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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] New post 04 Feb 2014, 00:39
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64% (02:01) correct 36% (00:58) wrong based on 126 sessions
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] New post 04 Feb 2014, 00:40
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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.

Answer: A.
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Re: How long did it take Betty to drive nonstop on a trip from h [#permalink] New post 04 Feb 2014, 06:35
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Answer A is sufficient.

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] New post 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

ANSWER: A
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Re: How long did it take Betty to drive nonstop on a trip from h [#permalink] New post 08 Feb 2014, 04:13
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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.

Answer: A.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
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

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
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Re: How long did it take Betty to drive nonstop on a trip from h   [#permalink] 08 Feb 2014, 04:13
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