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Machine A can produce toys at a constant rate of 2 units per hour and

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Machine A can produce toys at a constant rate of 2 units per hour and  [#permalink]

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New post 22 Feb 2017, 00:59
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  95% (hard)

Question Stats:

48% (02:57) correct 52% (03:00) wrong based on 144 sessions

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Machine A can produce toys at a constant rate of 2 units per hour and machine B can produce toys at a constant rate of 5 units per hour. If at least one of either machine A or machine B produces toys, what is the greatest possible hours when machine A and machine B work together at their constant rates so that two machines, A and B, can produce 88 units of toys in 20 hours?

A. 5hrs    
B. 6hrs    
C. 7hrs    
D. 8hrs    
E. 9hrs

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Re: Machine A can produce toys at a constant rate of 2 units per hour and  [#permalink]

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New post 22 Feb 2017, 01:35
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1
AustinKL wrote:
Machine A can produce toys at a constant rate of 2 units per hour and machine B can produce toys at a constant rate of 5 units per hour. If at least one of either machine A or machine B produces toys, what is the greatest possible hours when machine A and machine B work together at their constant rates so that two machines, A and B, can produce 88 units of toys in 20 hours?

A. 5hrs    
B. 6hrs    
C. 7hrs    
D. 8hrs    
E. 9hrs


A Produces @ 2 Units per hour
B Produces @ 5 Units per hour

Greatest Number of Hours of A and B together will be obtained when the remaining job (job done by one machine while working alone) is done by the individual machines (which is A in this case)

A and B together can produce = (2+5) = 7 Units per Hour

Let's start with biggest option
If both A&B work for 9 Hours the production = 7*9 = 63 and the remaining work (88-63=25 units) can be finished in 11 hours (1 hour of B i.e. 5 units and 10 hours of A i.e. 20 units) Hence Correct Option

Answer: Option E
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Re: Machine A can produce toys at a constant rate of 2 units per hour and  [#permalink]

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New post 22 Feb 2017, 01:57
GMATinsight wrote:
AustinKL wrote:
Machine A can produce toys at a constant rate of 2 units per hour and machine B can produce toys at a constant rate of 5 units per hour. If at least one of either machine A or machine B produces toys, what is the greatest possible hours when machine A and machine B work together at their constant rates so that two machines, A and B, can produce 88 units of toys in 20 hours?

A. 5hrs    
B. 6hrs    
C. 7hrs    
D. 8hrs    
E. 9hrs


A Produces @ 2 Units per hour
B Produces @ 5 Units per hour

Greatest Number of Hours of A and B together will be obtained when the remaining job (job done by one machine while working alone) is done by the individual machines (which is A in this case)

A and B together can produce = (2+5) = 7 Units per Hour

Let's start with biggest option
If both A&B work for 9 Hours the production = 7*9 = 63 and the remaining work (88-63=25 units) can be finished in 11 hours (1 hour of B i.e. 5 units and 10 hours of A i.e. 20 units) Hence Correct Option

Answer: Option E


Dear GMATinsight, Could you share with me why shall we consider the remaining job?
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Re: Machine A can produce toys at a constant rate of 2 units per hour and  [#permalink]

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New post 22 Feb 2017, 02:06
AustinKL wrote:
GMATinsight wrote:
AustinKL wrote:
Machine A can produce toys at a constant rate of 2 units per hour and machine B can produce toys at a constant rate of 5 units per hour. If at least one of either machine A or machine B produces toys, what is the greatest possible hours when machine A and machine B work together at their constant rates so that two machines, A and B, can produce 88 units of toys in 20 hours?

A. 5hrs    
B. 6hrs    
C. 7hrs    
D. 8hrs    
E. 9hrs


A Produces @ 2 Units per hour
B Produces @ 5 Units per hour

Greatest Number of Hours of A and B together will be obtained when the remaining job (job done by one machine while working alone) is done by the individual machines (which is A in this case)

A and B together can produce = (2+5) = 7 Units per Hour

Let's start with biggest option
If both A&B work for 9 Hours the production = 7*9 = 63 and the remaining work (88-63=25 units) can be finished in 11 hours (1 hour of B i.e. 5 units and 10 hours of A i.e. 20 units) Hence Correct Option

Answer: Option E


Dear GMATinsight, Could you share with me why shall we consider the remaining job?


Because we need to ensure that work is done in 20 Hours which is a mentioned fact which needs to be abide by
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Machine A can produce toys at a constant rate of 2 units per hour and  [#permalink]

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New post 22 Feb 2017, 06:03
Quote:
Because we need to ensure that work is done in 20 Hours which is a mentioned fact which needs to be abide by


Dear GMATinsight, However, the question is asking about greatest possible hours so that machine A & B can produce 88 units and not the remaining.
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Re: Machine A can produce toys at a constant rate of 2 units per hour and  [#permalink]

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New post 22 Feb 2017, 07:32
2
AustinKL wrote:
Machine A can produce toys at a constant rate of 2 units per hour and machine B can produce toys at a constant rate of 5 units per hour. If at least one of either machine A or machine B produces toys, what is the greatest possible hours when machine A and machine B work together at their constant rates so that two machines, A and B, can produce 88 units of toys in 20 hours?

A. 5hrs    
B. 6hrs    
C. 7hrs    
D. 8hrs    
E. 9hrs


Hi,
This problem can be thought as a three machine problem. Let's call A+B together as Machine C.
Let
Machine A works for \(x\) hrs @ 2unit/hr
Machine B works for \(y\) hrs @ 5 units/hr, and
Machine C works for \(z\) hrs @ 7 units/hr

Equation for time constraint:
\(x + y + z = 20\) --- (1)

Production constraint:
\(2x + 5y + 7z = 88\) --- (2)

Eqn(2) - 2*Eqn(1)
\(2x + 5y + 3z - 2x -2y -2z = 88 - 40 \Rightarrow 3y + 5z = 48 \Rightarrow z = \frac{48 - 3y}{5}\)

Maximum possible integral value of \(z = 9\) for \(y = 1\)

Answer: 9hrs (E).

Plug in the value of z and y in Eqn (1), we get x = 11. These values satisfy both the equations.

Thanks.
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Machine A can produce toys at a constant rate of 2 units per hour and  [#permalink]

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New post 22 Feb 2017, 11:45
AustinKL wrote:
Machine A can produce toys at a constant rate of 2 units per hour and machine B can produce toys at a constant rate of 5 units per hour. If at least one of either machine A or machine B produces toys, what is the greatest possible hours when machine A and machine B work together at their constant rates so that two machines, A and B, can produce 88 units of toys in 20 hours?

A. 5hrs    
B. 6hrs    
C. 7hrs    
D. 8hrs    
E. 9hrs


quick and dirty approach:
let x=number of units produced by A and B
x/7+(88-x)/2=20 hrs
x≈67 units
67/7≈9 hrs
9
E
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Machine A can produce toys at a constant rate of 2 units per hour and  [#permalink]

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New post 02 May 2017, 22:12
ziyuen wrote:
Machine A can produce toys at a constant rate of 2 units per hour and machine B can produce toys at a constant rate of 5 units per hour. If at least one of either machine A or machine B produces toys, what is the greatest possible hours when machine A and machine B work together at their constant rates so that two machines, A and B, can produce 88 units of toys in 20 hours?

A. 5hrs    
B. 6hrs    
C. 7hrs    
D. 8hrs    
E. 9hrs


OFFICIAL EXPLANATION


If machine A produces toys for "a" hours and machine B produces toys for "b" hours, and both machine A and B produce toys for "c" hours at the same time, you get \(a+b+c=20\) ---(1).

\(2a+5b+(2+5)c=88\)
\(2a+5b+7c=88\) ---(2)

Multiply (1) by 2, \(2a+2b+2c=40\) ---(3).

Equation (2) minus Equation (3), \(3b+5c=48\) ---(4)

(a, b, c) = (10, 1, 9), (8, 6, 6), (6, 11, 3)

Among these, the possible maximum value of c is 9.

Answer : E
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Re: Machine A can produce toys at a constant rate of 2 units per hour and  [#permalink]

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New post 05 May 2017, 09:41
a=2
b=5
a+b=7
option checking from higher value
option E
7*9=63
remain=88-63=25
2*10+5*1=25
answer:E
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Re: Machine A can produce toys at a constant rate of 2 units per hour and  [#permalink]

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New post 06 May 2017, 04:04
1
GMATinsight wrote:
AustinKL wrote:
Machine A can produce toys at a constant rate of 2 units per hour and machine B can produce toys at a constant rate of 5 units per hour. If at least one of either machine A or machine B produces toys, what is the greatest possible hours when machine A and machine B work together at their constant rates so that two machines, A and B, can produce 88 units of toys in 20 hours?

A. 5hrs    
B. 6hrs    
C. 7hrs    
D. 8hrs    
E. 9hrs


A Produces @ 2 Units per hour
B Produces @ 5 Units per hour

Greatest Number of Hours of A and B together will be obtained when the remaining job (job done by one machine while working alone) is done by the individual machines (which is A in this case)

A and B together can produce = (2+5) = 7 Units per Hour

Let's start with biggest option
If both A&B work for 9 Hours the production = 7*9 = 63 and the remaining work (88-63=25 units) can be finished in 11 hours (1 hour of B i.e. 5 units and 10 hours of A i.e. 20 units) Hence Correct Option

Answer: Option E


Good question, bad wording. Agree?
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Re: Machine A can produce toys at a constant rate of 2 units per hour and  [#permalink]

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New post 31 May 2017, 10:36
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hazelnut wrote:
Machine A can produce toys at a constant rate of 2 units per hour and machine B can produce toys at a constant rate of 5 units per hour. If at least one of either machine A or machine B produces toys, what is the greatest possible hours when machine A and machine B work together at their constant rates so that two machines, A and B, can produce 88 units of toys in 20 hours?

A. 5hrs    
B. 6hrs    
C. 7hrs    
D. 8hrs    
E. 9hrs


Similar question to practice: https://gmatclub.com/forum/machine-a-pr ... 98123.html
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Re: Machine A can produce toys at a constant rate of 2 units per hour and  [#permalink]

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Re: Machine A can produce toys at a constant rate of 2 units per hour and   [#permalink] 10 Aug 2018, 19:27
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