GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 19 Jan 2019, 07:19

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.

Close

Request Expert Reply

Confirm Cancel
Events & Promotions in January
PrevNext
SuMoTuWeThFrSa
303112345
6789101112
13141516171819
20212223242526
272829303112
Open Detailed Calendar
  • FREE Quant Workshop by e-GMAT!

     January 20, 2019

     January 20, 2019

     07:00 AM PST

     07:00 AM PST

    Get personalized insights on how to achieve your Target Quant Score.
  • Free GMAT Strategy Webinar

     January 19, 2019

     January 19, 2019

     07:00 AM PST

     09:00 AM PST

    Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT.

Three machines X, Y, and Z operate independently of one another.

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

 
Intern
Intern
avatar
B
Joined: 16 Oct 2017
Posts: 38
Three machines X, Y, and Z operate independently of one another.  [#permalink]

Show Tags

New post Updated on: 03 Apr 2018, 12:26
1
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

73% (01:53) correct 27% (02:52) wrong based on 126 sessions

HideShow timer Statistics

Three machines X, Y, and Z operate independently of one another. Machine X working alone can complete a job in 12 hours, machine Y working alone can complete the job in y hours, machine Z working alone can complete the job in 4 hours, and all three machines working together and independently can complete the job in 1 3/5 hours. What is the value of y?

A) 1 3/5
B) 3
C) 3 3/7
D) 5 1/4
E) 17 3/5

Originally posted by OCDianaOC on 03 Apr 2018, 11:50.
Last edited by OCDianaOC on 03 Apr 2018, 12:26, edited 1 time in total.
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 52294
Re: Three machines X, Y, and Z operate independently of one another.  [#permalink]

Show Tags

New post 03 Apr 2018, 12:20
1
OCDianaOC wrote:
Three machines X, Y, and Z operate independently of one another. Machine X working alone can complete a job in 12 hours, machine Y working alone can complete the job in y hours, machine Z working alone can complete the job in 4 hours, and all three machines working together and independently can complete the job in hours. What is the value of y?

A) 1 3/5
B) 3
C) 3 3/7
D) 5 1/4
E) 17 3/5


Please edit the highlighted part: 8/5 hours?

Thank you.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

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?
Extra-hard Quant Tests with Brilliant Analytics

Intern
Intern
avatar
B
Joined: 16 Oct 2017
Posts: 38
Re: Three machines X, Y, and Z operate independently of one another.  [#permalink]

Show Tags

New post 03 Apr 2018, 12:26
Bunuel wrote:
OCDianaOC wrote:
Three machines X, Y, and Z operate independently of one another. Machine X working alone can complete a job in 12 hours, machine Y working alone can complete the job in y hours, machine Z working alone can complete the job in 4 hours, and all three machines working together and independently can complete the job in hours. What is the value of y?

A) 1 3/5
B) 3
C) 3 3/7
D) 5 1/4
E) 17 3/5


Please edit the highlighted part: 8/5 hours?

Thank you.


Edited! Thanks, didn't realize it didn't paste over at first.
Senior SC Moderator
avatar
V
Joined: 22 May 2016
Posts: 2347
Three machines X, Y, and Z operate independently of one another.  [#permalink]

Show Tags

New post 03 Apr 2018, 14:30
2
OCDianaOC wrote:
Three machines X, Y, and Z operate independently of one another. Machine X working alone can complete a job in 12 hours, machine Y working alone can complete the job in y hours, machine Z working alone can complete the job in 4 hours, and all three machines working together and independently can complete the job in 1 3/5 hours. What is the value of y?

A) 1 3/5
B) 3
C) 3 3/7
D) 5 1/4
E) 17 3/5

One approach, \(R*T = W\): find combined rate; add rates to solve for Y's rate; and use Y's rate to find Y's time

Given
Rates are in \(\frac{Jobs}{hour}\)
X's rate = \(\frac{1}{12}\)
Y's rate = \(\frac{1}{Y}\)
Z's rate = \(\frac{1}{4}\)
TIME all three machines take, working together, to finish the job = \(1\frac{3}{5}hrs=\frac{8}{5}\) hours

Combined RATE?
\(R*T = W\), so \(R=\frac{W}{T}\)
All three, RATE = \(\frac{1}{(\frac{8}{5})}=(1*\frac{5}{8})=\frac{5}{8}\)

Add rates, solve for Y's rate:
(\(\frac{1}{X}+\frac{1}{Y}+\frac{1}{Z})=(\frac{1}{12}+\frac{1}{Y}+\frac{1}{4})=\frac{5}{8}\)

\((\frac{5}{8}-\frac{1}{4}-\frac{1}{12})=\frac{1}{Y}=(\frac{15}{24}-\frac{6}{24}-\frac{2}{24})=\frac{7}{24}\)


Y's TIME?
\(\frac{7}{24}\) is Y's rate.
The job is 1
Rate and time are inversely proportional. Flip Y's rate fraction to get Y's time*:
\(\frac{24}{7}hrs=3\frac{3}{7}hrs\)

Answer C

*\(R*T=W\), so \(T=\frac{W}{R}\)
\(W = 1\)
\(T =\frac{1}{(\frac{7}{24})}=(1 * \frac{24}{7})=(\frac{24}{7})=3\frac{3}{7}\)hrs

_________________

Never look down on anybody unless you're helping them up.
--Jesse Jackson

Senior DS Moderator
User avatar
V
Joined: 27 Oct 2017
Posts: 1195
Location: India
Concentration: International Business, General Management
GPA: 3.64
WE: Business Development (Energy and Utilities)
Premium Member CAT Tests
Re: Three machines X, Y, and Z operate independently of one another.  [#permalink]

Show Tags

New post 03 Apr 2018, 16:52
1
The Total work can be assumed to be 120 (LCM of (time taken to complete the job) 12,4,8/5 (ignore the denominator )) =120 units
This will make the calculation quite easier.
Now No of units of works done by X per hour = \(120/12 =10\)
No of units of works done by Z per hour = \(120/4 =30\)
No of units of works done per hour by all three of them = \(120/(8/5) =75\)
Thus work done by Y per hour = work done by all three - (work done by X +work done by Z) =75-(10+30) =35
Hence the time taken by Y to complete the work = 120/35 = 24/7 = 3 3/7 = Answer = C

OCDianaOC wrote:
Three machines X, Y, and Z operate independently of one another. Machine X working alone can complete a job in 12 hours, machine Y working alone can complete the job in y hours, machine Z working alone can complete the job in 4 hours, and all three machines working together and independently can complete the job in 1 3/5 hours. What is the value of y?

A) 1 3/5
B) 3
C) 3 3/7
D) 5 1/4
E) 17 3/5

_________________

Win GMAT CLUB Test- Weekly Quant Quiz Contest
Weekly Quant Quiz Questions- Direct Download
SC: Confusable words

All you need for Quant, GMAT PS Question Directory,GMAT DS Question Directory
Error log/Key Concepts
Combination Concept: Division into groups
Question of the Day (QOTD)
Free GMAT CATS

VP
VP
avatar
P
Joined: 07 Dec 2014
Posts: 1152
Re: Three machines X, Y, and Z operate independently of one another.  [#permalink]

Show Tags

New post 03 Apr 2018, 21:21
OCDianaOC wrote:
Three machines X, Y, and Z operate independently of one another. Machine X working alone can complete a job in 12 hours, machine Y working alone can complete the job in y hours, machine Z working alone can complete the job in 4 hours, and all three machines working together and independently can complete the job in 1 3/5 hours. What is the value of y?

A) 1 3/5
B) 3
C) 3 3/7
D) 5 1/4
E) 17 3/5


1/y=[1/(8/5)-(1/4+1/12)]
y=24/7=3 3/7 hours
C
Intern
Intern
avatar
B
Joined: 31 Jul 2016
Posts: 9
Re: Three machines X, Y, and Z operate independently of one another.  [#permalink]

Show Tags

New post 03 Apr 2018, 22:16
Bunuel wrote:
OCDianaOC wrote:
Three machines X, Y, and Z operate independently of one another. Machine X working alone can complete a job in 12 hours, machine Y working alone can complete the job in y hours, machine Z working alone can complete the job in 4 hours, and all three machines working together and independently can complete the job in hours. What is the value of y?

A) 1 3/5
B) 3
C) 3 3/7
D) 5 1/4
E) 17 3/5


Please edit the highlighted part: 8/5 hours?

Thank you.

X can complete the work in 1/12 hours
Y can complete the work in 1/ x hours
Z can complete the work in 1/4 hours
Together they can complete the work in 5/8 hours

So 1/12+1/x+1/4=5/8
1/x=5/8-1/3
1/x=7/24
X=24/7 which is 3 3/7



Sent from my SM-G925I using GMAT Club Forum mobile app
Target Test Prep Representative
User avatar
G
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2830
Re: Three machines X, Y, and Z operate independently of one another.  [#permalink]

Show Tags

New post 06 Apr 2018, 07:47
OCDianaOC wrote:
Three machines X, Y, and Z operate independently of one another. Machine X working alone can complete a job in 12 hours, machine Y working alone can complete the job in y hours, machine Z working alone can complete the job in 4 hours, and all three machines working together and independently can complete the job in 1 3/5 hours. What is the value of y?

A) 1 3/5
B) 3
C) 3 3/7
D) 5 1/4
E) 17 3/5


The rate of machine X is 1/12, the rate of machine Y is 1/y, and the rate of machine Z is 1/4.

Since the 3 machines can complete the job in 1 3/5 = 8/5 hours, we can create the following equation for the combined rate of the 3 machines:

1/12 + 1/y + 1/4 = 1/(8/5)

1/12 + 1/y + 1/4 = 5/8

Multiplying by 24y, we have:

2y + 24 + 6y = 15y

24 = 7y

24/7 = 3 3/7 = y

Answer: C
_________________

Jeffery Miller
Head of GMAT Instruction

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Intern
Intern
avatar
B
Joined: 04 Jan 2018
Posts: 10
Re: Three machines X, Y, and Z operate independently of one another.  [#permalink]

Show Tags

New post 27 Nov 2018, 10:57
For me the easiest way to solve it would be:

X does 1/12 of the work in 1 hour
Y does 1/y of the work in 1 hour
Z does 1/4 of the work in 1 hour

When they work together they can do the work in 1 3/5 hours -> 8/5 hours

Hence in 1 hour only 1/(8/5) of the total work is done, what means that (1/12+1/y+1/4)=5/8

it follows that 4/12+1/y=5/8
so, (5/8)-(4/12)=1/y
finding the common denominator -> (15/24)-(8/24)=1/y
7/24=1/y
y=24/7
y= 3 and 3/7
GMAT Club Bot
Re: Three machines X, Y, and Z operate independently of one another. &nbs [#permalink] 27 Nov 2018, 10:57
Display posts from previous: Sort by

Three machines X, Y, and Z operate independently of one another.

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


Copyright

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

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

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®.