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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.

Each week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.

We'll be glad if you participate in development of this project: 1. Please provide your solutions to the questions; 2. Please vote for the best solutions by pressing Kudos button; 3. Please vote for the questions themselves by pressing Kudos button; 4. Please share your views on difficulty level of the questions, so that we have most precise evaluation.

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

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

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11 Jan 2015, 12:25

1

This post received KUDOS

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

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13 Jan 2016, 05:34

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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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.

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]

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10 Mar 2017, 21:56

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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

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23 Mar 2017, 13:01

st 2: gives the speed but we are missing the distance St 1: gives us Distance = 3/2 speed * 2 and we know that same Distance = Speed * time. Hence time = 3 hours
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Re: How long did it take Betty to drive nonstop on a trip from h [#permalink]

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23 Mar 2017, 13:01

st 2: gives the speed but we are missing the distance St 1: gives us Distance = 3/2 speed * 2 and we know that same Distance = Speed * time. Hence time = 3 hours

Answer is A
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Re: How long did it take Betty to drive nonstop on a trip from h
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23 Mar 2017, 13:01

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