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

It is currently 16 Apr 2014, 12:12

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

A boat traveled upstream 90 miles at an average speed of

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
2 KUDOS received
Intern
Intern
Joined: 06 Sep 2010
Posts: 17
Schools: HBS
WE 1: Management Consulting- 2 years
WE 2: Private Equity- 2 years
Followers: 1

Kudos [?]: 19 [2] , given: 6

GMAT Tests User
A boat traveled upstream 90 miles at an average speed of [#permalink] New post 09 Sep 2010, 16:29
2
This post received
KUDOS
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

72% (03:47) correct 27% (05:24) wrong based on 227 sessions
A boat traveled upstream 90 miles at an average speed of (v-3) miles per hour and then traveled the same distance downstream at an average speed of (v+3) miles per hour. If the trip upstream took a half hour longer than the trip downstream, then how many hours did it take the boat to travel downstream?

A. 2.5
B. 2.4
C. 2.3
D. 2.2
E. 2.1
[Reveal] Spoiler: OA
6 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 17283
Followers: 2868

Kudos [?]: 18333 [6] , given: 2345

GMAT Tests User CAT Tests
Re: Difficult PS Problem- Help! [#permalink] New post 09 Sep 2010, 16:54
6
This post received
KUDOS
Expert's post
jjewkes wrote:
Please help!

A boat traveled upstream 90 miles at an average speed of (v-3) miles per hour and then traveled the same distance downstream at an average speed of (v+3) miles per hour. If the trip upstream took a half hour longer than the trip downstream, then how many hours did it take the boat to travel downstream?

-2.5
-2.4
-2.3
-2.2
-2.1


Trip upstream took \frac{90}{v-3} hours and trip downstream took \frac{90}{v+3} hours. Also given that the difference in times was \frac{1}{2} hours --> \frac{90}{v-3}-\frac{90}{v+3}=\frac{1}{2};

\frac{90}{v-3}-\frac{90}{v+3}=\frac{1}{2} --> \frac{90(v+3)-90(v-3)}{v^2-9}=\frac{1}{2} --> \frac{90*6}{v^2-9}=\frac{1}{2} --> v^2=90*6*2+9 --> v^2=9*(10*6*2+1) --> v^2=9*121 --> v=3*11=33;

Trip downstream took \frac{90}{v+3}=\frac{90}{33+3}=2.5 hours.

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?
25 extra-hard Quant Tests

Joined: 31 Dec 1969
Location: United States
Concentration: Marketing, Other
GMAT 1: 710 Q49 V38
GMAT 2: 660 Q V
GPA: 3.64
WE: Accounting (Accounting)
Followers: 0

Kudos [?]: 46 [0], given: 72019

Re: Difficult PS Problem- Help! [#permalink] New post 11 Sep 2010, 20:33
90/(v-3)=90(v+3)+.5

90[v+3-v+3]/(v*v-9)=.5
90*6/(v*v-9)=.5
90*12+9=v*v
v*v=1089
v=33
v+3=36

Time required to travel downstream=90/36=2.5 hours
Senior Manager
Senior Manager
User avatar
Status: Time to step up the tempo
Joined: 24 Jun 2010
Posts: 413
Location: Milky way
Schools: ISB, Tepper - CMU, Chicago Booth, LSB
Followers: 6

Kudos [?]: 100 [0], given: 50

Re: Boat Traveling [#permalink] New post 30 Sep 2010, 21:43
Michmax3 wrote:
A boat traveled upstream a distance of 90 miles at an average speed of (V-3) miles per hour and then traveled the same distance downstream at an average speed of (V+3) miles per hour. If the upstream trip took half an hour longer than the downstream trip, how many hours did it take the boat to travel downstream?

A)2.5
B)2.4
C)2.3
D)2.2
E)2.1


Given 90/(v-3) = 90/(v+3) + (1/2)
90[(1/(v-3)) - (1/(v+3))] = 1/2
90[6/(v^2 - 9)] = 1/2

90*6*2 = v^2 - 9 => v^2 = 1089 => v = 33.

Downstream time -- 90/(v+3) => 90/36 => 2.5 (A).
_________________

:good Support GMAT Club by putting a GMAT Club badge on your blog :thanks

1 KUDOS received
Retired Moderator
User avatar
Joined: 02 Sep 2010
Posts: 807
Location: London
Followers: 74

Kudos [?]: 394 [1] , given: 25

GMAT ToolKit User GMAT Tests User Reviews Badge
Re: Boat Traveling [#permalink] New post 30 Sep 2010, 21:45
1
This post received
KUDOS
Michmax3 wrote:
A boat traveled upstream a distance of 90 miles at an average speed of (V-3) miles per hour and then traveled the same distance downstream at an average speed of (V+3) miles per hour. If the upstream trip took half an hour longer than the downstream trip, how many hours did it take the boat to travel downstream?

A)2.5
B)2.4
C)2.3
D)2.2
E)2.1


Upstream time = downstream time + 0.5

90/(v-3) = 90/(v+3) + 1/2
90 (1/(v-3) - 1/(v+3))= 1/2
90 (6/(v^2-9)) = 1/2
v^2 = 1089
V = 33

Downstream time = 90/36 = 2.5

Answer is (a)
_________________

Math write-ups
1) Algebra-101 2) Sequences 3) Set combinatorics 4) 3-D geometry

My GMAT story

Intern
Intern
Joined: 05 Oct 2010
Posts: 49
GMAT 1: Q V
GMAT 2: Q V
Followers: 0

Kudos [?]: 3 [0], given: 1

GMAT Tests User
Word problem need help solving [#permalink] New post 21 Nov 2010, 06:17
Hi I just took one gmat practice test and the pity about those test is that they don´t have explanations.

The problem i am struggling with in mathematical sense is something like this:

A boat that traveled 90 miles upstream a river at the rate average speed Y-3, on the way back he traveled the same distance (90 miles) at a average speed of Y+3, if the trip upstream took half an hour longer than the trip down stream. How long took the drip downstream ?

right answer is 2,5

please help me this is so annoying :)

thanks, I shall give my teacher kudos if I find out how to do that
Manager
Manager
User avatar
Joined: 01 Nov 2010
Posts: 183
Location: Zürich, Switzerland
Followers: 2

Kudos [?]: 12 [0], given: 20

Re: Difficult PS Problem- Help! [#permalink] New post 21 Nov 2010, 13:02
solve the below equation to reach upon speed of boat-

90/(v+3) - 90/(v-3) = 1/2
V=33

therefore time required while travelling downstream- 90/(33+3) = 90/36 = 2.5

Answer:- A
Intern
Intern
Joined: 05 Oct 2010
Posts: 49
GMAT 1: Q V
GMAT 2: Q V
Followers: 0

Kudos [?]: 3 [0], given: 1

GMAT Tests User
Re: Boat Traveling [#permalink] New post 22 Nov 2010, 01:19
shrouded1 wrote:
Michmax3 wrote:
v^2 = 1089
V = 33

Downstream time = 90/36 = 2.5

Answer is (a)


Hi I struggled with this one, I am wondering
Is there any good shortcut in how to take the root of 1089 ? how do you do that without spending too much time on it ? :roll:

many thanks
3 KUDOS received
Veritas Prep GMAT Instructor
User avatar
Joined: 16 Oct 2010
Posts: 4169
Location: Pune, India
Followers: 894

Kudos [?]: 3783 [3] , given: 148

Re: Boat Traveling [#permalink] New post 22 Nov 2010, 05:57
3
This post received
KUDOS
Expert's post
hafgola wrote:

Hi I struggled with this one, I am wondering
Is there any good shortcut in how to take the root of 1089 ? how do you do that without spending too much time on it ? :roll:

many thanks


Let me take your question first:

It is a good idea to remember squares of numbers till 20. They come in handy sometimes.
To find the square root of bigger numbers (which are perfect squares), observe the following:
1. A square of a number only ends in 0/1/4/5/6/9.
-If it ends in 0, it will have even number of 0s at the end and the square root will end in 0 (I know 1340 cannot be a perfect square.)
-If it ends in 1, the square root will end in 1/9 (e.g. root 361 = 1[highlight]9[/highlight], root 441 = 2[highlight]1[/highlight])
-If it ends in 4, the square root will end in 2/8
-If it ends in 5, there will be a 2 right before it and its square root will end in 5 (e.g. root 625 = 25, root 675 is not an integer)
-If it ends in 6, the square root will end in 4/6.
-If it ends in 9, the square root will end in 3/7.
These are all derived by just observing the last digits when we square a number.. You don't need to learn this.

Since 1089 ends in a 9, its square root will end in 3/7.
Also 30^2 = 900 so root of 1089 will be greater than 30.
But 40^2 = 1600 so root of 1089 will be much less than 40. The number that can be the square root of 1089 is 33 (if 1089 is a perfect square). You can square 33 to check.

Also, an equation like \frac{90}{{v -3}} - \frac{90}{{v + 3}} = \frac{1}{2}, doesnt need to be solved.

99% chance is that v will be an integer.
The options give me values for \frac{90}{{v + 3}}

Let me say if it is 2.5, then 90/2.5 = 36 and v = 33
Then \frac{90}{{v - 3}} = 3. I get the difference of 1/2 an hour. 2.5 satisfies my condition.

Had 2.5 not been the first option, you might say that it would take me a long time to check each option.
No. 90/2.4 = 900/24 which is not an integer since 900 is not divisible by 8 so it will not be divisible by 24
90/2.3. No ways 900 is divisible by 23
90/2.2. No ways 900 is divisible by 11
90/2.1. No ways 900 is divisible by 7
In fact, when I look at the options, the first one I try is 2.5. With practice, you will gain the instinct.
_________________

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

Director
Director
User avatar
Status: GMAT Learner
Joined: 14 Jul 2010
Posts: 655
Followers: 29

Kudos [?]: 158 [0], given: 32

GMAT Tests User
Re: Difficult PS Problem- Help! [#permalink] New post 25 Mar 2011, 10:22
problem is time consuming rather difficult for memorizing square root.
_________________

I am student of everyone-baten
Collections:-
PSof OG solved by GC members: http://gmatclub.com/forum/collection-ps-with-solution-from-gmatclub-110005.html
DS of OG solved by GC members: http://gmatclub.com/forum/collection-ds-with-solution-from-gmatclub-110004.html
100 GMAT PREP Quantitative collection http://gmatclub.com/forum/gmat-prep-problem-collections-114358.html
Collections of work/rate problems with solutions http://gmatclub.com/forum/collections-of-work-rate-problem-with-solutions-118919.html
Mixture problems in a file with best solutions: http://gmatclub.com/forum/mixture-problems-with-best-and-easy-solutions-all-together-124644.html

SVP
SVP
Joined: 16 Nov 2010
Posts: 1698
Location: United States (IN)
Concentration: Strategy, Technology
Followers: 29

Kudos [?]: 263 [0], given: 36

GMAT Tests User Premium Member Reviews Badge
Re: Difficult PS Problem- Help! [#permalink] New post 27 Mar 2011, 00:18
90/(v-3) = 90/(v+3) + 1/2

=> 90( V + 3 - v + 3)/(v-3)(v+3) = 1/2

=> 90 * 6 * 2 = v^2 - 9

=> v^2 = 1080 + 9

=> v^2 = 9 (120 + 1)

=> v^2 = 3^2 * 11^2

=> v = 3*11 = 33

So Downstream time = 90/36 = 30/12 = 2.5 hrs

Answer - A
_________________

Formula of Life -> Achievement/Potential = k * Happiness (where k is a constant)

Director
Director
Joined: 01 Feb 2011
Posts: 773
Followers: 12

Kudos [?]: 76 [0], given: 42

GMAT Tests User
Re: Difficult PS Problem- Help! [#permalink] New post 25 Aug 2011, 16:19
upstream v-3 t+1/2

downstream v+3 t

(v+3)t = (v-3)(t+1/2)

vt + 3t = vt +v/2 - 3t - 3/2

=> t = (v-3)/12 = 90/v+3 => v = 33

=> t = 30/12 = 2.5 hours

Answer is A.
Current Student
Joined: 14 May 2011
Posts: 277
Location: Costa Rica
Concentration: Healthcare, International Business
GMAT 1: 640 Q V0
GMAT 2: 710 Q42 V45
GMAT 3: 740 Q48 V42
GMAT 4: Q V0
GMAT 5: Q V0
GPA: 3.3
WE: Research (Consulting)
Followers: 10

Kudos [?]: 52 [0], given: 134

GMAT Tests User
Re: Downstream Rate Question [#permalink] New post 17 Aug 2012, 14:13
Can someone pls help with the above question? What is the most efficient way to do this. Here's what i've got..

If one takes the time for the trip downstream to to be T, then one gets
UPSTREAM:
V-3 = 90 / (T + 1/2)

DOWNSTREAM
V+3 = 90 / T

Now no matter how much I simplify I end up with a complicated equation, and then it will be plugging in off answer choices but that takes >3 minutes at least.
Any suggestions for a sohrtcut, I'm sure there's an easy way..
_________________


How to improve your RC score, pls Kudo if helpful! http://gmatclub.com/forum/how-to-improve-my-rc-accuracy-117195.html
Work experience (as of June 2012)
2.5 yrs (Currently employed) - Mckinsey & Co. (US Healthcare Analyst)
2 yrs - Advertising industry (client servicing)

Intern
Intern
Joined: 01 Jan 2011
Posts: 22
Location: Kansas, USA
Schools: INSEAD, Wharton
Followers: 2

Kudos [?]: 5 [0], given: 9

Re: Downstream Rate Question [#permalink] New post 17 Aug 2012, 16:40
I think the answer to the question posted here should be 2.5.

Basically, frame the equation in terms of the difference in time (= distance/ speed):

[90][/v-3]- [90][/v+3]= 1/2. Once you get this you could solve for V. Remember that the question is asking for the value of [90][/v+3].
1 KUDOS received
Moderator
Moderator
User avatar
Joined: 02 Jul 2012
Posts: 1208
Location: India
Concentration: Strategy
GMAT 1: 740 Q49 V42
GPA: 3.8
WE: Engineering (Energy and Utilities)
Followers: 52

Kudos [?]: 560 [1] , given: 111

GMAT Tests User Premium Member
Re: A boat traveled upstream a distance of 90miles at an average [#permalink] New post 19 Nov 2012, 00:10
1
This post received
KUDOS
Amateur wrote:
A boat traveled upstream a distance of 90miles at an average speed of (v-3) miles per hour and then traveled down stream at an average of (v+3) miles per hour. If upstream look 30 min more than downstream time, how much time did the boat travel downstream?
a) 2.5
b) 2.4
c) 2.3
d) 2.2
e) 2.1

how to solve these kind of questions in 2 min? any short way...
\frac{90}{(v-3)}=\frac{90}{(v+3)} +1/2
solving for v, value of \frac{90}{(v+3)} is tedious... and answer choices are in too close range to make an estimation.... how should I be tackling these?


The equation itself is simple enough..

\frac{90}{v-3}- \frac{90}{v+3} = \frac{1}{2}

\frac{540}{v^2-9} = \frac{1}{2}

v^2 - 9 = 1080

v^2 = 1089 = 3^2 * 11^2

v = 3*11 = 33

Answer = 90/36 = 2.5

Kudos Please... If my post helped.
_________________

Did you find this post helpful?... Please let me know through the Kudos button.

Thanks To The Almighty - My GMAT Debrief

GMAT Reading Comprehension: 7 Most Common Passage Types

Intern
Intern
Joined: 27 Dec 2012
Posts: 11
Followers: 0

Kudos [?]: 0 [0], given: 10

CAT Tests
Re: Boat Traveling [#permalink] New post 14 Mar 2013, 01:11
VeritasPrepKarishma wrote:
hafgola wrote:

Hi I struggled with this one, I am wondering
Is there any good shortcut in how to take the root of 1089 ? how do you do that without spending too much time on it ? :roll:

many thanks


Let me take your question first:

It is a good idea to remember squares of numbers till 20. They come in handy sometimes.
To find the square root of bigger numbers (which are perfect squares), observe the following:
1. A square of a number only ends in 0/1/4/5/6/9.
-If it ends in 0, it will have even number of 0s at the end and the square root will end in 0 (I know 1340 cannot be a perfect square.)
-If it ends in 1, the square root will end in 1/9 (e.g. root 361 = 19, root 441 = 21)
-If it ends in 4, the square root will end in 2/8
-If it ends in 5, there will be a 2 right before it and its square root will end in 5 (e.g. root 625 = 25, root 675 is not an integer)
-If it ends in 6, the square root will end in 4/6.
-If it ends in 9, the square root will end in 3/7.
These are all derived by just observing the last digits when we square a number.. You don't need to learn this.

Since 1089 ends in a 9, its square root will end in 3/7.
Also 30^2 = 900 so root of 1089 will be greater than 30.
But 40^2 = 1600 so root of 1089 will be much less than 40. The number that can be the square root of 1089 is 33 (if 1089 is a perfect square). You can square 33 to check.

Also, an equation like \frac{90}{{v -3}} - \frac{90}{{v + 3}} = \frac{1}{2}, doesnt need to be solved.

99% chance is that v will be an integer.
The options give me values for \frac{90}{{v + 3}}

Let me say if it is 2.5, then 90/2.5 = 36 and v = 33
Then \frac{90}{{v - 3}} = 3. I get the difference of 1/2 an hour. 2.5 satisfies my condition.

Had 2.5 not been the first option, you might say that it would take me a long time to check each option.
No. 90/2.4 = 900/24 which is not an integer since 900 is not divisible by 8 so it will not be divisible by 24
90/2.3. No ways 900 is divisible by 23
90/2.2. No ways 900 is divisible by 11
90/2.1. No ways 900 is divisible by 7
In fact, when I look at the options, the first one I try is 2.5. With practice, you will gain the instinct.

Hi karishma,
I have been able to solve most of the questions from work, speeed distane & mixtures. However i always solve them using the algebraic approach which eats up a lot of time. I have seen you solving questions by a logical approach that saves a considerable bit of time. I have tried solving that way but I just cant get going. Could you please advice me on how to develop this skill??
Veritas Prep GMAT Instructor
User avatar
Joined: 16 Oct 2010
Posts: 4169
Location: Pune, India
Followers: 894

Kudos [?]: 3783 [0], given: 148

Re: Boat Traveling [#permalink] New post 14 Mar 2013, 19:36
Expert's post
sauravleo123 wrote:
Hi karishma,
I have been able to solve most of the questions from work, speeed distane & mixtures. However i always solve them using the algebraic approach which eats up a lot of time. I have seen you solving questions by a logical approach that saves a considerable bit of time. I have tried solving that way but I just cant get going. Could you please advice me on how to develop this skill??


It needs practice. You need to believe that you can solve the question very quickly for you to be able to think up of logical approaches. In GMAT, you can solve almost every question within two minutes so if you get a big complicated equation, you can be sure that you are missing something. If the question looks really complicated, we know there has to be a trick (In fact, one tends to overlook the so called short-cuts when questions are simple and don't take much time anyway).
I would suggest you to read up and practice the logical solutions - once you understand the logic, try using it in other questions. Don't worry about the time factor. I discuss some logic based ideas regularly on my blog. Check it out:

http://www.veritasprep.com/blog/categor ... om/page/3/
_________________

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

Intern
Intern
Joined: 14 Aug 2012
Posts: 13
Followers: 0

Kudos [?]: 1 [0], given: 11

Re: A boat traveled upstream 90 miles at an average speed of [#permalink] New post 08 May 2013, 03:27
I would prefer substituting answers rather than solving the equation to save time. In actual test, i was way past time, took more than 3 mins to solve the Q. Later offline, i used substitution after arriving at the initial set of below equations for Time. It was so easy and less troublesome.

UPSTREAM:
V-3 = 90 / (T + 1/2)

DOWNSTREAM
V+3 = 90 / T
Manager
Manager
User avatar
Joined: 17 Sep 2013
Posts: 89
Location: United States
Concentration: Marketing, Strategy
GMAT Date: 04-30-2014
GPA: 3.24
WE: Analyst (Consulting)
Followers: 2

Kudos [?]: 22 [0], given: 25

GMAT ToolKit User
Re: A boat traveled upstream 90 miles at an average speed of [#permalink] New post 20 Mar 2014, 12:19
2.5 hrs..A set of best possible option spares u the horror of solving the equations..

90 miles is the distance traveled downstream..2.5 is the only only option that divides 90..I am pretty sure the speeds are never (25.12+3) & (25.12-3)..So we can safely assume an integer..2.5 & 3 are the set of speeds that aptly fit in.

took me just 10 secs..
_________________

Appreciate the efforts...KUDOS for all

Re: A boat traveled upstream 90 miles at an average speed of   [#permalink] 20 Mar 2014, 12:19
    Similar topics Author Replies Last post
Similar
Topics:
This topic is locked, you cannot edit posts or make further replies. New 4 Experts publish their posts in the topic A boat traveled upstream a distance of 90 miles at an CfaMiami 9 23 Jul 2006, 08:02
New posts 1 A boat traveled upstream a distance of 90 miles at an diegmat 4 23 Sep 2006, 22:01
New posts 1 A boat traveled upstream a distance of 90 miles at an uphillclimb 4 21 Oct 2006, 09:50
New posts A boat traveled upstream a distance of 90 miles at an Mishari 4 01 Jun 2007, 13:04
New posts A boat traveled upstream a distance of 90 miles at an LM 2 23 Jun 2007, 02:04
Display posts from previous: Sort by

A boat traveled upstream 90 miles at an average speed of

  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®.