How long did it take Betty to drive nonstop on a trip from h : GMAT Data Sufficiency (DS)
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# How long did it take Betty to drive nonstop on a trip from h

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How long did it take Betty to drive nonstop on a trip from h [#permalink]

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04 Feb 2014, 00:39
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The Official Guide For GMAT® Quantitative Review, 2ND Edition

How long did it take Betty to drive nonstop on a trip from her home to Denver, Colorado?

(1) If Betty's average speed for the trip had been 3/2 times as fast, the trip would have taken 2 hours.
(2) Betty's average speed for the trip was 50 miles per hour.

Data Sufficiency
Question: 71
Category: Arithmetic Distance/ rate problems
Page: 158
Difficulty: 600

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Re: How long did it take Betty to drive nonstop on a trip from h [#permalink]

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04 Feb 2014, 00:40
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SOLUTION

How long did it take Betty to drive nonstop on a trip from her home to Denver, Colorado?

Time = Distance/Rate ?

(1) If Betty's average speed for the trip had been 3/2 times as fast, the trip would have taken 2 hours.

(3/2*Rate)*2 = Distance;

Distance/Rate = 3. Sufficient.

(2) Betty's average speed for the trip was 50 miles per hour. Only the rate is clearly not sufficient, to get the time. Not sufficient.

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Re: How long did it take Betty to drive nonstop on a trip from h [#permalink]

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04 Feb 2014, 06:35
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it is the same distance - so S1*T1=S2*T2

let us assume that the original speed is x and original time t

x*t=3/2x*2
t=3x/x
t=3

the trip took 3 hours.

The answer B is not sufficient because we only know the speed but not distance.
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Re: How long did it take Betty to drive nonstop on a trip from h [#permalink]

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04 Feb 2014, 14:24
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Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

How long did it take Betty to drive nonstop on a trip from her home to Denver, Colorado?

(1) If Betty's average speed for the trip had been 3/2 times as fast, the trip would have taken 2 hours.
(2) Betty's average speed for the trip was 50 miles per hour.

(1)
We need to know how long it took Betty to drive, so time=distance/speed.

Let's denote:
s1 is average speed
t1 is the time needed to complete the journey when travelling at speed s1
s2 is the average speed when travelling at faster speed
t2 is the time needed to complete the journey when travelling at speed s2.

Then,
t1=d/s1

But also as per (1):
s1=3/2*s2
or s2=2/3*s1 (equation #1)

And:
t2=d/s2=2hours (from statement 1)

But also as per (eq. #1):
t2= d/s2 = d/((2/3)*s1) = 2 hours --> t2 = (2/3)*(d/s1) = 2 --> (2/3)*t1 = 2 --> t1= 3 hours

Hence,
(1) is SUFFICIENT

(2) Nothing is said about distance between "her home" and Colorado, hence we have no means to determine t or d/s.
(2) IS INSUFFICIENT

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Re: How long did it take Betty to drive nonstop on a trip from h [#permalink]

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08 Feb 2014, 04:13
SOLUTION

How long did it take Betty to drive nonstop on a trip from her home to Denver, Colorado?

Time = Distance/Rate ?

(1) If Betty's average speed for the trip had been 3/2 times as fast, the trip would have taken 2 hours.

(3/2*Rate)*2 = Distance;

Distance/Rate = 3. Sufficient.

(2) Betty's average speed for the trip was 50 miles per hour. Only the rate is clearly not sufficient, to get the time. Not sufficient.

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Re: How long did it take Betty to drive nonstop on a trip from h [#permalink]

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11 Jan 2015, 11:25
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Even though you can plug in numbers to solve this question, it is important to notice one important algebraic caveat in this type of problems.

Statement 1 is sufficient. However it provides only 1 equation with 2 variables.
R (1.5) (2) = D

At first glance, it looks like you cannot solve this using the Equation Rule of Sufficiency (the one that states that "you need n number of distinct, linear equations to solve for n variables..."). The catch is that all Distance problems are already giving us 1 equation and 3 variables, namely R * T = D.

So when you look at statement 1 you actually have 2 equations and 3 variables

(1.5) (2) = D/R
T = D/R

If you substitute, you kill one variable and thus you can solve.

(1.5) (2) = T
3 = T

Statement 2 is insufficient.
The equations you have are:
T = D/R
R = 50
3 Variables, 2 Equations --> Insufficient.
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13 Jan 2016, 04:34
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Re: How long did it take Betty to drive nonstop on a trip from h [#permalink]

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13 Jan 2016, 22:07
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Expert's post
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.

How long did it take Betty to drive nonstop on a trip from her home to Denver, Colorado?

(1) If Betty's average speed for the trip had been 3/2 times as fast, the trip would have taken 2 hours.
(2) Betty's average speed for the trip was 50 miles per hour.

In the original condition, from vt=d, there are 3 variables(v,t,d) and 1 equation(vt=d), which should match with the number of equations. So you need 2 equations. For 1) 1 equation, for 2) 1 equation, which is likely to make C the answer. When 1) &2), you can easily find out that C is the answer. However, in 1), you can get 2 equations(time and velocity). That is, use vt=d from (3/2)v*2=d and you can get t=3, which is sufficient. Therefore, the answer is A.

 For cases where we need 2 more equations, such as original conditions with “2 variables”, or “3 variables and 1 equation”, or “4 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 70% chance that C is the answer, while E has 25% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since C is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, D or E.
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Re: How long did it take Betty to drive nonstop on a trip from h   [#permalink] 13 Jan 2016, 22:07
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