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

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

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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Did it take Pei more than 2 hours to walk a distance of 10 miles along [#permalink]
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Did it take Pei more than 2 hours to walk a distance of 10 miles along a certain trail? (1 mile = 1.6 kilometers, rounded to the nearest tenth.)

Did Pei take more than 2 hrs to walk 10 miles (= 10*1.6 = 16 kms)
In other words, was his speed less than 16/2 = 8 kmph?
Is Pei's speed < 8 kmph?

(1) Pei walked this distance at an average rate of less than 6.4 kilometers per hour.
Pei's speed < 6.4 kmph
This means his speed is definitely less than 8 kmph. Suffiient alone.

(2) On average, it took Pei more than 9 minutes per kilometer to walk this distance.
Pei's speed < 1 km in 9 mins
Pei's speed < 1 km in 9/60 hrs i.e. 60/9 km per hour
So Pei's speed < 6.66 kmph
This means his speed is definitely less than 8 kmph. Suffiient alone.

Note that if a statement had told us that his speed is less than 10 km per hr, we could not have answered the question. Less than 10 could be 9 and could be 7. We couldn't say whether his speed is less than 8 or more than 8 km per hour.
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Re: Did it take Pei more than 2 hours to walk a distance of 10 miles along [#permalink]
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
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Re: Did it take Pei more than 2 hours to walk a distance of 10 miles along [#permalink]
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 miles along [#permalink]
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given : 10 miles covered total

1. speed = 6.4 kmph
speed = distance / time
time = distance / speed = 10 * 1.6 kms/ 6.4 = 2.5 hr

suffiicient

2. 9 m / kms
total kms = 10 * 1.6 = 16 kms
time for 16 kms = 16 * 9 = 144 min = 2.4 hr

Sufficient

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

Bunuel, do you happen to have more of this question type? "Did it take longer/shorter than x?" or "Was the rate faster/slower than x?"
Would be highly appreciated
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Did it take Pei more than 2 hours to walk a distance of 10 miles along [#permalink]
Did it take Pei more than 2 hours to walk a distance of 10 miles along a certain trail? (1 mile = 1.6 kilometers, rounded to the nearest tenth.)

Did Pei take more than 2 hrs to walk 10 miles (= 10*1.6 = 16 kms)
In other words, was his speed less than 16/2 = 8 kmph?
Is Pei's speed < 8 kmph?

(1) Pei walked this distance at an average rate of less than 6.4 kilometers per hour.
Pei's speed < 6.4 kmph
This means his speed is definitely less than 8 kmph. Suffiient alone.

(2) On average, it took Pei more than 9 minutes per kilometer to walk this distance.
Pei's speed < 1 km in 9 mins
Pei's speed < 1 km in 9/60 hrs i.e. 60/9 km per hour
So Pei's speed < 6.66 kmph
This means his speed is definitely less than 8 kmph. Sufficient alone.

Note that if a statement had told us that his speed is less than 10 km per hr, we could not have answered the question. Less than 10 could be 9 and could be 7. We couldn't say whether his speed is less than 8 or more than 8 km per hour.

Hi karishma

Does my strategy work

You re-phrased question as Is Pei's speed < 8 kmph? for the purposes of solving S1

Could i then again re-phrase what you did to solve S2 specifically

Is $$\frac{1}{Pei's speed}$$ > $$\frac{1}{8kmph}$$ { in versing your rephrase questioned to make my re-phrase question for S2)

Hence,
$$\frac{1}{Pei's speed}$$ > $$\frac{60}{8}$$ min per km

Hence

Is $$\frac{1}{Pei's speed}$$ > 7.5 min per km

Given S2 is referring to Pie's speed more than 9 minutes per km -- this too is sufficient
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Did it take Pei more than 2 hours to walk a distance of 10 miles along [#permalink]
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.

Hi Bunuel

For the GMAT -- the rate is always in the form of kmph (distance over time)

But per S2 (red above) -- this seems inversed..

Is S2' essentially talking about the inverse of Pei's rate (i.e. $$1[/Rate of Pei]$$) > 9 minutes per kilometer
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Re: Did it take Pei more than 2 hours to walk a distance of 10 miles along [#permalink]

Thank you for all your assistance !
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Re: Did it take Pei more than 2 hours to walk a distance of 10 miles along [#permalink]
Did it take Pei more than 2 hours to walk a distance of 10 miles along a certain trail?
Did it take Pei more than ONE hour to walk a distance of 5 miles along a certain trail?
Did it take Pei more than ONE hour to walk a distance of 8 kilometers along a certain trail? (16 kilometers = 10 miles. 8 kilometers = 5 miles)

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

6.4 kilometers < 8 kilometers. Sufficient.

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

9 * 8 = 72 minutes
72 minutes > 60 minutes. Sufficient.
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Re: Did it take Pei more than 2 hours to walk a distance of 10 miles along [#permalink]
Is this really 700 level?
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Did it take Pei more than 2 hours to walk a distance of 10 miles along [#permalink]
In data sufficiency, you always want to ask yourself, "What's the question behind the question?"

Originally posted by CrushTheQuant on 08 Nov 2020, 11:08.
Last edited by CrushTheQuant on 08 Nov 2020, 14:17, edited 1 time in total.
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Re: Did it take Pei more than 2 hours to walk a distance of 10 miles along [#permalink]
The Question is

"Are we able to determine average speed?"
Doesnt matter if in M/Hr or KM/Hr or KM/Min

Statement 1 - Yes
Statement 2 - Yes

No need for calculations IMO.

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