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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]

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New post 02 Jul 2012, 02:42
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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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Difficulty: 600
[Reveal] Spoiler: OA

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New post 02 Jul 2012, 02:43
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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. If distance=500 and rate=500 then time=500/500=1<3 but if distance=500 and rate=100 then time=500/100=5>3. Not sufficient.

(2) The distance that Paula drove from her home to her college was less than 205 kilometers. Even if the distance were 205 kilometers (maximum) and the rate were 70 kilometers per hour (minimum), still the time would be less than 3 hours: 205/70<3. Sufficient.

Answer: B.
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Re: If Paula drove the distance from her home to her college at [#permalink]

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New post 02 Jul 2012, 05:33
Hi,

Difficulty level: 600

Average speed = 70km/hr
Time = Distance/speed

Using (1),
Distance > 200 or time > 200/70, The time taken might/might not be less than 3 hours. Insufficient.

Using (2),
Distance < 205 or time < 205/70, The time taken is definitely less than 3 hours. Sufficient.

Thus, Answer is (B).

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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]

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New post 05 Jul 2012, 12:59
statement 2 alone is sufficient. Option B
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Re: If Paula drove the distance from her home to her college at [#permalink]

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New post 05 Jul 2012, 13:19
+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]

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New post 06 Jul 2012, 04:28
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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. If distance=500 and rate=500 then time=500/500=1<3 but if distance=500 and rate=100 then time=500/100=5>3. Not sufficient.

(2) The distance that Paula drove from her home to her college was less than 205 kilometers. Even if the distance were 205 kilometers (maximum) and the rate were 70 kilometers per hour (minimum), still the time would be less than 3 hours: 205/70<3. Sufficient.

Answer: B.
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PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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

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New post 01 Aug 2013, 14:40
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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New post 17 Feb 2016, 23:14
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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.
Therefore, the answer is B.


 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] 17 Feb 2016, 23:14
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