Find all School-related info fast with the new School-Specific MBA Forum

It is currently 25 Oct 2014, 04:50

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

To arrive at its destination on time the bus should have

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Director
Director
avatar
Joined: 11 Jun 2007
Posts: 932
Followers: 1

Kudos [?]: 51 [0], given: 0

To arrive at its destination on time the bus should have [#permalink] New post 29 Oct 2007, 16:02
1
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

41% (02:24) correct 59% (01:52) wrong based on 53 sessions
To arrive at its destination on time, a bus should have maintained a speed of V kmh throughout its journey. Instead, after going the first third of the distance at V kmh, the bus increased its speed and went the rest of the distance at (1.2)*V kmh. If, as a result, the bus arrived at its destination X minutes earlier than planned, what was the actual duration of the trip?

(1) V = 60
(2) X = 20

(C) 2008 GMAT Club - m10#8

OPEN DISCUSSION OF THIS QUESTION IS HERE: to-arrive-at-its-destination-on-time-a-bus-should-have-main-105223.html
[Reveal] Spoiler: OA
Kaplan Promo CodeKnewton GMAT Discount CodesGMAT Pill GMAT Discount Codes
GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 07 Jul 2004
Posts: 5095
Location: Singapore
Followers: 19

Kudos [?]: 155 [0], given: 0

Re: To arrive at its destination on time the bus should have [#permalink] New post 29 Oct 2007, 17:29
If distance = d,

then time taken travelling at constant speed v kmh = d/v h
time taken travelling at v kmh for x/3km and 6v/5 kmh for 2x/3 km = d/3v + 5d/9v = 8d/9v

8d/9v = d/v - x/60 -- [1]

St1:
v = 60 ---> Reduces [1] to d = 9x. Insufficient.

St2:
x = 20 --> Reduce [1] to v = 3d. Insufficient.

St1 and St2:
d = 9x --[a]
d = v/3 --[b]

[a] = [b]
9x = v/3
x = v/27 = 2.22 kmh. Sufficient.

Ans C
VP
VP
avatar
Joined: 28 Mar 2006
Posts: 1388
Followers: 2

Kudos [?]: 19 [0], given: 0

Re: To arrive at its destination on time the bus should have [#permalink] New post 29 Oct 2007, 18:09
I think B should do it
CEO
CEO
User avatar
Joined: 29 Mar 2007
Posts: 2593
Followers: 16

Kudos [?]: 198 [0], given: 0

Re: To arrive at its destination on time the bus should have [#permalink] New post 29 Oct 2007, 19:52
beckee529 wrote:
To arrive at its destination on time the bus should have maintained a speed of V kmh throughout the journey. Instead, after going the first third of the distance at V kmh, the bus increased its speed and went the rest of the distance at (1.2)*V kmh. As a result, the bus arrived at its destination X minutes earlier than planned. What was the actual duration of the trip?

1. V = 60
2. X = 20


We have 3 rates: Original rate, 1/3 original rate, and 2/3 new rate.

Let: t be the time for 1/3 rate
T be the time for 2/3 rate
Z be the time for the original rate.
d be the distance

We really want to know what T+t is. But the problem isn't that easy so well need to do some rewording. So here are a few equations well need


:Z- (T+t)=X

:original time: Z=d/V

:1/3 time: t=(d/3)/V --> (6d/18)/V

:2/3 time: T= (2d/3)/1.2V --> (10d/18)/V


Now we can reword our first equation to: d/V - ((10d/18)/V+(6d/18)/V)

(18d/18)/V - (16d/18)/V --> (2d/18)/V = X --> (d/9)/V=X


Now we can finally look at the statements:

S1: V=60. This doesn't help us. We cannot find out what T+t is.

All we can get is that (16d/18)/60= T+t We still have d in there and there is no way to elim the d without adding another variable. Insuff.

S2: x=20 well now we can refer back to our original Z-(T+t)=X

Convieniently reworked to: (d/9)/V=20 180V=d. Plug this into

T+t--> T+t= (16(180V)/18)/V ---> 160V^2=T+t...

ughhh NOOOOOOO on paper I was able to cancel out the V's now i cant. Arghhh!!!
VP
VP
avatar
Joined: 10 Jun 2007
Posts: 1467
Followers: 6

Kudos [?]: 108 [0], given: 0

Re: To arrive at its destination on time the bus should have [#permalink] New post 29 Oct 2007, 20:49
beckee529 wrote:
To arrive at its destination on time the bus should have maintained a speed of V kmh throughout the journey. Instead, after going the first third of the distance at V kmh, the bus increased its speed and went the rest of the distance at (1.2)*V kmh. As a result, the bus arrived at its destination X minutes earlier than planned. What was the actual duration of the trip?

1. V = 60
2. X = 20


I got B.

d = total distance
d/v is the original total time
d/(3v) + 2d/(3*(1.2v)) is the new total time
Therefore,
d/v - d/(3v) - 2d/(3.6v) = x
d/v*(1 - 1/3 - 1/1.8) = x

Looking for d/v = ?

(1) Given v, you can find d in term of x. This doesn't help us. Imagine the distance is infinite, there is no way we can find the actual time. INSUFFICIENT

(2) Given x, we can plug in
d/v*(1 - 1/3 - 1/1.8) = x
to obtain d/v
SUFFICIENT
Manager
Manager
avatar
Joined: 30 Sep 2007
Posts: 144
Followers: 1

Kudos [?]: 5 [0], given: 0

Re: To arrive at its destination on time the bus should have [#permalink] New post 30 Oct 2007, 02:49
bkk145 wrote:
beckee529 wrote:
To arrive at its destination on time the bus should have maintained a speed of V kmh throughout the journey. Instead, after going the first third of the distance at V kmh, the bus increased its speed and went the rest of the distance at (1.2)*V kmh. As a result, the bus arrived at its destination X minutes earlier than planned. What was the actual duration of the trip?

1. V = 60
2. X = 20


I got B.

d = total distance
d/v is the original total time
d/(3v) + 2d/(3*(1.2v)) is the new total time
Therefore,
d/v - d/(3v) - 2d/(3.6v) = x
d/v*(1 - 1/3 - 1/1.8) = x

Looking for d/v = ?

(1) Given v, you can find d in term of x. This doesn't help us. Imagine the distance is infinite, there is no way we can find the actual time. INSUFFICIENT

(2) Given x, we can plug in
d/v*(1 - 1/3 - 1/1.8) = x
to obtain d/v
SUFFICIENT


wow!!! what a fundoo way.. great bkk..
Intern
Intern
avatar
Joined: 26 Oct 2011
Posts: 1
Followers: 0

Kudos [?]: 0 [0], given: 0

Re: To arrive at its destination on time the bus should have [#permalink] New post 01 Nov 2011, 14:52
Just showing some more of the steps a little different way....

velocity * time = distance
vt = d
t = d/v

Thus, if we can find d/v, we can find t.

Now, Let:
t = original planned time (hours)
x = minutes arrived early; Must divide by 60 to convert to hours
v= original velocity (km/h)
d = total distance

Then, actual time of the trip (what we are solving for) is (t - x/60) which equals (from substitution from above):
(d/v) - x/60; So, if we know d/r and x, we can find the actual time of the trip

For the later 2/3rds of the trip, what is given in the problem is:

(1.2v)(2/3t - x/60)= (2/3)d

For B, plug in x = 20

(1.2v)(2/3t - 20/60) = (2/3)d

Substitute t= d/v
(1.2v)((2/3)(d/v)) - 1/3) = (2/3)d

Multiple out, .8d - 0.4v = (2/3)d
(2/15)d = 0.4v
d= (0.4*15/2) v
d = 3v
d/v =3

now, we know d/v and we know x (which is given), so we can find the actual time for the trip.

The answer is B.

Choice A doesn't work for reason explained in earlier posts...
Expert Post
Veritas Prep GMAT Instructor
User avatar
Joined: 16 Oct 2010
Posts: 4877
Location: Pune, India
Followers: 1157

Kudos [?]: 5381 [0], given: 165

Re: To arrive at its destination on time the bus should have [#permalink] New post 01 Nov 2011, 22:34
Expert's post
beckee529 wrote:
To arrive at its destination on time the bus should have maintained a speed of V kmh throughout the journey. Instead, after going the first third of the distance at V kmh, the bus increased its speed and went the rest of the distance at (1.2)*V kmh. As a result, the bus arrived at its destination X minutes earlier than planned. What was the actual duration of the trip?

1. V = 60
2. X = 20


Here is my take.
Let the actual duration of the trip be t.
Distance is same in both the cases.
So, V*t = Increased Average Speed*(t - X/60)

What is the Increased Average Speed?
Average Speed = Total Distance/Total Time = \frac{1}{[\frac{\frac{1}{3}}{V} + \frac{\frac{2}{3}}{1.2V}]}
We will get this increased average speed in terms of V.

When we put it in the equation above, V will get canceled leaving us with t in terms of X. So to get t, we only need X.
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Save $100 on Veritas Prep GMAT Courses And Admissions Consulting
Enroll now. Pay later. Take advantage of Veritas Prep's flexible payment plan options.

Veritas Prep Reviews

Manager
Manager
User avatar
Joined: 03 Jul 2013
Posts: 81
Followers: 1

Kudos [?]: 29 [0], given: 14

Re: To arrive at its destination on time the bus should have [#permalink] New post 12 Sep 2014, 01:22
I think statement 2 itself is enough

T1 = d/v

T2 = d/3v+(2/3)(d/1.2V)

We get T2 = 8/9(d/v)

Given that T1-X/60 = T2

(d/v)-(X/60) = 8/9(d/v)

Simplifying, we get X/60=d/9v; d/v=9X/60

We need to find only T1 that is d/v hence statement 2 is sufficient.
_________________

Sometimes standing still can be, the best move you ever make......

Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 23412
Followers: 3614

Kudos [?]: 28942 [0], given: 2874

Re: To arrive at its destination on time the bus should have [#permalink] New post 12 Sep 2014, 03:33
Expert's post
m10 q08

To arrive at its destination on time the bus should have maintained a speed of v kilometers per hour throughout the journey. Instead, after going the first third of the distance at v kilometers per hour, the bus increased its speed and went the rest of the distance at 1.2v kilometers per hour. As a result, the bus arrived at its destination x minutes earlier than planned. What was the actual duration of the trip?

A bus covered 1/3 of the distance at v kilometers per hour and the remaining 2/3 of the distance at 1.2v kilometers per hour.

Say the actual duration of the trip is t and the distance is d;

Then t=\frac{(\frac{d}{3})}{v}+\frac{(\frac{d2}{3})}{1.2v} --> t=\frac{d}{v}*(\frac{1}{3}+\frac{2}{3.6}) --> t=\frac{d}{v}*\frac{8}{9}

Also we know that if the speed throughout the journey had been v kilometers per hour the bus would need \frac{x}{60} hours more time to cover the same distance: t+\frac{x}{60}=\frac{d}{v};

Substitute \frac{d}{v} in the first equation: t=(t+\frac{x}{60})*\frac{8}{9}. So, to get t we need to know the value of x.

(1) v = 60. Not sufficient.
(2) x = 20. Sufficient.

Answer: B.

OPEN DISCUSSION OF THIS QUESTION IS HERE: to-arrive-at-its-destination-on-time-a-bus-should-have-main-105223.html
_________________

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?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Re: To arrive at its destination on time the bus should have   [#permalink] 12 Sep 2014, 03:33
    Similar topics Author Replies Last post
Similar
Topics:
Not math savvy, having a hard time with it, failing. crystallite 0 28 Mar 2013, 19:48
6 Experts publish their posts in the topic To arrive at its destination on time, a bus should have main Knesl 8 22 Nov 2010, 09:40
To arrive at its destination on time the bus should have amitdgr 2 30 Oct 2008, 02:08
Nearly all mail that is correctly addressed arrives at its r019h 10 23 Aug 2007, 11:50
Nearly all mail that is correctly addressed arrives at its gmatcrook 12 30 Aug 2006, 15:16
Display posts from previous: Sort by

To arrive at its destination on time the bus should have

  Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Privacy Policy| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.