Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 20 Feb 2012
Posts: 40

Machines X and Y work at their respective constant rates
[#permalink]
Show Tags
23 Feb 2012, 09:05
Question Stats:
58% (01:06) correct 42% (01:14) wrong based on 1922 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 twothirds 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.
Official Answer and Stats are available only to registered users. Register/ Login.




Math Expert
Joined: 02 Sep 2009
Posts: 48067

Re: DATA12
[#permalink]
Show Tags
23 Feb 2012, 09:13
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: \(yx=?\) (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.
_________________
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




Manager
Joined: 11 Dec 2011
Posts: 51
Location: Malaysia
Concentration: Nonprofit, Sustainability
GPA: 3.16
WE: Consulting (Computer Software)

Re: Machines X and Y work at their respective constant rates
[#permalink]
Show Tags
05 Mar 2012, 06:35
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
Joined: 02 Sep 2009
Posts: 48067

Machines X and Y work at their respective constant rates
[#permalink]
Show Tags
05 Mar 2012, 08:08
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 > yx=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.
_________________
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



Manager
Joined: 13 May 2010
Posts: 117

Re: Machines X and Y work at their respective constant rates
[#permalink]
Show Tags
07 Aug 2012, 04:59
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: yx=?
(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.
Above is the solution posted by Bunnel (sorry I always misspell your name)
When we solve statement 1 we really need to discard one solution x =0 (when you solve you get two solutions) Can we safely discard X =0 in rate. time questions since 0 time does not make sense; 0 time spent means machine did not work at all. Question says Machine x did work so X =0 is not a possible solution and that is why we can discard that solution keeping Y =2x



Manager
Joined: 26 Feb 2013
Posts: 165

Re: DATA12
[#permalink]
Show Tags
25 Sep 2013, 06:58
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: \(yx=?\)
(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. Is xy/x+y the total time or the combined rate?



Math Expert
Joined: 02 Sep 2009
Posts: 48067

Re: DATA12
[#permalink]
Show Tags
25 Sep 2013, 08:51
Skag55 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: \(yx=?\)
(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. Is xy/x+y the total time or the combined rate? Total time. Check here: machinesxandvproducedidenticalbottlesatdifferent104208.html#p812628Hope it 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



Manager
Joined: 20 Apr 2013
Posts: 144

Re: Machines X and Y work at their respective constant rates
[#permalink]
Show Tags
11 May 2015, 04:49
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 (yx)
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 twothirds 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.



Senior Manager
Joined: 02 Mar 2012
Posts: 334

Re: Machines X and Y work at their respective constant rates
[#permalink]
Show Tags
11 May 2015, 08:20
E
let us suppose rate of machine x is Rx and rate of machine y is Ry given to us is Rx>Ry
statement 1.
let us suppose it takes t hours to fill an order
so Rx=1/t
given Rx + Ry = 3/2t
substituing value of Rx in the above eq
Ry = 1/2t
we dont know the value of t. So insufficient
statement 2.
let us suppose here also that it takes t hours to fill and order
given Ry = 1/2t and Rx = 1/t
we dont have the value of t so ,insufficient.
Combining both
either of the statements above imply same and value of t still remains unsaid.
SO E
hope it helps



SVP
Joined: 06 Nov 2014
Posts: 1888

Re: Machines X and Y work at their respective constant rates
[#permalink]
Show Tags
12 May 2015, 03:35
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 BA. 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
Joined: 08 Jun 2015
Posts: 113

Machines X and Y work at their respective constant rates
[#permalink]
Show Tags
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
Joined: 02 Sep 2009
Posts: 48067

Re: Machines X and Y work at their respective constant rates
[#permalink]
Show Tags
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.
_________________
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



Manager
Joined: 08 Jun 2015
Posts: 113

Re: Machines X and Y work at their respective constant rates
[#permalink]
Show Tags
06 Jul 2015, 12:06
Bunuel wrote: 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. Thanks that clears it up. Hence, the name "data sufficiency"!



Manager
Joined: 23 Nov 2014
Posts: 58
Location: India
GPA: 3.14
WE: Sales (Consumer Products)

Machines X and Y work at their respective constant rates
[#permalink]
Show Tags
08 Jul 2015, 12:26
Let x finish x% of the total work/min => 100% of the work will be done in 100/x mins Let y finish y% of the total work/min => 100% of the work will be done in 100/y mins
1) 100/x+y = 2/3 * 100/x => x = 2y 2) 100/y = 2 * 100/x => x = 2y 1+2) No new info => Ans = (E)
For the sake of clarity, does it matter that both statements give me x = 2y as opposed to the y = 2x that everyone else has been getting? I think not, but would appreciate an input nonetheless  have my retake in less than 2 weeks now!
Thanks



Manager
Joined: 08 Jun 2015
Posts: 113

Machines X and Y work at their respective constant rates
[#permalink]
Show Tags
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 yx = 1). Thus, insufficient. Answer is E.



BSchool Thread Master
Joined: 13 Jul 2015
Posts: 46
Location: Singapore
WE: Operations (Investment Banking)

Machines X and Y work at their respective constant rates
[#permalink]
Show Tags
29 Sep 2015, 20:00
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: \(yx=?\)
(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. Hey Bunuel, I did it by setting \(x\) = speed of Machine X and \(y\) = speed of Machine Y, which eventually led me to the equation \(x\) = 2\(y\) However, I am trying to reconcile the logic of your working because I am still quite weak in this topic. It may seem like a stupid question but \(\frac{1}{x}+\frac{1}{y}=\frac{1}{total \ time}\) 1. Does this working mean > Speed of X + Speed of Y = Total Speed? 2. Would you recommend that we adopt this general formula to all work/rate problems? 3. Is there any potential trap in my method? Unrelated: 4. As you can see I have just joined, I find that when I do a search on the forum for any type of question, it always shows me questions from as long ago as 2009. Is there any way I can get access to the most recent questions? Do you think there is any difference in doing more recent questions? The way I see it is that more recent questions = more accurate to the current standard i'm up against if I were to take the GMAT during this period.



Intern
Joined: 22 Oct 2015
Posts: 17

Machines X and Y work at their respective constant rates
[#permalink]
Show Tags
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: \(yx=?\)
(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
Joined: 02 Sep 2009
Posts: 48067

Re: Machines X and Y work at their respective constant rates
[#permalink]
Show Tags
05 Feb 2016, 01:30
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: \(yx=?\)
(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.... \(\frac{xy}{x+y}=\frac{2x}{3}\); Crossmultiply: \(3xy=2x(x+y)\); \(3xy = 2x^2 + 2xy\); \(xy = 2x^2\); Reduce by x: \(y=2x\). 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
Joined: 21 Mar 2017
Posts: 40
Location: Zimbabwe
Concentration: General Management, Entrepreneurship
GMAT 1: 680 Q45 V38 GMAT 2: 750 Q49 V42
GPA: 3.3
WE: Accounting (Accounting)

Re: Machines X and Y work at their respective constant rates
[#permalink]
Show Tags
27 Sep 2017, 09:58
Bunuel wrote: 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 can not 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 > yx=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 can not 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. Hi BunuelYour example contains the mention of a distinct number of hours (10 hours) therefore this can be solved. However, the actual question just tells us the relationship between the different rates, therefore it cannot be solved. Please correct me if i am wrong
_________________
Kudos if you like my response please




Re: Machines X and Y work at their respective constant rates &nbs
[#permalink]
27 Sep 2017, 09:58






