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# Machines X and V produced identical bottles at different

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Re: Word Translations - Rates & Work [#permalink]
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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

HTH
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Re: Word Translations - Rates & Work [#permalink]
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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.
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Re: Word Translations - Rates & Work [#permalink]
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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?
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Re: Word Translations - Rates & Work [#permalink]
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Thanks Bunuel! I like your work/rate resume. It is really helpful. +1
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Re: Machines X and V produced identical bottles at different [#permalink]
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Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE

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
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Re: Machines X and V produced identical bottles at different [#permalink]
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4R = X

3R* = Total - X

4R = 2(3R*)

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

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

3R* = Total - 4R

2R = Total - 4R

6R = Total

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Re: Machines X and V produced identical bottles at different [#permalink]
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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

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Re: Machines X and V produced identical bottles at different [#permalink]
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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
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Machines X and V produced identical bottles at different [#permalink]
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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.

(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

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Re: Machines X and V produced identical bottles at different [#permalink]
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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.

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

Cheers,
Brent
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Re: Machines X and V produced identical bottles at different [#permalink]
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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.