Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 02 May 2010
Posts: 53
Schools: IU, UT Dallas, Univ of Georgia, Univ of Arkansas, Miami University
WE 1: 5.5 Yrs IT

It takes machine A 'x' hours to manufacture a deck of cards that [#permalink]
Show Tags
Updated on: 11 Feb 2018, 08:24
5
This post received KUDOS
34
This post was BOOKMARKED
Question Stats:
65% (02:02) correct 35% (01:57) wrong based on 647 sessions
HideShow timer Statistics
It takes machine A 'x' hours to manufacture a deck of cards that machine B can manufacture in 'y' hours. If machine A operates alone for 'z' hours and is then joined by machine B until 100 decks are finished, for how long will the two machines operate simultaneously? A. \(\frac{100xy – z}{x + y}\) B. \(\frac{y(100x – z)}{x + y}\) C. \(\frac{100y(x – z)}{x + y}\) D. \(\frac{x + y}{100xy – z}\) E. \(\frac{x + y – z}{100xy}\)
Official Answer and Stats are available only to registered users. Register/ Login.
Originally posted by sjayasa on 10 Jun 2010, 06:23.
Last edited by Bunuel on 11 Feb 2018, 08:24, edited 2 times in total.
Renamed the topic and edited the question.



Math Expert
Joined: 02 Sep 2009
Posts: 44596

It takes machine A 'x' hours to manufacture a deck of cards that [#permalink]
Show Tags
10 Jun 2010, 06:51
22
This post received KUDOS
Expert's post
6
This post was BOOKMARKED
It takes machine A 'x' hours to manufacture a deck of cards that machine B can manufacture in 'y' hours. If machine A operates alone for 'z' hours and is then joined by machine B until 100 decks are finished, for how long will the two machines operate simultaneously? A. \(\frac{100xy – z}{x + y}\) B. \(\frac{y(100x – z)}{x + y}\) C. \(\frac{100y(x – z)}{x + y}\) D. \(\frac{x + y}{100xy – z}\) E. \(\frac{x + y – z}{100xy}\) Note that we are asked: "for how long will the two machines operate simultaneously?". In first \(z\) hours machine A alone will manufacture \(\frac{z}{x}\) decks. So there are \(100\frac{z}{x}=\frac{100xz}{x}\) decks left to manufacture. Combined rate of machines A and B would be \(\frac{1}{x}+\frac{1}{y}=\frac{x+y}{xy}\) decks/hour, (remember we can easily sum the rates). As \(time=\frac{job}{rate}\), then \(time=\frac{100xz}{x}*\frac{xy}{x+y}=\frac{y(100xz)}{x+y}\). Answer: B. Hope it's clear.
_________________
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? Extrahard Quant Tests with Brilliant Analytics



Intern
Affiliations: NYSSA
Joined: 07 Jun 2010
Posts: 32
Location: New York City
Schools: Wharton, Stanford, MIT, NYU, Columbia, LBS, Berkeley (MFE program)
WE 1: Senior Associate  Thomson Reuters
WE 2: Analyst  TIAA CREF

Re: It takes machine A 'x' hours to manufacture a deck of cards that [#permalink]
Show Tags
10 Jun 2010, 11:06
1
This post received KUDOS
sjayasa wrote: It takes machine A 'x' hours to manufacture a deck of cards that machine B can manufacture in 'y' hours. If machine A operates alone for 'z' hours and is then joined by machine B until 100 decks are finished, for how long will the two machines operate simultaneously? A) (100xy – z)/(x + y) B) y(100x – z)/(x + y) C) 100y(x – z)/(x + y) D) (x + y)/(100xy – z) E) (x + y – z)/100xy If you're having trouble w/ the above method you can try plugging numbers, but it does take longer. Use values for x, y, and z. Say x = 2, y = 4 and z =20. We have then 90 (100  1/2*20) decks left to complete. So we should have (100  10)/(1/x+1/y) hours left. 90/(1/2+1/4) > 90/.75 = 120hrs. Now you can eyeball a few of the answer choices and realize that only A/B/C are going to produce anything close to 120hrs. For B: (100*2*4  20*4)/(2+4) > 720/6 = 120. This is our answer. Next



Senior Manager
Status: Yeah well whatever.
Joined: 18 Sep 2009
Posts: 328
Location: United States
GMAT 1: 660 Q42 V39 GMAT 2: 730 Q48 V42
GPA: 3.49
WE: Analyst (Insurance)

Re: It takes machine A 'x' hours to manufacture a deck of cards that [#permalink]
Show Tags
10 Jun 2010, 17:17
1
This post was BOOKMARKED
Yikes!! I could never do this algebraically like Bunuel did it. Dude's a super human. But I did stay at a holiday in express last night (not really... I just like bad jokes). Here's what I got. if rt=d then A's rate of work is 1/x and B's rate of work is 1/y. I made x=2 and y=4 so that rate A is 1/2 and rate B is 1/4. So then we're told that A starts out on 100 decks by itself at 1/2 a deck an hour for z hours. So then I assigned a value for z. I said, "If z>200 then A finishes the 100 decks and B doesn't work at all." So I made z arbitrarily less than 200. For me z=50. So, 100 = (1/2)50 + (1/2+1/4)h, whereas h= the number of hours they worked together that I'll compare all answers to later. 100= 25 + 3h/4 75=3h/4 what do you know? h=100!! So then I plug it the values I had for x, y and z into answer choices A B C D E to see which one is 100 A) = 550/6 which whatever it is isn't 100 B) = 600/6 which is 100 C) = some large negative number because a positive is multiplied by (xz) or (250) D) = some really small fraction E) = some negative number We have a winner in B!!
_________________
He that is in me > he that is in the world.  source 1 John 4:4



SVP
Status: Three Down.
Joined: 09 Jun 2010
Posts: 1870
Concentration: General Management, Nonprofit

Re: It takes machine A 'x' hours to manufacture a deck of cards that [#permalink]
Show Tags
08 Jul 2010, 13:31
7
This post received KUDOS
3
This post was BOOKMARKED
Speed of Machine A = \(\frac{1}{x}\) decks/hour Speed of Machine B = \(\frac{1}{y}\) decks/hour
Combined Speed of both machines = \(\frac{1}{x}+ \frac{1}{y}\) decks/hour
Now, Machine A initially worked for z hours, so the number of decks produced in z hours = \(\frac{1}{x}\) decks/hour * z hours = \(\frac{z}{x}\) decks
Decks remaining to be produced = \(100  \frac{z}{x}\)
So, the time taken for both to work together and finish this would be = Number of decks left/Combined Speed = \(\frac{100  \frac{z}{x}}{\frac{1}{x}+ \frac{1}{y}}\) = \(\frac{(100xz)y}{x+y}\)
So the answer is B.



Manager
Joined: 12 Jun 2007
Posts: 111

Re: It takes machine A 'x' hours to manufacture a deck of cards that [#permalink]
Show Tags
16 Jul 2010, 02:41
whats i did:
lets x= 10hrs y= 20hrs
they both can do 20/3 Deck in 1 hrs
now lets say both A and B work together and made 90 decks, while 10decks made by A alone
A & B both time will be 600 hrs A alone time will be 100 hrs which is the value of Z
now put all the values in the answer choices.
Correct answer is B



Senior Manager
Joined: 13 Aug 2012
Posts: 444
Concentration: Marketing, Finance
GPA: 3.23

Re: It takes machine A 'x' hours to manufacture a deck of cards that [#permalink]
Show Tags
02 Dec 2012, 01:35
1
This post received KUDOS
\(\frac{1}{x}(z)+\frac{x+y}{yx}(t)=100\) \(\frac{x+y}{xy}(t)=100\frac{z}{x}\) \(t=\frac{100xz}{x}(\frac{xy}{x+y})\) \(t=\frac{y(100xz)}{x+y}\)
_________________
Impossible is nothing to God.



Director
Joined: 03 Aug 2012
Posts: 838
Concentration: General Management, General Management
GMAT 1: 630 Q47 V29 GMAT 2: 680 Q50 V32
GPA: 3.7
WE: Information Technology (Investment Banking)

Re: It takes machine A 'x' hours to manufacture a deck of cards that [#permalink]
Show Tags
18 Mar 2014, 04:23
Folks, I have seen the replies of experts. However, I have one query on this question. Solution: Work to be performed =100 decks Rate * time = work 100/x * x = 100 Rate 1: 100/x Similarly Rate 2 : 100/y Then why posters have taken the rates as 1/x and 1/y. Rgds, TGC!
_________________
Rgds, TGC! _____________________________________________________________________ I Assisted You => KUDOS Please _____________________________________________________________________________



Math Expert
Joined: 02 Sep 2009
Posts: 44596

Re: It takes machine A 'x' hours to manufacture a deck of cards that [#permalink]
Show Tags
18 Mar 2014, 05:39



Manager
Joined: 26 May 2013
Posts: 61

Re: It takes machine A 'x' hours to manufacture a deck of cards that [#permalink]
Show Tags
07 Feb 2016, 21:23
Bunuel wrote: sjayasa wrote: It takes machine A 'x' hours to manufacture a deck of cards that machine B can manufacture in 'y' hours. If machine A operates alone for 'z' hours and is then joined by machine B until 100 decks are finished, for how long will the two machines operate simultaneously? A) (100xy – z)/(x + y) B) y(100x – z)/(x + y) C) 100y(x – z)/(x + y) D) (x + y)/(100xy – z) E) (x + y – z)/100xy Note that we are asked: "for how long will the two machines operate simultaneously?". In first \(z\) hours machine A alone will manufacture \(\frac{z}{x}\) decks. So there are \(100\frac{z}{x}=\frac{100xz}{x}\) decks left to manufacture. Combined rate of machines A and B would be \(\frac{1}{x}+\frac{1}{y}=\frac{x+y}{xy}\) decks/hour, (remember we can easily sum the rates). As \(time=\frac{job}{rate}\), then \(time=\frac{100xz}{x}*\frac{xy}{x+y}=\frac{y(100xz)}{x+y}\). Answer: B. Hope it's clear. Hi Bunuel, I applied a different approach but failed to get the correct option. Pls. guide. Working together at x & y rate machines A & B will manufacture 2 decks in x + y hours, so to manufacture 1 deck it will take (x +y)/2 hours. Now to manufacture 100z/x decks it must take (100z/x)*2/(x+y).



Director
Joined: 07 Dec 2014
Posts: 962

Re: It takes machine A 'x' hours to manufacture a deck of cards that [#permalink]
Show Tags
16 Feb 2016, 14:14
let t=time machines operate simultaneously z/x+t(1/x+1/y)=100 t=(100z/x)/[(x+y)/xy] t=y(100xz)/(x+y)



Director
Status: Professional GMAT Tutor
Affiliations: AB, cum laude, Harvard University (Class of '02)
Joined: 10 Jul 2015
Posts: 595
Location: United States (CA)
Age: 38
GMAT 1: 770 Q47 V48 GMAT 2: 730 Q44 V47 GMAT 3: 750 Q50 V42
GRE 1: 337 Q168 V169
WE: Education (Education)

Re: It takes machine A 'x' hours to manufacture a deck of cards that [#permalink]
Show Tags
31 Mar 2016, 18:26
Attached is a visual that should help. Bundle's solution is the most elegant, but if you can't pull that off (which many testtakers can't), then this illustrates an admittedly more workintensive second option.
Attachments
Screen Shot 20160331 at 6.25.39 PM.png [ 216.18 KiB  Viewed 6791 times ]
Screen Shot 20160331 at 6.26.17 PM.png [ 117.77 KiB  Viewed 6792 times ]
_________________
Harvard grad and 99% GMAT scorer, offering expert, private GMAT tutoring and coaching, both inperson (San Diego, CA, USA) and online worldwide, since 2002.
One of the only known humans to have taken the GMAT 5 times and scored in the 700s every time (700, 710, 730, 750, 770), including verified section scores of Q50 / V47, as well as personal bests of 8/8 IR (2 times), 6/6 AWA (4 times), 50/51Q and 48/51V (1 question wrong).
You can download my official testtaker score report (all scores within the last 5 years) directly from the Pearson Vue website: https://tinyurl.com/y8zh6qby Date of Birth: 09 December 1979.
GMAT Action Plan  McElroy Tutoring



Director
Status: Professional GMAT Tutor
Affiliations: AB, cum laude, Harvard University (Class of '02)
Joined: 10 Jul 2015
Posts: 595
Location: United States (CA)
Age: 38
GMAT 1: 770 Q47 V48 GMAT 2: 730 Q44 V47 GMAT 3: 750 Q50 V42
GRE 1: 337 Q168 V169
WE: Education (Education)

Re: It takes machine A 'x' hours to manufacture a deck of cards that [#permalink]
Show Tags
02 Apr 2016, 11:32
...and here is a visual version of Bunuel 's explanation.
Attachments
Screen Shot 20160402 at 11.31.19 AM.png [ 125.72 KiB  Viewed 6719 times ]
_________________
Harvard grad and 99% GMAT scorer, offering expert, private GMAT tutoring and coaching, both inperson (San Diego, CA, USA) and online worldwide, since 2002.
One of the only known humans to have taken the GMAT 5 times and scored in the 700s every time (700, 710, 730, 750, 770), including verified section scores of Q50 / V47, as well as personal bests of 8/8 IR (2 times), 6/6 AWA (4 times), 50/51Q and 48/51V (1 question wrong).
You can download my official testtaker score report (all scores within the last 5 years) directly from the Pearson Vue website: https://tinyurl.com/y8zh6qby Date of Birth: 09 December 1979.
GMAT Action Plan  McElroy Tutoring



Manager
Joined: 14 Dec 2015
Posts: 50
Concentration: Entrepreneurship, General Management
WE: Information Technology (Computer Software)

Re: It takes machine A 'x' hours to manufacture a deck of cards that [#permalink]
Show Tags
18 Apr 2016, 10:54
It takes machine A 'x' hours to manufacture a deck of cards that machine B can manufacture in 'y' hours. If machine A operates alone for 'z' hours and is then joined by machine B until 100 decks are finished, for how long will the two machines operate simultaneously? A. (100xy – z)/(x + y) B. y(100x – z)/(x + y) C. 100y(x – z)/(x + y) D. (x + y)/(100xy – z) E. (x + y – z)/100xy A takes x hours to manufacture a deck of cards, so fraction of work x does is (\(\frac{1}{x}\)) corollary B's fraction of work is (\(\frac{1}{y}\)) 1. A operates for 'z' hours = (\(\frac{z}{x}\)) or (\(\frac{1}{x}\))*z 2. On top of z/p, machine B joins with A and works for 'X' hours i.e; (\(\frac{1}{x}\)+\(\frac{1}{y}\))* X => X(\(\frac{x+y}{xy}\)) ; unknown is colored red. adding 1 and 2 => (\(\frac{z}{x}\))+ \(\frac{(x+y)}{(xy)}\) X = 100 Solve for X => (\(\frac{x+y}{xy})\) X = 100  (\(\frac{z}{x}\)) =>(\(\frac{x+y}{xy})\) X = \(\frac{(100x  z)}{x}\) ; cancel out x term in the denominator. => X = y\(\frac{(100x  z)}{(x+y)}\) "Encourage me with kudos, if its worth! "
_________________
"Fight the HARDEST battle that anyone can ever imagine"



Intern
Joined: 23 May 2016
Posts: 10

Re: It takes machine A 'x' hours to manufacture a deck of cards that [#permalink]
Show Tags
30 May 2016, 13:39
Bunuel why is the rate (y+x / yx). Isnt that time? Work rule is 1/r + 1/s = 1/h so doing 1/x + 1/y actually delivers time not rate?



Math Expert
Joined: 02 Sep 2009
Posts: 44596

Re: It takes machine A 'x' hours to manufacture a deck of cards that [#permalink]
Show Tags
30 May 2016, 13:45
rjivani wrote: Bunuel why is the rate (y+x / yx). Isnt that time? Work rule is 1/r + 1/s = 1/h so doing 1/x + 1/y actually delivers time not rate? Time is a reciprocal of rate: 1/r + 1/s = 1/h (s + r)/(rs) = 1/h h = rs/(r+s). THEORYThere 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. Hope this helps
_________________
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? Extrahard Quant Tests with Brilliant Analytics



Target Test Prep Representative
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2273

Re: It takes machine A 'x' hours to manufacture a deck of cards that [#permalink]
Show Tags
20 Jun 2017, 19:11
sjayasa wrote: It takes machine A 'x' hours to manufacture a deck of cards that machine B can manufacture in 'y' hours. If machine A operates alone for 'z' hours and is then joined by machine B until 100 decks are finished, for how long will the two machines operate simultaneously? A. (100xy – z)/(x + y) B. y(100x – z)/(x + y) C. 100y(x – z)/(x + y) D. (x + y)/(100xy – z) E. (x + y – z)/100xy We can let the rate of machine A = 1/x and the rate of machine B = 1/y. We are given that machine A operates for z hours, so machine A completes (1/x)(z) = z/x decks of cards when operating alone. Thus, there will be 100  z/x decks left to complete when machines A and B work together. We can let n = the number of hours that machines A and B work together to complete (100  z/x) decks and we can create the following equation: (1/x + 1/y)(n) = 100  z/x Multiplying the entire equation by xy, we have: (y + x)(n) = 100xy  zy n = y(100x  z)/(y + x) Answer: B
_________________
Jeffery Miller
Head of GMAT Instruction
GMAT Quant SelfStudy Course
500+ lessons 3000+ practice problems 800+ HD solutions



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 11492
Location: United States (CA)
GRE 1: 340 Q170 V170

Re: It takes machine A 'x' hours to manufacture a deck of cards that [#permalink]
Show Tags
04 Feb 2018, 12:47
Hi All, This question can be solved by TESTing VALUES. Machine A takes X hours to make a deck of cards. Machine B takes Y hours to make a deck of cards. Since the answers are suitably complexlooking, let's choose really small, easy numbers to work with: X = 1 Y = 2 So… Machine A takes 1 hour to make a deck of cards Machine B takes 2 hours to make a deck of cards When both machines work together for 2 total hours, 3 decks of cards are made. The question goes on to state that Machine A will work alone for Z hours, then be joined by Machine B until 100 decks are made. Z = 1 In that first hour, Machine A will produce 1 deck of cards, leaving 99 decks to go. Since the two machines together can produce 3 decks every 2 hours, the remaining 99 decks will take… 2 hours x 33 sets = 66 hours. We're looking for the answer that equals 66 when we plug in X=1, Y=2 and Z=1 into the answer choices. While it "looks like" there's a lot of math to be done, most of the answers are way too small to be 66 (and it shouldn't take too long to figure that out). Only one answer equals 66 Final Answer: GMAT assassins aren't born, they're made, Rich
_________________
760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com
Rich Cohen
CoFounder & GMAT Assassin
Special Offer: Save $75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/
***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***********************



Senior Manager
Joined: 31 Jul 2017
Posts: 332
Location: Malaysia
WE: Consulting (Energy and Utilities)

Re: It takes machine A 'x' hours to manufacture a deck of cards that [#permalink]
Show Tags
04 Feb 2018, 14:55
sjayasa wrote: It takes machine A 'x' hours to manufacture a deck of cards that machine B can manufacture in 'y' hours. If machine A operates alone for 'z' hours and is then joined by machine B until 100 decks are finished, for how long will the two machines operate simultaneously? A. (100xy – z)/(x + y) B. y(100x – z)/(x + y) C. 100y(x – z)/(x + y) D. (x + y)/(100xy – z) E. (x + y – z)/100xy Given, \(ax = by = 1\) \(az + t(a+b) = 100\) \(\frac{x}{z} + t(\frac{x+y}{xy}) = 100\) \(t = y(100xz)/(x+y)\)
_________________
If my Post helps you in Gaining Knowledge, Help me with KUDOS.. !!



SVP
Joined: 26 Mar 2013
Posts: 1612

Re: It takes machine A 'x' hours to manufacture a deck of cards that [#permalink]
Show Tags
05 Feb 2018, 13:06
sjayasa wrote: It takes machine A 'x' hours to manufacture a deck of cards that machine B can manufacture in 'y' hours. If machine A operates alone for 'z' hours and is then joined by machine B until 100 decks are finished, for how long will the two machines operate simultaneously? A. (100xy – z)/(x + y) B. y(100x – z)/(x + y) C. 100y(x – z)/(x + y) D. (x + y)/(100xy – z) E. (x + y – z)/100xy Another easy way Let x = 1 hour..........then rate of A = 1 deck/hour. Let y = 2 hours. If A completes the the whole job..... then the time that A takes to produce all 100 decks = 100 hours. Then z=100. Since A completes the whole job, the number of hours that A and B work together = 0. Let's plug x=1, y=2 and z=100 into the answers choices. y(100x  z)/(x+y) = 2(100*1  100)/(1+2) = 0. Answer: B.




Re: It takes machine A 'x' hours to manufacture a deck of cards that
[#permalink]
05 Feb 2018, 13:06



Go to page
1 2
Next
[ 21 posts ]



