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# If Paula drove the distance from her home to her college at

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If Paula drove the distance from her home to her college at [#permalink]  03 Feb 2008, 11:53
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If Paula drove the distance from her home to her college at an average speed that was greater than 70 kilometers per hour, did it take her less than 3 hours to drive this distance?

1) The distance that Paula drove from her home to her college was greater than 200 kilometers.
2) The distance that Paula drove from her home to her college was less than 205 kilometers.

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Re: paula [#permalink]  03 Feb 2008, 13:27
Expert's post
B

1. (70kmh and 20000km: t>3h) and (70000kmh and 201km: t<3h). insuff.
2. t<205/70~2.93h. suff.
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Re: paula [#permalink]  03 Feb 2008, 15:16
walker wrote:
B

1. (70kmh and 20000km: t>3h) and (70000kmh and 201km: t<3h). insuff.
2. t<205/70~2.93h. suff.

hey can u please explain it more clearly satement 1 ? from where does it come 20000 and 70000.

-thanx
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Re: paula [#permalink]  03 Feb 2008, 18:17
walker is just picking numbers to demonstrate.

stat 1 just tells us what the distance is greater than ... think about it ... paula could have driven 210 kms, 300 ... 400 ... 500 ... any of these distances would change the amount of time she drove (varying with speed of course). so it could be less than 3 hrs, or more ... no way to tell.

stat 2 tells us what the distance is less than. lets say it was 204 kms ... take a speed of anything over 70, and you will see that the time always works out to less than 3 hours. suff
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Re: paula [#permalink]  03 Feb 2008, 22:49
Expert's post
[quote="blog"]If paula drove the distance from her home to her college at an average speed that was greater than 70 kms per hour, did it take her less than 3 hrs to drive the distance ?

1. The distance that paula drove from her home to her college was greater than 200 kms.

$$V_{av}>70kmh$$

$$L>200kmh$$

$$t=\frac{L}{V_{av}}$$

$$max(t)=\frac{max(L)}{min(V_{av})}=\frac{\infty}{70}=\infty$$

$$min(t)=\frac{min(L)}{max(V_{av})}=\frac{200}{\infty}=0$$

I used 70000kmh and 20000km instead of $$\infty$$
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Re: paula [#permalink]  04 Feb 2008, 02:23
Avg Speed is > 70 KMH => let us say 71 km

1-> Distance Greater than 200 Kms => the distance could be 201 or any value above 200 Kms

if it is 71*3=> 213 Km ( if the distance is less than 213, then it will be less than 3 hours) but if the distance is greater than 213 it would be more thus 1 is not sufficient.

2-> 205 Kms is less than 213 Kms thus it is sufficient if we know B to answer the questions

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data sufficiency with inequality help needed [#permalink]  19 Sep 2011, 22:42
If Paula drove the distance from her home to her
college at an average speed that was greater than
70 kilometers per hour, did it take her less than
3 hours to drive this distance?
(1) The distance that Paula drove from her home to
her college was greater than 200 kilometers.
(2) The distance that Paula drove from her home to
her college was less than 205 kilometers.

I'm a bit confused on how to do this problem, i know the basic D=RT, but I really get thrown off since two of the variables are given as > or <
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Re: data sufficiency with inequality help needed [#permalink]  19 Sep 2011, 22:48
pinchharmonic wrote:
If Paula drove the distance from her home to her
college at an average speed that was greater than
70 kilometers per hour, did it take her less than
3 hours to drive this distance?
(1) The distance that Paula drove from her home to
her college was greater than 200 kilometers.
(2) The distance that Paula drove from her home to
her college was less than 205 kilometers.

I'm a bit confused on how to do this problem, i know the basic D=RT, but I really get thrown off since two of the variables are given as > or <

For the total time to be less than 3 hrs @ 70km/hr the distance shud be less than 3*70 = 210km
St1: distance is >200 km
suppose the distance is 201 , then at an avg speed of 70km/hr it will take him 201/70 , which is less then 3 hrs
but suppose the distance is 280 km then it will take 280/70 = 4 , more then 3 hrs

hence insufficient

st2: this tells us that distance was <205 , which means its <210 as well .
Hence sufficient
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Re: data sufficiency with inequality help needed [#permalink]  19 Sep 2011, 22:57
The question says paula drove from her home to her college at a speed more than 70 kmph. how much more ? we don't know. may be 70.0001 kmph , may be 75 kmph etc etc. atleast her speed is more than 70. for convenience take her speed 70 kmph. so at this speed if she drives for 3 hrs she will travel atleast 3 * 70 =210 km. so essentially if her college's distance is less than 210 km we will get a definite answer as it will mean she does travels the distance in less than 3hrs.

statement 1 ) Insufficient - this statement says the distance to her college is more than 200 km. it could be 205 , it could be 300 km. If distance is 205 km then she did travel in less than 3 hrs, if distance is 300 km , we cant say she travelled in less than 3hrs or not. so insufficient.

statement 2 ) sufficient - the statement says the distance was less than 205 km, we know from question stem itself if distance is less than 210, paula definitely will travel that in less than 3 hrs. this is sufficient.

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Re: DS: Paula drove the distance from her home to her college [#permalink]  20 Sep 2011, 02:28
+ 1 for B. Took me 2 minutes.
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Re: DS: Paula drove the distance from her home to her college [#permalink]  20 Sep 2011, 02:49
If paula drove the distance from her home to her college at an average speed that was greater than 70 kms per hour, did it take her less than 3 hrs to drive the distance ?

1. The distance that paula drove from her home to her college was greater than 200 kms.
If distance is greater than 200 kms then it could be 201 kms.
With assume speed 71 kms; 201/71 = 2.83 hrs less than 3 hours
But then distance can be 400kms which is greater than 200 kms.
With assumed speed of 71 ; 400/71 = 5.6 hrs more than 3 hours.
Insufficient.

2. The distance that paula drove from her home to her college was less than 205 kms.
With distance less than 205 kms, pick 204 kms...
Speed 71; 204/71 = 2.83 hrs...
The numerator can only drop thereby reducing the time.
Sufficient.
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Re: DS: Paula drove the distance from her home to her college [#permalink]  20 Sep 2011, 09:30
i notice a lot of people doing what i inititally tried, using 71 for > 70, etc. I did not think that was the right approach, in fact, the answer explanation uses none of that.

i think my question is better clarified by modifying the problem a bit, i see now that because this is data sufficiency, the details I'm after can be ignored.

speed > 70mph
distance > 210

what is the range of values for t? in other words, are there decimal values of speed & distance that can make t exactly 3?
Re: DS: Paula drove the distance from her home to her college   [#permalink] 20 Sep 2011, 09:30
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