November 17, 2018 November 17, 2018 07:00 AM PST 09:00 AM PST Nov. 17, 7 AM PST. Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT. November 17, 2018 November 17, 2018 09:00 AM PST 11:00 AM PST Join the Quiz Saturday November 17th, 9 AM PST. The Quiz will last approximately 2 hours. Make sure you are on time or you will be at a disadvantage.
Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 02 Dec 2012
Posts: 177

Three machines, K, M, and P, working simultaneously and
[#permalink]
Show Tags
03 Dec 2012, 02:40
Question Stats:
78% (01:18) correct 22% (01:38) wrong based on 1427 sessions
HideShow timer Statistics
Three machines, K, M, and P, working simultaneously and independently at their respective constant rates, can complete a certain task in 24 minutes. How long does it take Machine K, working alone at its constant rate, to complete the task? (1) Machines M and P, working simultaneously and independently at their respective constant rates, can complete the task in 36 minutes. (2) Machines K and P, working simultaneously and independently at their respective constant rates, can complete the task in 48 minutes.
Official Answer and Stats are available only to registered users. Register/ Login.




Math Expert
Joined: 02 Sep 2009
Posts: 50613

Re: Three machines, K, M, and P, working simultaneously and
[#permalink]
Show Tags
03 Dec 2012, 02:42
Three machines, K, M, and P, working simultaneously and independently at their respective constant rates, can complete a certain task in 24 minutes. How long does it take Machine K, working alone at its constant rate, to complete the task?Say k, m, and p are the numbers of minutes machines K, M, and P take, respectively, to complete the task. Then we have that \(\frac{1}{k}+\frac{1}{m}+\frac{1}{p}=\frac{1}{24}\). (1) Machines M and P, working simultaneously and independently at their respective constant rates, can complete the task in 36 minutes > \(\frac{1}{m}+\frac{1}{p}=\frac{1}{36}\), thus \(\frac{1}{k}+\frac{1}{36}=\frac{1}{24}\) > we can find the value of \(k\). Sufficient. (2) Machines K and P, working simultaneously and independently at their respective constant rates, can complete the task in 48 minutes > \(\frac{1}{k}+\frac{1}{p}=\frac{1}{48}\). The value of k cannot be determined from the data we have. Not sufficient. Answer: A.
_________________
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: 22 Nov 2010
Posts: 228
Location: India
WE: Consulting (Telecommunications)

Re: Three machines, K, M, and P, working simultaneously and
[#permalink]
Show Tags
04 Mar 2013, 01:57
Three machines, K, M, and P, working simultaneously and independently at their respective constant rates, can complete a certain task in 24 minutes. How long does it take Machine K, working alone at its constant rate, to complete the task? (1) Machines M and P, working simultaneously and independently at their respective constant rates, can complete the task in 36 minutes. RATE K + M + P)  RATE : (M+P) = RATE : K. SUFFICIENT(2) Machines K and P, working simultaneously and independently at their respective constant rates, can complete the task in 48 minutes. RATE K + M + P)  RATE : (K+P) = RATE : M. NOT SUFFICIENT
_________________
YOU CAN, IF YOU THINK YOU CAN



Intern
Joined: 23 Oct 2012
Posts: 28

Re: Three machines, K, M, and P, working simultaneously and
[#permalink]
Show Tags
28 Nov 2013, 05:29
Bunuel wrote: Three machines, K, M, and P, working simultaneously and independently at their respective constant rates, can complete a certain task in 24 minutes. How long does it take Machine K, working alone at its constant rate, to complete the task?
Say k, m, and p are the numbers of minutes machines K, M, and P take, respectively, to complete the task. Then we have that \(\frac{1}{k}+\frac{1}{m}+\frac{1}{p}=\frac{1}{24}\).
(1) Machines M and P, working simultaneously and independently at their respective constant rates, can complete the task in 36 minutes > \(\frac{1}{m}+\frac{1}{p}=\frac{1}{36}\), thus \(\frac{1}{k}+\frac{1}{36}=\frac{1}{24}\) > we can find the value of \(k\). Sufficient.
(2) Machines K and P, working simultaneously and independently at their respective constant rates, can complete the task in 48 minutes > \(\frac{1}{k}+\frac{1}{p}=\frac{1}{48}\). The value of k cannot be determined from the data we have. Not sufficient.
Answer: A. I approached this pbm a little differently. Pls. Explain where I am going wrong...is it OK to reason this way? Let Rk, Rm and Rp be the rates for the machines K,M and P respectively. Then 1/Rk +1/Rm+1/Rp = 24 St 1 gives > 1/Rm + 1/Rp = 36 So, we get 1/Rk + 36 = 24. Solving, 1/Rk = 2436=12 Why am I getting a negative value?



Math Expert
Joined: 02 Sep 2009
Posts: 50613

Re: Three machines, K, M, and P, working simultaneously and
[#permalink]
Show Tags
29 Nov 2013, 09:12
audiogal101 wrote: Bunuel wrote: Three machines, K, M, and P, working simultaneously and independently at their respective constant rates, can complete a certain task in 24 minutes. How long does it take Machine K, working alone at its constant rate, to complete the task?
Say k, m, and p are the numbers of minutes machines K, M, and P take, respectively, to complete the task. Then we have that \(\frac{1}{k}+\frac{1}{m}+\frac{1}{p}=\frac{1}{24}\).
(1) Machines M and P, working simultaneously and independently at their respective constant rates, can complete the task in 36 minutes > \(\frac{1}{m}+\frac{1}{p}=\frac{1}{36}\), thus \(\frac{1}{k}+\frac{1}{36}=\frac{1}{24}\) > we can find the value of \(k\). Sufficient.
(2) Machines K and P, working simultaneously and independently at their respective constant rates, can complete the task in 48 minutes > \(\frac{1}{k}+\frac{1}{p}=\frac{1}{48}\). The value of k cannot be determined from the data we have. Not sufficient.
Answer: A. I approached this pbm a little differently. Pls. Explain where I am going wrong...is it OK to reason this way? Let Rk, Rm and Rp be the rates for the machines K,M and P respectively. Then 1/Rk +1/Rm+1/Rp = 24St 1 gives > 1/Rm + 1/Rp = 36So, we get 1/Rk + 36 = 24. Solving, 1/Rk = 2436=12 Why am I getting a negative value? 1/Rk, 1/Rm, and 1/Rp are the numbers of minutes machines K, M, and P take to complete the task alone. Each must be greater than the time needed for three machines to complete a certain task together (24 minutes), thus 1/Rk +1/Rm+1/Rp = 24 is not right. The same for 1/Rm + 1/Rp = 36. 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: 23 Oct 2012
Posts: 28

Re: Three machines, K, M, and P, working simultaneously and
[#permalink]
Show Tags
29 Nov 2013, 21:35
Bunuel wrote: audiogal101 wrote: Bunuel wrote: Three machines, K, M, and P, working simultaneously and independently at their respective constant rates, can complete a certain task in 24 minutes. How long does it take Machine K, working alone at its constant rate, to complete the task?
Say k, m, and p are the numbers of minutes machines K, M, and P take, respectively, to complete the task. Then we have that \(\frac{1}{k}+\frac{1}{m}+\frac{1}{p}=\frac{1}{24}\).
(1) Machines M and P, working simultaneously and independently at their respective constant rates, can complete the task in 36 minutes > \(\frac{1}{m}+\frac{1}{p}=\frac{1}{36}\), thus \(\frac{1}{k}+\frac{1}{36}=\frac{1}{24}\) > we can find the value of \(k\). Sufficient.
(2) Machines K and P, working simultaneously and independently at their respective constant rates, can complete the task in 48 minutes > \(\frac{1}{k}+\frac{1}{p}=\frac{1}{48}\). The value of k cannot be determined from the data we have. Not sufficient.
Answer: A. I approached this pbm a little differently. Pls. Explain where I am going wrong...is it OK to reason this way? Let Rk, Rm and Rp be the rates for the machines K,M and P respectively. Then 1/Rk +1/Rm+1/Rp = 24St 1 gives > 1/Rm + 1/Rp = 36So, we get 1/Rk + 36 = 24. Solving, 1/Rk = 2436=12 Why am I getting a negative value? 1/Rk, 1/Rm, and 1/Rp are the numbers of minutes machines K, M, and P take to complete the task alone. Each must be greater than the time needed for three machines to complete a certain task together (24 minutes), thus 1/Rk +1/Rm+1/Rp = 24 is not right. The same for 1/Rm + 1/Rp = 36. Hope it's clear. Got it. So would it be correct to say that 1/ (Rk+Rm+Rp) = 24? (since the denominator has combined rate now)?



Target Test Prep Representative
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2830

Re: Three machines, K, M, and P, working simultaneously and
[#permalink]
Show Tags
11 Dec 2017, 10:28
Walkabout wrote: Three machines, K, M, and P, working simultaneously and independently at their respective constant rates, can complete a certain task in 24 minutes. How long does it take Machine K, working alone at its constant rate, to complete the task?
(1) Machines M and P, working simultaneously and independently at their respective constant rates, can complete the task in 36 minutes. (2) Machines K and P, working simultaneously and independently at their respective constant rates, can complete the task in 48 minutes. We are given that machines K, M, and P, working simultaneously and independently at their respective constant rates, can complete a certain task in 24 minutes. If we consider the entire task to be equal to 1, and the time in minutes for machines K, M, and P to complete the task to be k, m, and p, respectively, then the rates of machines K, M, and P are: 1/k = rate of machine K to complete the task 1/m = rate of machine M to complete the task 1/p = rate of machine P to complete the task Since it takes machines K, M, and P, working simultaneously and independently, 24 minutes, the combined rate of machines K, M, and P is 1 task per 24 minutes. That is: 1/k + 1/m + 1/p = 1/24 We need to determine how long it takes machine K to complete the task, or in other words, the value of k. Since 1/k + 1/m + 1/p = 1/24, the rate of machine K is: 1/k = 1/24  1/m  1/p 1/k = 1/24  (1/m + 1/p) Thus, if we can determine the value of (1/m + 1/p), we can determine the value of 1/k and hence the value of k. Statement One Alone: Machines M and P, working simultaneously and independently at their respective constant rates, can complete the task in 36 minutes. From statement one we know: 1/m + 1/p = 1/36 Thus, the rate for machine K to complete the task is 1/24  1/36 = 3/72  2/72 = 1/72, and therefore, the time for machine K to complete the task is 72 minutes. Statement one alone is sufficient to answer the question. We can eliminate answer choices B, C, and E. Statement Two Alone: Machines K and P, working simultaneously and independently at their respective constant rates, can complete the task in 48 minutes. From statement two we know: 1/k + 1/p = 1/48 Since we don’t know the value of p, this is not enough information to determine the value of k. Statement two alone is not sufficient to answer the question. Answer: A
_________________
Jeffery Miller
Head of GMAT Instruction
GMAT Quant SelfStudy Course
500+ lessons 3000+ practice problems 800+ HD solutions



VP
Status: It's near  I can see.
Joined: 13 Apr 2013
Posts: 1286
Location: India
Concentration: International Business, Operations
GPA: 3.01
WE: Engineering (Consulting)

Re: Three machines, K, M, and P, working simultaneously and
[#permalink]
Show Tags
27 Mar 2018, 04:13
Bunuel wrote: Three machines, K, M, and P, working simultaneously and independently at their respective constant rates, can complete a certain task in 24 minutes. How long does it take Machine K, working alone at its constant rate, to complete the task?
Say k, m, and p are the numbers of minutes machines K, M, and P take, respectively, to complete the task. Then we have that \(\frac{1}{k}+\frac{1}{m}+\frac{1}{p}=\frac{1}{24}\).
(1) Machines M and P, working simultaneously and independently at their respective constant rates, can complete the task in 36 minutes > \(\frac{1}{m}+\frac{1}{p}=\frac{1}{36}\), thus \(\frac{1}{k}+\frac{1}{36}=\frac{1}{24}\) > we can find the value of \(k\). Sufficient.
(2) Machines K and P, working simultaneously and independently at their respective constant rates, can complete the task in 48 minutes > \(\frac{1}{k}+\frac{1}{p}=\frac{1}{48}\). The value of k cannot be determined from the data we have. Not sufficient.
Answer: A. At first glance it was (D) for me as both statement looks identical. Bunuel, why we are not able to answer the question with Statement 2.
_________________
"Do not watch clock; Do what it does. KEEP GOING."



Math Expert
Joined: 02 Sep 2009
Posts: 50613

Re: Three machines, K, M, and P, working simultaneously and
[#permalink]
Show Tags
28 Mar 2018, 02:45
QZ wrote: Bunuel wrote: Three machines, K, M, and P, working simultaneously and independently at their respective constant rates, can complete a certain task in 24 minutes. How long does it take Machine K, working alone at its constant rate, to complete the task?
Say k, m, and p are the numbers of minutes machines K, M, and P take, respectively, to complete the task. Then we have that \(\frac{1}{k}+\frac{1}{m}+\frac{1}{p}=\frac{1}{24}\).
(1) Machines M and P, working simultaneously and independently at their respective constant rates, can complete the task in 36 minutes > \(\frac{1}{m}+\frac{1}{p}=\frac{1}{36}\), thus \(\frac{1}{k}+\frac{1}{36}=\frac{1}{24}\) > we can find the value of \(k\). Sufficient.
(2) Machines K and P, working simultaneously and independently at their respective constant rates, can complete the task in 48 minutes > \(\frac{1}{k}+\frac{1}{p}=\frac{1}{48}\). The value of k cannot be determined from the data we have. Not sufficient.
Answer: A. At first glance it was (D) for me as both statement looks identical. Bunuel, why we are not able to answer the question with Statement 2. Good question. We are given \(\frac{1}{k}+\frac{1}{m}+\frac{1}{p}=\frac{1}{24}\). and want to find the value of k. (2) says that \(\frac{1}{k}+\frac{1}{p}=\frac{1}{48}\). If we substitute this above, we'll get: \(\frac{1}{m}+\frac{1}{48}=\frac{1}{24}\) (linear equation with one unknown m). From this we can find that m = 48 but still no way of finding k. In (1) on the other hand we are also getting a linear equation with one unknown, but that unknown there is k itself: \(\frac{1}{k}+\frac{1}{36}=\frac{1}{24}\). 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




Re: Three machines, K, M, and P, working simultaneously and &nbs
[#permalink]
28 Mar 2018, 02:45






