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

It is currently 23 Oct 2019, 19:43

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

Machines X and Y work at their respective constant rates. How many mor

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

Hide Tags

Find Similar Topics 
Intern
Intern
avatar
Joined: 12 Sep 2010
Posts: 10
Machines X and Y work at their respective constant rates. How many  [#permalink]

Show Tags

New post 18 Sep 2010, 21:13
1
26
00:00
A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

56% (02:05) correct 44% (02:00) wrong based on 1445 sessions

HideShow timer Statistics

Machines X and Y work at their respective constant rates. How many more hours does it take machine Y, working alone, to fill a production order of a certain size than it takes machine X, working alone?

(1) Machines X and Y, working together, fill a production order of this size in two-thirds the time that machine X, working alone, does

(2) Machine Y, working alone, fills a production order of this size in twice the time that machine X, working alone, does

Can you explain this one Bunuel plz?

At the end,we are having a definite quantity "X"..Right?So I still feel the answer is D.

Because there is no other value/variable affecting the outcome except for the "X".Please clarify if I am going badly wrong somewhere!

Attachment:
DS-3 (1).jpg
DS-3 (1).jpg [ 143.42 KiB | Viewed 11561 times ]
Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58464
Re: Machines X and Y work at their respective constant rates. How many mor  [#permalink]

Show Tags

New post 23 Feb 2012, 09:13
38
50
Machines X and Y work at their respective constant rates. How many more hours does it take machine Y, working alone, to fill a production order of a certain size than it takes machine X, working alone?

Let \(x\) and \(y\) be the times needed for machines X and Y respectively working alone to fill a production order of this size.

Question: \(y-x=?\)

(1) Machines X and Y, working together, fill a production order of this size in 2/3 the time that machine X, working alone, does --> general relationship: \(\frac{1}{x}+\frac{1}{y}=\frac{1}{total \ time}\) --> Total time needed for machines X and Y working together is \(total \ time=\frac{xy}{x+y}\) (general formula) --> given \(\frac{xy}{x+y}=x*\frac{2}{3}\) --> \(2x=y\). Not sufficient

(2) Machine Y, working alone, fills a production order of this size in twice the time that machine X, working alone, does --> \(2x=y\), the same info. Not sufficient

(1)+(2) Nothing new. Not Sufficient.

Answer: E.

Hope it helps.
_________________
General Discussion
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58464
Re: Machines X and Y work at their respective constant rates. How many  [#permalink]

Show Tags

New post 18 Sep 2010, 21:31
7
4
Machines X and Y work at their respective constant rates. How many more hours does it take machine Y, working alone, to fill a production order of a certain size than it takes machine X, working alone?

Let \(x\) and \(y\) be the times needed for machines X and Y respectively working alone to fill a production order of this size.

Question: \(y-x=?\)

(1) Machines X and Y, working together, fill a production order of this size in 2/3 the time that machine X, working alone, does --> general relationship: \(\frac{1}{x}+\frac{1}{y}=\frac{1}{total \ time}\) --> Total time needed for machines X and Y working together is \(total \ time=\frac{xy}{x+y}\) (general formula) --> given \(\frac{xy}{x+y}=x*\frac{2}{3}\) --> \(2x=y\). Not sufficient

(2) Machine Y, working alone, fills a production order of this size in twice the time that machine X, working alone, does --> \(2x=y\), the same info. Not sufficient

(1)+(2) Nothing new. Not Sufficient.

Answer: E.

Hope it helps.

P.S. Please post one question per topic. Also you can attach image files directly so no need to attach zip files.
_________________
Manager
Manager
avatar
Joined: 23 Sep 2009
Posts: 97
Re: Machines X and Y work at their respective constant rates. How many  [#permalink]

Show Tags

New post 19 Sep 2010, 17:52
Bunuel wrote:
Machines X and Y work at their respective constant rates. How many more hours does it take machine Y, working alone, to fill a production order of a certain size than it takes machine X, working alone?

Let \(x\) and \(y\) be the times needed for machines X and Y respectively working alone to fill a production order of this size.

Question: \(y-x=?\)

(1) Machines X and Y, working together, fill a production order of this size in 2/3 the time that machine X, working alone, does --> general relationship: \(\frac{1}{x}+\frac{1}{y}=\frac{1}{total \ time}\) --> Total time needed for machines X and Y working together is \(total \ time=\frac{xy}{x+y}\) (general formula) --> given \(\frac{xy}{x+y}=x*\frac{2}{3}\) --> \(2x=y\). Not sufficient

(2) Machine Y, working alone, fills a production order of this size in twice the time that machine X, working alone, does --> \(2x=y\), the same info. Not sufficient

(1)+(2) Nothing new. Not Sufficient.

Answer: E.

Hope it helps.

P.S. Please post one question per topic. Also you can attach image files directly so no need to attach zip files.


Pardon me if this is a stupid approach. but still I want to get it clarified.
From 1, as you said, \frac{1}{x}+\frac{1}{y}=\frac{2x}{3}
threfore \frac{1}{y}=\frac{2x}{3}-\frac{1}{x}
this gives \frac{1}{y}=\frac{2x^2-3}{3x}
Now using the value y=2x, substitute in the above equation and u get 2x^2=\frac{9}{4}
hence x=\frac{3}{2}
with this we can even find y.
Hence answer is C.
What is wrong in this approach?
_________________
Thanks,
VP
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58464
Re: Machines X and Y work at their respective constant rates. How many  [#permalink]

Show Tags

New post 19 Sep 2010, 23:26
2
vigneshpandi wrote:
Bunuel wrote:
Machines X and Y work at their respective constant rates. How many more hours does it take machine Y, working alone, to fill a production order of a certain size than it takes machine X, working alone?

Let \(x\) and \(y\) be the times needed for machines X and Y respectively working alone to fill a production order of this size.

Question: \(y-x=?\)

(1) Machines X and Y, working together, fill a production order of this size in 2/3 the time that machine X, working alone, does --> general relationship: \(\frac{1}{x}+\frac{1}{y}=\frac{1}{total \ time}\) --> Total time needed for machines X and Y working together is \(total \ time=\frac{xy}{x+y}\) (general formula) --> given \(\frac{xy}{x+y}=x*\frac{2}{3}\) --> \(2x=y\). Not sufficient

(2) Machine Y, working alone, fills a production order of this size in twice the time that machine X, working alone, does --> \(2x=y\), the same info. Not sufficient

(1)+(2) Nothing new. Not Sufficient.

Answer: E.

Hope it helps.

P.S. Please post one question per topic. Also you can attach image files directly so no need to attach zip files.


Pardon me if this is a stupid approach. but still I want to get it clarified.
From 1, as you said, ...\(\frac{1}{x}+\frac{1}{y}=\frac{2x}{3}\)
threfore \(\frac{1}{y}=\frac{2x}{3}-\frac{1}{x}\)
this gives \(\frac{1}{y}=\frac{2x^2-3}{3x}\)
Now using the value y=2x, substitute in the above equation and u get 2x^2=\frac{9}{4}
hence x=\frac{3}{2}

with this we can even find y.
Hence answer is C.
What is wrong in this approach?


What you are basically saying is that you can solve 1 equation \(\frac{xy}{x+y}=x*\frac{2}{3}\) with 2 unknowns \(x\) and \(y\). Though it's not generally impossible (for example: 2x+y=y+4) this is not the case here.

Next, we have \(total \ time=\frac{xy}{x+y}=x*\frac{2}{3}\) and not \(\frac{1}{x}+\frac{1}{y}=\frac{2x}{3}\) as you wrote (the calculation in red is not correct, it should be: \(\frac{1}{x}+\frac{1}{y}=\frac{1}{total \ time}=\frac{1}{x*\frac{2}{3}}=\frac{3}{2x}\)). So if you substitute \(y\) by \(2x\) in \(total \ time=\frac{xy}{x+y}=x*\frac{2}{3}\) (which by the way gives this relationship) you don't get the \(x=\frac{3}{2}\), you'll get \(x*\frac{2}{3}=x*\frac{2}{3}\) --> \(\frac{2}{3}=\frac{2}{3}\) as \(x\) will cancel out.

Hope it's clear.
_________________
Veritas Prep GMAT Instructor
User avatar
V
Joined: 16 Oct 2010
Posts: 9705
Location: Pune, India
Re: Machines X and Y work at their respective constant rates. How many  [#permalink]

Show Tags

New post 30 Nov 2010, 10:14
10
1
In this question, I would like to discuss the use of logic.

Ques: How many more hours does it take machine Y than it does machine X.
So I am looking for a number like 2 hrs or something.
Neither of the statements gives me a number of hours for anything. Only relative time taken. So we can straight away say the answer is (E).

Also, how to deal with a statement like without getting into equations and variables: Machines X and Y, working together, fill an order in 2/3 the time that machine X, working alone, does.

Together, they take 2/3 the time taken by machine X. i.e. if machine X took 6 hrs, together they took 4 hrs. The 2 hrs were saved because machine Y was also working for those 4 hrs. In 4 hrs machine Y did what machine X would have done in 2 hrs. So time taken by machine Y alone will be twice the time taken by machine X alone.
_________________
Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
Intern
Intern
avatar
Joined: 11 Dec 2011
Posts: 45
Location: Malaysia
Concentration: Nonprofit, Sustainability
GMAT 1: 730 Q49 V40
GPA: 3.16
WE: Consulting (Computer Software)
GMAT ToolKit User
Re: Machines X and Y work at their respective constant rates. How many mor  [#permalink]

Show Tags

New post 05 Mar 2012, 06:35
1
Just a question regarding this problem.
I choose E because I decided that there's no concrete value indicating the hours. The values they give from both statements indicate relative values. Is this a good approach or did I just get lucky?
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58464
Re: Machines X and Y work at their respective constant rates. How many mor  [#permalink]

Show Tags

New post 05 Mar 2012, 08:08
7
2
calvin1984 wrote:
Just a question regarding this problem.
I choose E because I decided that there's no concrete value indicating the hours. The values they give from both statements indicate relative values. Is this a good approach or did I just get lucky?


No that's not correct. We have two exactly the same linear equations from both statements, that's why we cannot solve for x and y. But if we had two distinct linear equations then we would be able to solve.

For example if either of statement were: the time needed for Machines X working alone to fill a production order of this size plus the time needed for Machines Y working alone to fill a production order of double the size is 10 hours --> x+2y=10.

So, for (1)+(2) we would have x+2y=10 and 2x=y --> x=2 and y=4 --> y-x=2.

Generally if you have n distinct linear equations and n variables then you can solve for them. "Distinct linear equations" means that no equation can be derived with the help of others or by arithmetic operation (multiplication, addition).

For example:
\(x+y=2\) and \(3x+3y=6\) --> we do have two linear equations and two variables but we cannot solve for \(x\) or \(y\) as the second equation is just the first one multiplied by 3 (basically we have only one distinct equation);
OR
\(x+y=1\), \(y+z=2\) and \(x+2y+z=3\) --> we have 3 linear equations and 3 variables but we cannot solve for \(x\), \(y\) or \(z\) as the third equation can be derived with the help of first two if we sum them (basically we have only two distinct equation).

Hope it's clear.
_________________
Intern
Intern
avatar
Joined: 11 Nov 2013
Posts: 15
GMAT Date: 12-26-2013
GPA: 3.6
WE: Consulting (Computer Software)
Re: Machines X and Y work at their respective constant rates. How many  [#permalink]

Show Tags

New post 04 Dec 2013, 12:15
Bunuel wrote:
Machines X and Y work at their respective constant rates. How many more hours does it take machine Y, working alone, to fill a production order of a certain size than it takes machine X, working alone?

Let \(x\) and \(y\) be the times needed for machines X and Y respectively working alone to fill a production order of this size.

Question: \(y-x=?\)

(1) Machines X and Y, working together, fill a production order of this size in 2/3 the time that machine X, working alone, does --> general relationship: \(\frac{1}{x}+\frac{1}{y}=\frac{1}{total \ time}\) --> Total time needed for machines X and Y working together is \(total \ time=\frac{xy}{x+y}\) (general formula) --> given \(\frac{xy}{x+y}=x*\frac{2}{3}\) --> \(2x=y\). Not sufficient

(2) Machine Y, working alone, fills a production order of this size in twice the time that machine X, working alone, does --> \(2x=y\), the same info. Not sufficient

(1)+(2) Nothing new. Not Sufficient.

Answer: E.

Hope it helps.

P.S. Please post one question per topic. Also you can attach image files directly so no need to attach zip files.


Hi,

I am not understanding statement 1.
If x & Y are the rates respectively , then 1/X and 1/Y are the time taken to complete the task.
Shouldnt the equation be

1/X + 1/Y = 2/3X

It gives a degree 3 equation but I am not sure where I am going wrong in logic ?
Veritas Prep GMAT Instructor
User avatar
V
Joined: 16 Oct 2010
Posts: 9705
Location: Pune, India
Re: Machines X and Y work at their respective constant rates. How many  [#permalink]

Show Tags

New post 04 Dec 2013, 21:27
A4G wrote:
Bunuel wrote:
Machines X and Y work at their respective constant rates. How many more hours does it take machine Y, working alone, to fill a production order of a certain size than it takes machine X, working alone?

Let \(x\) and \(y\) be the times needed for machines X and Y respectively working alone to fill a production order of this size.

Question: \(y-x=?\)

(1) Machines X and Y, working together, fill a production order of this size in 2/3 the time that machine X, working alone, does --> general relationship: \(\frac{1}{x}+\frac{1}{y}=\frac{1}{total \ time}\) --> Total time needed for machines X and Y working together is \(total \ time=\frac{xy}{x+y}\) (general formula) --> given \(\frac{xy}{x+y}=x*\frac{2}{3}\) --> \(2x=y\). Not sufficient

(2) Machine Y, working alone, fills a production order of this size in twice the time that machine X, working alone, does --> \(2x=y\), the same info. Not sufficient

(1)+(2) Nothing new. Not Sufficient.

Answer: E.

Hope it helps.

P.S. Please post one question per topic. Also you can attach image files directly so no need to attach zip files.


Hi,

I am not understanding statement 1.
If x & Y are the rates respectively , then 1/X and 1/Y are the time taken to complete the task.
Shouldnt the equation be

1/X + 1/Y = 2/3X

It gives a degree 3 equation but I am not sure where I am going wrong in logic ?


As Bunuel noted above, X is the time taken by machine X and Y is the time taken by machine Y. Combined time taken is 2X/3
Rates are 1/X and 1/Y which are additive. The combined rate is 3/2X
1/X + 1/Y = 3/2X

Also note that you are trying to add individual time taken in your equation. But times are not additive, only rates are additive. e.g. if you take 2 hrs to complete a work and I take 3 hrs, together will we take 5 hrs? I hope you understand that we will take less than 2 hrs for sure because you alone can complete it in 2 hrs. So times are NOT additive.
_________________
Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
Manager
Manager
avatar
Joined: 28 Apr 2014
Posts: 195
GMAT ToolKit User
Re: Machines X and Y work at their respective constant rates. How many  [#permalink]

Show Tags

New post 05 May 2014, 00:29
Bunuel wrote:
Machines X and Y work at their respective constant rates. How many more hours does it take machine Y, working alone, to fill a production order of a certain size than it takes machine X, working alone?

Let \(x\) and \(y\) be the times needed for machines X and Y respectively working alone to fill a production order of this size.

Question: \(y-x=?\)

(1) Machines X and Y, working together, fill a production order of this size in 2/3 the time that machine X, working alone, does --> general relationship: \(\frac{1}{x}+\frac{1}{y}=\frac{1}{total \ time}\) --> Total time needed for machines X and Y working together is \(total \ time=\frac{xy}{x+y}\) (general formula) --> given \(\frac{xy}{x+y}=x*\frac{2}{3}\) --> \(2x=y\). Not sufficient

(2) Machine Y, working alone, fills a production order of this size in twice the time that machine X, working alone, does --> \(2x=y\), the same info. Not sufficient

(1)+(2) Nothing new. Not Sufficient.

Answer: E.

Hope it helps.

P.S. Please post one question per topic. Also you can attach image files directly so no need to attach zip files.


Bunuel my thought process was that - No where in the question is the absolute time mentioned for any any machine so none of the 2 points are sufficent . hence E.
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58464
Re: Machines X and Y work at their respective constant rates. How many  [#permalink]

Show Tags

New post 05 May 2014, 01:36
1
himanshujovi wrote:
Bunuel wrote:
Machines X and Y work at their respective constant rates. How many more hours does it take machine Y, working alone, to fill a production order of a certain size than it takes machine X, working alone?

Let \(x\) and \(y\) be the times needed for machines X and Y respectively working alone to fill a production order of this size.

Question: \(y-x=?\)

(1) Machines X and Y, working together, fill a production order of this size in 2/3 the time that machine X, working alone, does --> general relationship: \(\frac{1}{x}+\frac{1}{y}=\frac{1}{total \ time}\) --> Total time needed for machines X and Y working together is \(total \ time=\frac{xy}{x+y}\) (general formula) --> given \(\frac{xy}{x+y}=x*\frac{2}{3}\) --> \(2x=y\). Not sufficient

(2) Machine Y, working alone, fills a production order of this size in twice the time that machine X, working alone, does --> \(2x=y\), the same info. Not sufficient

(1)+(2) Nothing new. Not Sufficient.

Answer: E.

Hope it helps.

P.S. Please post one question per topic. Also you can attach image files directly so no need to attach zip files.


Bunuel my thought process was that - No where in the question is the absolute time mentioned for any any machine so none of the 2 points are sufficent . hence E.


That's not entirely correct.

For example, if the first statement were: machines X and Y, working together, fill a production order of this size in 1/2 the time that machine X, working alone, does, then this would be sufficient. Because in this case we would have x=y, and hence x-y=0.

Does this make sense?
_________________
Manager
Manager
User avatar
Joined: 20 Apr 2013
Posts: 122
Re: Machines X and Y work at their respective constant rates. How many mor  [#permalink]

Show Tags

New post 11 May 2015, 04:49
2
2
Let us suppose that machine X takes x hours, while machine Y takes y hours, to fill production order. According to question, we have to find (y-x)

So, in 1 hour, X finishes 1/x while Y finishes 1/y production order

(1) says: Machines X and Y, working together, fill a production order of this size in two-thirds the time that machine X, working alone, does.

Working together, X and Y complete (1/x+1/y) production order in 1 hour

=> Working together, X and Y complete production order in 1/(1/x+1/y) hours

But, (1) says that 1/(1/x+1/y) = (2/3) x

Solving this, we get: y = 2x

So, clearly not sufficient for us to say what is (y – x)

(2) says that Machine Y, working alone, fills a production order of this size in twice the time that machine X, working alone, does.
=> y = 2x

So, clearly not sufficient for us to say what is (y – x)

Combining the two statements, again, both actually say the same thing (y=2x) and so, this is not sufficient for us to say what is (y – x).

Hence, E.
SVP
SVP
avatar
B
Joined: 06 Nov 2014
Posts: 1873
Re: Machines X and Y work at their respective constant rates. How many mor  [#permalink]

Show Tags

New post 12 May 2015, 03:35
1
2
The rates of Machine X and Machine Y can be 1/A and 1/B, respectively. A and B represent the number of hours to complete the task. The question is asking for B-A.
Statement 1 tells you that (1/B) + (1/A) = (2/3)(1/A). There are still 2 unknowns, so eliminate A, D.
Statement 2 tells you that (1/B) = (1/2A) or B=2A. Still, we have 2 unknowns. Eliminate B.
No new information can be obtained by combining to the two statements. Therefore E is the answer.
Manager
Manager
avatar
Joined: 08 Jun 2015
Posts: 99
Re: Machines X and Y work at their respective constant rates. How many mor  [#permalink]

Show Tags

New post 05 Jul 2015, 21:24
If y = 2x, then I can't simply leave the answer as y - x = 2x - x = x?

That is, machine y takes x hours longer than x? It doesn't solve for the value of x, but isn't that technically an answer?

Or, does the GMAT require a value for x, since we're still left to wonder how many hours x is... e.g. x could be 1 hour or 10 hours, or so forth? So, even if you get an answer but there's still at least one variable in the answer, the data is missing and thus insufficient?
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58464
Re: Machines X and Y work at their respective constant rates. How many mor  [#permalink]

Show Tags

New post 06 Jul 2015, 00:47
iPen wrote:
If y = 2x, then I can't simply leave the answer as y - x = 2x - x = x?

That is, machine y takes x hours longer than x? It doesn't solve for the value of x, but isn't that technically an answer?

Or, does the GMAT require a value for x, since we're still left to wonder how many hours x is... e.g. x could be 1 hour or 10 hours, or so forth? So, even if you get an answer but there's still at least one variable in the answer, the data is missing and thus insufficient?


Official Guide:

In data sufficiency problems that ask for the value of a quantity, the data given in the statements are sufficient only when it is possible to determine exactly one numerical value for the quantity.
_________________
Manager
Manager
avatar
Joined: 08 Jun 2015
Posts: 99
Re: Machines X and Y work at their respective constant rates. How many mor  [#permalink]

Show Tags

New post 08 Jul 2015, 16:00
I did it a little differently.


\(\frac{1}{x} + \frac{1}{y} = \frac{1}{h}\)

\(\frac{y}{xy} + \frac{x}{xy} = \frac{1}{h} = \frac{y + x}{xy}\)

(1) \(\frac{1}{2/3*x} = \frac{3}{2x} = \frac{y + x}{xy}\)

\(\frac{3}{2} = \frac{y + x}{y}\); 3y = 2(y + x); 3y = 2y + 2x; y = 2x

Two variables - we don't know the values of either x or y, so insufficient.

(2) \(\frac{1}{y} = \frac{1}{2x}\); y = 2x

Again, two variables remain, so it's insufficient.

(1) + (2): Two different equations, same result of y = 2x

\(\frac{3}{2} = \frac{y + x}{y}\)
\(\frac{3}{2} = 2x + \frac{x}{2x}\);\(\frac{3}{2} = 2x + \frac{1}{}2\); \(2x = 1\); \(x =\frac{1}{2}\)
\(y = 2(\frac{1}{2}) = 1\)

Together, they finish a given job in 1/3 hours.
Machine x does it in 1/2 hours.
Machine y does it in 1 hour.
y - x = 1/2 hours.

But, plugging the same y = 2x only gives us a relative difference. And, the three results above would need to be multiplied by a constant, because the equation holds true for any positive value of x (e.g. If x is 1, then y is 2, together it's 2/3, and y-x = 1). Thus, insufficient. Answer is E.
Intern
Intern
avatar
Joined: 22 Oct 2015
Posts: 17
Re: Machines X and Y work at their respective constant rates. How many mor  [#permalink]

Show Tags

New post 04 Feb 2016, 15:27
Bunuel wrote:
Machines X and Y work at their respective constant rates. How many more hours does it take machine Y, working alone, to fill a production order of a certain size than it takes machine X, working alone?

Let \(x\) and \(y\) be the times needed for machines X and Y respectively working alone to fill a production order of this size.

Question: \(y-x=?\)

(1) Machines X and Y, working together, fill a production order of this size in 2/3 the time that machine X, working alone, does --> general relationship: \(\frac{1}{x}+\frac{1}{y}=\frac{1}{total \ time}\) --> Total time needed for machines X and Y working together is \(total \ time=\frac{xy}{x+y}\) (general formula) --> given \(\frac{xy}{x+y}=x*\frac{2}{3}\) --> \(2x=y\). Not sufficient

(2) Machine Y, working alone, fills a production order of this size in twice the time that machine X, working alone, does --> \(2x=y\), the same info. Not sufficient

(1)+(2) Nothing new. Not Sufficient.

Answer: E.

Hope it helps.


\(\frac{xy}{x+y}=x*\frac{2}{3}\) --> \(2x=y\)

Could you go through the bolded part and explain how you derived 2x=y? I am quite confused how you got rid of the x....
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58464
Re: Machines X and Y work at their respective constant rates. How many mor  [#permalink]

Show Tags

New post 05 Feb 2016, 01:30
2
ZaydenBond wrote:
Bunuel wrote:
Machines X and Y work at their respective constant rates. How many more hours does it take machine Y, working alone, to fill a production order of a certain size than it takes machine X, working alone?

Let \(x\) and \(y\) be the times needed for machines X and Y respectively working alone to fill a production order of this size.

Question: \(y-x=?\)

(1) Machines X and Y, working together, fill a production order of this size in 2/3 the time that machine X, working alone, does --> general relationship: \(\frac{1}{x}+\frac{1}{y}=\frac{1}{total \ time}\) --> Total time needed for machines X and Y working together is \(total \ time=\frac{xy}{x+y}\) (general formula) --> given \(\frac{xy}{x+y}=x*\frac{2}{3}\) --> \(2x=y\). Not sufficient

(2) Machine Y, working alone, fills a production order of this size in twice the time that machine X, working alone, does --> \(2x=y\), the same info. Not sufficient

(1)+(2) Nothing new. Not Sufficient.

Answer: E.

Hope it helps.


\(\frac{xy}{x+y}=x*\frac{2}{3}\) --> \(2x=y\)

Could you go through the bolded part and explain how you derived 2x=y? I am quite confused how you got rid of the x....


\(\frac{xy}{x+y}=\frac{2x}{3}\);

Cross-multiply: \(3xy=2x(x+y)\);

\(3xy = 2x^2 + 2xy\);

\(xy = 2x^2\);

Reduce by x: \(y=2x\).

Hope it's clear.
_________________
Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 13417
Re: Machines X and Y work at their respective constant rates.  [#permalink]

Show Tags

New post 05 Jun 2019, 06:20
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Club Bot
Re: Machines X and Y work at their respective constant rates.   [#permalink] 05 Jun 2019, 06:20
Display posts from previous: Sort by

Machines X and Y work at their respective constant rates. How many mor

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





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