Machines X and V produced identical bottles at different

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?

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)

(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.

Bunuel · Accepted Answer

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.

KarishmaB · Answer

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 Here is a video discussion on work-rate: https://youtu.be/88NFTttkJmA and check out these posts: https://anaprep.com/arithmetic-applying ... -concepts/ https://anaprep.com/arithmetic-work-rat ... s-and-all/ https://anaprep.com/arithmetic-avoiding ... work-rate/

dimitri92 · Answer

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

KarishmaB · Answer

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.

cgl7780 · Answer

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?

Burnkeal · Answer

Thanks Bunuel! I like your work/rate resume. It is really helpful. +1

Bunuel · Answer

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: https://gmatclub.com/forum/work-word-pr ... 87357.html
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Alexmsi · Answer

4R = X

3R* = Total - X

4R = 2(3R*)

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

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

3R* = Total - 4R

2R = Total - 4R

6R = Total

Answer: 6. B.

shivanigs · Answer

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

cht1128 · Answer

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

LogicGuru1 · Answer

(1) Machine X produced 30 bottles per minute.
Machine x worked for 4 hours so it made = 30*60*4 bottles 
How many bottles Y made is unknown ; Total number of bottles unknown 
Without knowing total production we cannot use X's rate to derive its time 
INSUFFICIENT

(2) Machine X produced twice as many bottles in 4 hours as Machine Y produced in 3 hours.
Machine x produces 2B bottles and rest of the remaining B bottles were made by Y
therefore total number of bottles = 3B
now X makes 2B bottles in 4 hour therefore it can make the remaining B bottles in 2 hours 
total time X takes to complete the production is 4hour + 2 hour = 6 hours

SUFFICIENT

ANSWER IS B

BrentGMATPrepNow · Answer

Given : 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.   
Let x = Machine X's RATE (in terms of the  fraction  of the job completed PER HOUR)
Let y = Machine Y's RATE (in terms of the  fraction  of the job completed PER HOUR)

So, in 4 hours, the portion of the job completed by Machine X = 4x
Likewise, in 3 hours, the portion of the job completed by Machine Y = 3y

Since the entire job is completed after both machines perform their individual tasks, we can write:  4x + 3y = 1  (1 represents the entire job completed)

Target question :    How many hours would it have taken Machine X operating alone to fill the entire production lot?

Statement 1 : Machine X produced 30 bottles per minute.  
Since we're given no information about Machine Y, it is impossible to answer the  target question  with certainty
Statement 1 is NOT SUFFICIENT

Statement 2 : Machine X produced twice as many bottles in 4 hours as Machine Y produced in 3 hours.  
In 4 hours, the portion of the job completed by Machine X = 4x
In 3 hours, the portion of the job completed by Machine Y = 3y
From statement 2, we can write: 4x = (2)(3y)
Simplified to get:  4x = 6y

We now have the following system of equations: 
 4x + 3y = 1 
 4x = 6y

Since we COULD solve this system of equations for x and for y, we COULD determine Machine X's RATE, which means we COULD determine  how many hours it would have taken machine X to fill the entire production lot on its own . 
Of course, we would never waste valuable time on test day performing such tedious calculations. We need only determine that we COULD answer the target question. 
Since we COULD answer the  target question  with certainty, the combined statements are SUFFICIENT

Answer: B

Cheers,
Brent

Basshead · Answer

No equations are necessary for this question -- we simply need to think logically.

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?

We know Machine X works for 4 hours and completes a portion of the job. Then Machine Y works for 3 hours and finishes the job. To determine how many hours it would have taken Machine X to complete the job alone, we need to be told the rate per hour for each machine. Lets take a look at the statements:

(1) Machine X produced 30 bottles per minute.

Great, we know the rate of Machine X. However, we need the rate of both machines. Insufficient.

(2) Machine X produced twice as many bottles in 4 hours as Machine Y produced in 3 hours.

Machine X produced twice as many bottles in 4 hours as Machine Y produced in 3 hours. If Machine X produced twice as many bottles as Machine Y produced in 3 hours, this means Machine X completed 2/3 of the job and Machine Y completed 1/3 of the job. If we know Machine X took  4 hours to complete 2/3 of the job , then Machine X will take  6 hours to complete 3/3 of the job . This statement is sufficient.

Answer is B.

krishna_sunder_ · Answer

https://gmatclub.com/forum/download/file.php?id=81519 GMAT-Club-Forum-gwohs73f.png

MohdSadique · Answer

Alternate solution
 as the question says x fills a part and then y fills the rest, so doesnt it imply that they together fill the complete lot ?
i assumed 1 as whole lot machine x worked for 4hrs at constant rate assume p machine y worked for 3 hrs at contantc rate assume q that leads me to this eq: 4p+3q=1

Statement (1): Machine X produced 30 bottles per minute. 
 p=30×60=1800bottles/hour 
Now we substitute p=1800p into equation 1:
4(1800)+3q=1
q=-7199/3
 This results in a negative rate, which doesn't make sense in the context of the problem. So,  Statement 1 alone is not sufficient .

Statement (2): Machine X produced twice as many bottles in 4 hours as Machine Y produced in 3 hours. 
 4p=2×3q 
 4p=6q 
p=3q/2

Now we substitute equation 2 into equation 1: 
 4(23/q)+3q=1 
 q=1/9
 Now that we know q, substitute it back into equation 2 to find p: 
p=1/6

Now that we know both ppp and qqq, we can calculate the total time it would take  Machine X  to fill the entire lot by itself.
The time it takes Machine X to fill the lot is 1/p
where p=1/6
TIME=1/(1/6)
=6hours
 Conclusion: 
Statement (2) is sufficient to determine that it would take  Machine X 6 hours  to fill the entire production lot.

after writing it down i realised it pretty lengthy but in my head i was able to obtain the answer in under 3 minutes

totaltestprepNick · Answer

B https://www.youtube.com/watch?v=noId1eubnEQ Nick Slavkovich, GMAT/GRE tutor with 20+ years of experience tutoring@totaltestprep.net

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