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

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Re: If Paula drove the distance from her home to her college at [#permalink]
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q. stems says that D/t>70. is t<3?

1. d>200 . it means that t could be less than 3 (but not necessarily)

2. D<205 it means that t<2,.... it is less than 3. so B is the answ
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Re: If Paula drove the distance from her home to her college at [#permalink]
+1 B

$$\frac{205}{(>70)} = < 3$$

Less than three hous.
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Re: If Paula drove the distance from her home to her college at [#permalink]
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?

r > 70 km/hour

This question is looking for time.

(1) The distance that Paula drove from her home to her college was greater than 200 kilometers.
Time = distance/rate

Lets go with two hypothetical cases: d=201, d=1000

d=201
Time = 201/71
Time = 2.8 hours

d=1000
Time = 1000/71
Time = 14 hours

All we know is that her rate was greater than 70 and the distance was greater than 200. There are an infinite number of cases where her trip could have taken less than or more than three hours.

INSUFFICIENT

(2) The distance that Paula drove from her home to her college was less than 205 kilometers.
If the distance traveled is less than 205 and her speed is greater than 71 then we know for sure that her travel time is under three hours. Just to be sure, let's minimize and maximize the values given:

d = 204.99999999
s = 70.00000001

Time = distance/rate
204.99999999/70.00000001 = 2.929
Obviously we would never be required to be that precise on the GMAT, but just to show as an example, the time will always be less than three hours.
SUFFICIENT

(B)
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Re: If Paula drove the distance from her home to her college at [#permalink]
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Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

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.

When it comes to inequality questions, it is important that if range of que includes range of con, that con is sufficient.
When you modify the original condition and the question, if Paula drove greater than 70 kilometers per hour, it would take less than 3 hours, which is less than 70km*3=210km. Then, you need to figure out the distance, which makes 1 variable and it should match with the number of equations. So you need 1 equation.
For 1), if the distance is farther than 200km, the range of que doesn’t include the range of con, which is not sufficient.
For 2), if the distance is less than 205km, the range of que includes the range of con, which is sufficient.

 For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.
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Re: If Paula drove the distance from her home to her college at [#permalink]
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Bunuel 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.

Statement One Alone:

The distance that Paula drove from her home to her college was greater than 200 kilometers.

We don’t have enough information to determine whether it takes her less than 3 hours to drive to school. For example, if the distance is 320 km, and her speed is 80 kmph, then it takes her 4 hours to drive to school. However, if the distance is 220 km, and her speed is 80 kmph, then it takes her 2.75 hours to drive to school.

Statement one alone is not sufficient.

Statement One Alone:

The distance that Paula drove from her home to her college was less than 205 kilometers.

We do have enough information to determine whether it takes her less than 3 hours to drive to school. Let’s say the distance is exactly 205 km and her speed is exactly 70 kmph. Then it takes her approximately 2.93 hours to drive to school. However, since the distance is less than 205 km and her speed is greater than 70 kmph, it will definitely take her less than 2.93 hours (and hence less than 3 hours) to drive to school.

Statement two alone is sufficient.

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Re: If Paula drove the distance from her home to her college at [#permalink]
Hi chetan2u, Bunuel, gmatbusters karishma

A quick question regarding the direction of the inequality sign specifically

Per question :

-- Rate is > 70 km per hour
-- Question is asking if time < 3 hours

I always try to re-phrase before looking at the answer choices

a) is distance > 210 kms
or
b) is distance < 210 kms

If so -- which of the two options can be inferred (if you could state your logic, that would be great !)
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Re: If Paula drove the distance from her home to her college at [#permalink]
If you can prove that the distance is less than 210, you can definitely answer the question uniquely.

This is because if the speed > 70km/hr, even if take the lowest speed 70.00001
Ans time =3hr, then also the distance travelled would be 210km.
So, if the distance travelled would be less than 210km, then time has to be 3 hrs.

jabhatta@umail.iu.edu wrote:
Hi chetan2u, Bunuel, gmatbusters karishma

A quick question regarding the direction of the inequality sign specifically

Per question :

-- Rate is > 70 km per hour
-- Question is asking if time < 3 hours

I always try to re-phrase before looking at the answer choices

a) is distance > 210 kms
or
b) is distance < 210 kms

If so -- which of the two options can be inferred (if you could state your logic, that would be great !)
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Re: If Paula drove the distance from her home to her college at [#permalink]
gmatbusters wrote:
If you can prove that the distance is less than 210, you can definitely answer the question uniquely.

This is because if the speed > 70km/hr, even if take the lowest speed 70.00001
Ans time =3hr, then also the distance travelled would be 210km.
So, if the distance travelled would be less than 210km, then time has to be 3 hrs.

jabhatta@umail.iu.edu wrote:
Hi chetan2u, Bunuel, gmatbusters karishma

A quick question regarding the direction of the inequality sign specifically

Per question :

-- Rate is > 70 km per hour
-- Question is asking if time < 3 hours

I always try to re-phrase before looking at the answer choices

a) is distance > 210 kms
or
b) is distance < 210 kms

If so -- which of the two options can be inferred (if you could state your logic, that would be great !)

Hi gmatbusters

Thank you for responding

Just wondering -- other than testing, can we use logic to solve this ( or alternatively algebra perhaps ?)
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Re: If Paula drove the distance from her home to her college at [#permalink]
The algebric method would be inefficient.

The logic is simple.
if the speed > 70km/hr, even if take the lowest speed 70.00001
Ans time =3hr, then also the distance travelled would be 210km.
So, if the distance travelled would be less than 210km, then time has to be 3 hrs.

St 1) distance more than 200 so it can be 100000000 or 201
Hence sufficient.
St2) distance less than 205, hence it is less than 210. So sufficient, time taken is less than 3hrs.

jabhatta@umail.iu.edu wrote:
gmatbusters wrote:
If you can prove that the distance is less than 210, you can definitely answer the question uniquely.

This is because if the speed > 70km/hr, even if take the lowest speed 70.00001
Ans time =3hr, then also the distance travelled would be 210km.
So, if the distance travelled would be less than 210km, then time has to be 3 hrs.

jabhatta@umail.iu.edu wrote:
Hi chetan2u, Bunuel, gmatbusters karishma

A quick question regarding the direction of the inequality sign specifically

Per question :

-- Rate is > 70 km per hour
-- Question is asking if time < 3 hours

I always try to re-phrase before looking at the answer choices

a) is distance > 210 kms
or
b) is distance < 210 kms

If so -- which of the two options can be inferred (if you could state your logic, that would be great !)

Hi gmatbusters

Thank you for responding

Just wondering -- other than testing, can we use logic to solve this ( or alternatively algebra perhaps ?)
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Re: If Paula drove the distance from her home to her college at [#permalink]
Thank you for responding gmatbusters

Just wondering

If rate > 10 km/hr and time is < 3 hours

Can one infer that :

distance > 30 km or is distance < 30 km or is distance = 30 km
or
you cant really make a judgement call on the direction of distance at all ?

Just wondering -- in d = r * t equation -- if rate has one direction for inequality and time has another opposite direction

what is the resulting direction of the distance ?

It is based off of this question i attempted so just wondering

Thank you !!
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Re: If Paula drove the distance from her home to her college at [#permalink]
If rate > 10 km/hr and time is < 3 hours

distance > 30 km - May be, but not necessarily
distance < 30 km - May be, but not necessarily
Distance = 30 km - May be, but not necessarily

But if rate >10km/hr and distance <30km
Then time must be <3hrs

jabhatta@umail.iu.edu wrote:
Thank you for responding gmatbusters

Just wondering

If rate > 10 km/hr and time is < 3 hours

Can one infer that :

distance > 30 km or is distance < 30 km or is distance = 30 km
or
you cant really make a judgement call on the direction of distance at all ?

Just wondering -- in d = r * t equation -- if rate has one direction for inequality and time has another opposite direction

what is the resulting direction of the distance ?

It is based off of this question i attempted so just wondering

Thank you !!
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Re: If Paula drove the distance from her home to her college at [#permalink]
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Re: If Paula drove the distance from her home to her college at [#permalink]
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