of mathematics and everyday facts (such as the number of days in July or the meaning of the word counterclockwise), you must indicate whether—

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
C. BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
E. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

I suggest you to go through the following posts:
ALL YOU NEED FOR QUANT.

Hope this helps.
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Re: Did it take Pei more than 2 hours to walk a distance of 10 &nbs [#permalink] 05 Aug 2018, 04:33
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