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

It is currently 30 Aug 2014, 10:34

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

Machines X and V produced identical bottles at different

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
6 KUDOS received
Intern
Intern
User avatar
Joined: 13 May 2010
Posts: 26
Followers: 0

Kudos [?]: 7 [6] , given: 13

GMAT ToolKit User
Machines X and V produced identical bottles at different [#permalink] New post 03 Nov 2010, 16:36
6
This post received
KUDOS
10
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

64% (02:18) correct 36% (01:28) wrong based on 746 sessions
Machines X and Y produced identical bottles at different constant rates. Machine X, operating alone for 4 hours, filled part of a production lot; then Machine Y, operating alone for 3 hours, filled the rest of this lot. How many hours would it have taken Machine X operating alone to fill the entire production lot?

(1) Machine X produced 30 bottles per minute.
(2) Machine X produced twice as many bottles in 4 hours as Machine Y produced in 3 hours.
[Reveal] Spoiler: OA

_________________

"Effort only fully releases its reward after a person refuses to quit." - Napoleon Hill

If my post helped you in any way please give KUDOS!

Expert Post
26 KUDOS received
Veritas Prep GMAT Instructor
User avatar
Joined: 16 Oct 2010
Posts: 4688
Location: Pune, India
Followers: 1084

Kudos [?]: 4872 [26] , given: 163

Re: Word Translations - Rates & Work [#permalink] New post 03 Nov 2010, 17:08
26
This post received
KUDOS
Expert's post
4
This post was
BOOKMARKED
cgl7780 wrote:
Machines X and Y produced identical bottles at different constant rates. Machine X, operating alone for 4 hours, filled part of a production lot; then Machine Y, operating alone for 3 hours, filled the rest of this lot. How many hours would it have taken Machine X operating alone to fill the entire production lot?

1. Machine X produced 30 bottles per minute
2. Machine X produced twice as many bottles in 4 hours as Machine Y produced in
3 hours.

(I think you guys know the choices for DS)


We know that Machine X worked for 4 hrs alone and then Machine Y worked for 3 hrs alone. This filled up the production lot.
Ques: If Machine X were operating alone, how many hours would it take?
The first thing that comes to mind is that it would take more than 4 hrs since it filled only a part of the lot in 4 hrs.

Statement I: I know the rate at which Machine X produces bottles. It is 30 bottles/min or 1800 bottles/hr. So Machine X must have made 7200 bottles in 4 hours. But I do not know how many bottles fills the lot since I do not know how many bottles were made by Machine Y in 3 hours. This statement alone is not sufficient.

Statement II: Machine X produced twice as many bottles in 4 hours as Machine Y did in 3 hrs. Then I can say that Machine X filled 2/3 rd of the lot in 4 hrs. (If this is unclear, think Machine Y made 'b' bottles in 3 hrs, then Machine X made '2b' bottles in 4 hrs and together the lot contained '3b' bottles. So Machine X filled 2/3 of the lot in 4 hours.) In how much time will Machine X fill the rest of the 1/3 rd lot? In 2 hours. Hence, it takes a total of 6 hours to fill the lot on its own. This is sufficient to answer the question.

Answer: B
_________________

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

1 KUDOS received
Intern
Intern
User avatar
Joined: 13 May 2010
Posts: 26
Followers: 0

Kudos [?]: 7 [1] , given: 13

GMAT ToolKit User
Re: Word Translations - Rates & Work [#permalink] New post 03 Nov 2010, 17:22
1
This post received
KUDOS
Thank you that clears it up, I was timing myself so trying to get through the problem in 2min or less. When I read the two statements I came to the exact same conclusion you did on statement 1; I can determine exactly how many bottles machine X made, but I don't know how many bottles = 1 lot, Insufficient.

However in reading statement 2 I felt it wasn't enough to answer the question by itself (Machine X produced twice as many bottles as Y) I didn't have a rate or a total, However, from statement 1, I could get an exact answer of how many Machine X produced, then simply divide by 2 to get the amount Machine Y produced. Adding these two together will give me the total bottles in one lot. With both statements I have all the information I need to determine how long it would take Machine X to fill the lot by itself because now I have it's rate and the total number of bottles in one lot. So I chose "C" Both statements together are sufficient

How could this logic be wrong?
_________________

"Effort only fully releases its reward after a person refuses to quit." - Napoleon Hill

If my post helped you in any way please give KUDOS!

Expert Post
8 KUDOS received
Veritas Prep GMAT Instructor
User avatar
Joined: 16 Oct 2010
Posts: 4688
Location: Pune, India
Followers: 1084

Kudos [?]: 4872 [8] , given: 163

Re: Word Translations - Rates & Work [#permalink] New post 03 Nov 2010, 18:13
8
This post received
KUDOS
Expert's post
cgl7780 wrote:
Thank you that clears it up, I was timing myself so trying to get through the problem in 2min or less. When I read the two statements I came to the exact same conclusion you did on statement 1; I can determine exactly how many bottles machine X made, but I don't know how many bottles = 1 lot, Insufficient.

However in reading statement 2 I felt it wasn't enough to answer the question by itself (Machine X produced twice as many bottles as Y) I didn't have a rate or a total, However, from statement 1, I could get an exact answer of how many Machine X produced, then simply divide by 2 to get the amount Machine Y produced. Adding these two together will give me the total bottles in one lot. With both statements I have all the information I need to determine how long it would take Machine X to fill the lot by itself because now I have it's rate and the total number of bottles in one lot. So I chose "C" Both statements together are sufficient

How could this logic be wrong?


:)
Word of caution in DS questions. One trick they use often is that they give you partial information in Statement (1), they give the rest in statement (II) so you think, "Of course, answer is an easy (C)." Mind you, if it seems to be an easy (C), go back to the question, read it again and then try and solve it using statement (II) alone, Try to 'wipe' statement (I) from your mind for the time being.
Here, I don't need to know how many bottles Machine A produced in total. I only need to know how many hours it will take to fill the lot. Since it filled 2/3rd in 4 hrs, it will the rest 1/3 in 2 hrs.
_________________

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

Expert Post
22 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 25207
Followers: 3419

Kudos [?]: 25092 [22] , given: 2702

Re: Word Translations - Rates & Work [#permalink] New post 03 Nov 2010, 23:22
22
This post received
KUDOS
Expert's post
11
This post was
BOOKMARKED
cgl7780 wrote:
Machines X and Y produced identical bottles at different constant rates. Machine X, operating alone for 4 hours, filled part of a production lot; then Machine Y, operating alone for 3 hours, filled the rest of this lot. How many hours would it have taken Machine X operating alone to fill the entire production lot?

1. Machine X produced 30 bottles per minute
2. Machine X produced twice as many bottles in 4 hours as Machine Y produced in
3 hours.

(I think you guys know the choices for DS)


There are several important things you should know to solve work problems:

1. Time, rate and job in work problems are in the same relationship as time, speed (rate) and distance in rate problems.

time*speed=distance <--> time*rate=job \ done. For example when we are told that a man can do a certain job in 3 hours we can write: 3*rate=1 --> rate=\frac{1}{3} job/hour. Or when we are told that 2 printers need 5 hours to complete a certain job then 5*(2*rate)=1 --> so rate of 1 printer is rate=\frac{1}{10} job/hour. Another example: if we are told that 2 printers need 3 hours to print 12 pages then 3*(2*rate)=12 --> so rate of 1 printer is rate=2 pages per hour;

So, time to complete one job = reciprocal of rate. For example if 6 hours (time) are needed to complete one job --> 1/6 of the job will be done in 1 hour (rate).

2. We can sum the rates.

If we are told that A can complete one job in 2 hours and B can complete the same job in 3 hours, then A's rate is rate_a=\frac{job}{time}=\frac{1}{2} job/hour and B's rate is rate_b=\frac{job}{time}=\frac{1}{3} job/hour. Combined rate of A and B working simultaneously would be rate_{a+b}=rate_a+rate_b=\frac{1}{2}+\frac{1}{3}=\frac{5}{6} job/hour, which means that they will complete \frac{5}{6} job in one hour working together.

3. For multiple entities: \frac{1}{t_1}+\frac{1}{t_2}+\frac{1}{t_3}+...+\frac{1}{t_n}=\frac{1}{T}, where T is time needed for these entities to complete a given job working simultaneously.

For example if:
Time needed for A to complete the job is A hours;
Time needed for B to complete the job is B hours;
Time needed for C to complete the job is C hours;
...
Time needed for N to complete the job is N hours;

Then: \frac{1}{A}+\frac{1}{B}+\frac{1}{C}+...+\frac{1}{N}=\frac{1}{T}, where T is the time needed for A, B, C, ..., and N to complete the job working simultaneously.

For two and three entities (workers, pumps, ...):

General formula for calculating the time needed for two workers A and B working simultaneously to complete one job:

Given that t_1 and t_2 are the respective individual times needed for A and B workers (pumps, ...) to complete the job, then time needed for A and B working simultaneously to complete the job equals to T_{(A&B)}=\frac{t_1*t_2}{t_1+t_2} hours, which is reciprocal of the sum of their respective rates (\frac{1}{t_1}+\frac{1}{t_2}=\frac{1}{T}).

General formula for calculating the time needed for three A, B and C workers working simultaneously to complete one job:

T_{(A&B&C)}=\frac{t_1*t_2*t_3}{t_1*t_2+t_1*t_3+t_2*t_3} hours.

BACK TO THE ORIGINAL QUESTION:
Machines X and Y produced identical bottles at different constant rates. Machine X, operating alone for 4 hours, filled part of a production lot; then Machine Y, operating alone for 3 hours, filled the rest of this lot. How many hours would it have taken Machine X operating alone to fill the entire production lot?

You can solve this question as Karishma proposed in her post above or algebraically:

Let the rate of X be x bottle/hour and the rate of Y y bottle/hour.
Given: 4x+3y=job. Question: t_x=\frac{job}{rate}=\frac{job}{x}=?

(1) Machine X produced 30 bottles per minute --> x=30*60=1800 bottle/hour, insufficient as we don't know how many bottles is in 1 lot (job).

(2) Machine X produced twice as many bottles in 4 hours as Machine Y produced in 3 hours --> 4x=2*3y, so 3y=2x --> 4x+3y=4x+2x=6x=job --> t_x=\frac{job}{rate}=\frac{job}{x}=\frac{6x}{x}=6 hours. Sufficient.

Answer: B.

Some work problems with solutions:
time-n-work-problem-82718.html
facing-problem-with-this-question-91187.html
what-am-i-doing-wrong-to-bunuel-91124.html
gmat-prep-ps-93365.html
questions-from-gmat-prep-practice-exam-please-help-93632.html
a-good-one-98479.html
solution-required-100221.html
work-problem-98599.html
hours-to-type-pages-102407.html

Hope it helps.
_________________

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

1 KUDOS received
Manager
Manager
avatar
Joined: 21 Jul 2010
Posts: 56
Followers: 1

Kudos [?]: 7 [1] , given: 3

GMAT ToolKit User
Re: Word Translations - Rates & Work [#permalink] New post 03 Nov 2010, 23:54
1
This post received
KUDOS
Thanks Bunuel! I like your work/rate resume. It is really helpful. +1
3 KUDOS received
Senior Manager
Senior Manager
User avatar
Affiliations: SPG
Joined: 15 Nov 2006
Posts: 326
Followers: 11

Kudos [?]: 262 [3] , given: 20

GMAT Tests User
Re: Word Translations - Rates & Work [#permalink] New post 16 Jan 2011, 05:38
3
This post received
KUDOS

1) does not tell us anything about Y. INSUFFICIENT

2) machine X produced twice as much as Y did i.e. did \frac{2}{3} of the work.

\frac{2}{3} work required 4 hours

1 complete work requires \frac{4*3}{2} = 6 hours

Answer: B

HTH

_________________

press kudos, if you like the explanation, appreciate the effort or encourage people to respond.

Download the Ultimate SC Flashcards

Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 25207
Followers: 3419

Kudos [?]: 25092 [0], given: 2702

Re: Machines X and V produced identical bottles at different [#permalink] New post 30 May 2013, 03:56
Expert's post
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE

Theory on work/rate problems: work-word-problems-made-easy-87357.html
All DS work/rate problems to practice: search.php?search_id=tag&tag_id=46
All PS work/rate problems to practice: search.php?search_id=tag&tag_id=66

_________________

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

1 KUDOS received
Intern
Intern
avatar
Joined: 18 Mar 2013
Posts: 5
Followers: 0

Kudos [?]: 2 [1] , given: 45

Re: Machines X and V produced identical bottles at different [#permalink] New post 01 Jun 2013, 18:17
1
This post received
KUDOS
But dont we have to consider the 4 and 3 hrs for machine X and machine Y?
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 25207
Followers: 3419

Kudos [?]: 25092 [0], given: 2702

Re: Machines X and V produced identical bottles at different [#permalink] New post 02 Jun 2013, 03:40
Expert's post
1 KUDOS received
Intern
Intern
avatar
Joined: 19 Apr 2012
Posts: 28
Followers: 0

Kudos [?]: 2 [1] , given: 8

Re: Machines X and V produced identical bottles at different [#permalink] New post 02 Jun 2013, 05:38
1
This post received
KUDOS
4R = X

3R* = Total - X

4R = 2(3R*)

R* = 4R/6 = 2/3R

------------------------

3R* = Total - 4R

2R = Total - 4R

6R = Total

Answer: 6. B.
1 KUDOS received
Manager
Manager
avatar
Joined: 27 Apr 2012
Posts: 61
Location: United States
GMAT Date: 06-11-2013
GPA: 3.5
WE: Marketing (Consumer Products)
Followers: 1

Kudos [?]: 9 [1] , given: 18

GMAT ToolKit User Premium Member CAT Tests
Re: Machines X and V produced identical bottles at different [#permalink] New post 02 Jun 2013, 22:17
1
This post received
KUDOS
Stmt 1 : Machine X produced 30 bottles per minute hence in 4 hrs i.e. 240 minutes how many did machine X produce?

(30 * 240) = 7200 bottles

But we don’t know the exact size of the production lot so while we know X’s work rate, we don’t know how many hrs it will take for X to fill up the production lot.

Hence this stmt is insufficient.



Stmt 2 : Let a be the number of bottle machine Y produces in 3 hrs

Machine X produced twice as many bottles in 4 hours as Machine Y produced in 3 hours

Then 2a is the number of bottles machine X produced in 4 hrs

Hence the total lot size = a + 2a = 3a

If X produces 2a bottles ibn 4 hrs then how many hrs will it take to produce 3a bottles?

(3a * 4)/2a = 6 hrs

Answer : B
1 KUDOS received
Intern
Intern
avatar
Joined: 28 Apr 2013
Posts: 16
GMAT Date: 08-03-2013
GPA: 3.3
WE: Supply Chain Management (Military & Defense)
Followers: 0

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

GMAT ToolKit User
Re: Machines X and V produced identical bottles at different [#permalink] New post 09 Jul 2013, 20:08
1
This post received
KUDOS
I set up two rudimentary equations for each machine from the prompt before entering into determining the sufficiency of each statement:

x*4=n where x is the rate of Machine X and n is the amount of the job completed in four hours
y*3=m where y is the rate of Machine Y and m is the amount of the job completed in three hours
where n+m=1 in order to preserve the fact that X and Y complete one job together (yet individually)

Statement 1: I won't beat a dead horse here, we know this is clearly insufficient

Statement 2: Here we see that n=2m or that Machine X completed 2/3 of the work and Machine Y completed 1/3 of the work. By substituting 2/3 for n and 1/3 for m in the equations above we are able to determine how long it would take Machine X to complete 1 (one complete unit) of work since we have x*4=\frac{2}{3} ....Sufficient

Answer B
1 KUDOS received
Manager
Manager
avatar
Joined: 09 Jan 2013
Posts: 68
Followers: 0

Kudos [?]: 14 [1] , given: 6

Re: Machines X and V produced identical bottles at different [#permalink] New post 24 Sep 2013, 01:16
1
This post received
KUDOS
If we know total Work then can find out total time take by machine A(Asked)
Major Goal: Total Work.
Machine A's contribution: 4/X
Machine B's contribution: 3/Y
Total Work: 4/X+3/Y. ------------Eq(1)

Statement 1: Machine X produced 30 bottles per minute.
nothing has been said about machine Y....So not sufficient.

Statement 2: Machine X produced twice as many bottles in 4 hours as Machine Y produced in 3 hours.
4/X = 6/Y
Substitute in Eq(1) and get the raltionship between Total Work and X.
Finally total time....So Suffcient

Hence (B)
Intern
Intern
User avatar
Joined: 02 Jul 2014
Posts: 11
Followers: 0

Kudos [?]: 1 [0], given: 32

GMAT ToolKit User
Re: Machines X and V produced identical bottles at different [#permalink] New post 03 Jul 2014, 19:50
x = rate of machine X
y = rate of machine Y
one lot = 4x + 3y

1. we know x, but don't know y
not sufficient

2. 4x = 2*3y, so 3y = 2x
then, one lot = 4x + 2x = 6x -> 6 hours for machine x to complete the lot
sufficient
Re: Machines X and V produced identical bottles at different   [#permalink] 03 Jul 2014, 19:50
    Similar topics Author Replies Last post
Similar
Topics:
Machines X and Y produce identical bottles at different galaxyblue 3 08 Nov 2011, 19:21
Experts publish their posts in the topic Machines X and Y produced identical bottles at different sonibubu 8 28 Jan 2008, 12:38
1 Machines X and Y produced identical bottles at different GGUY 5 17 Jan 2008, 06:39
Machines X and Y produced identical bottles at different Hermione 8 23 Oct 2006, 00:21
Machines X and Y produced identical bottles at different joemama142000 4 24 Nov 2005, 21:27
Display posts from previous: Sort by

Machines X and V produced identical bottles at different

  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®.