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

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Senior SC Moderator
Joined: 14 Nov 2016
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Machine A can produce toys at a constant rate of 2 units per hour and  [#permalink]

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22 Feb 2017, 00:59
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00:00

Difficulty:

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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22 Feb 2017, 01:35
1
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

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

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

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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

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

Dear GMATinsight, Could you share with me why shall we consider the remaining job?
_________________
"Be challenged at EVERY MOMENT."

“Strength doesn’t come from what you can do. It comes from overcoming the things you once thought you couldn’t.”

"Each stage of the journey is crucial to attaining new heights of knowledge."

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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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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

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

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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Senior SC Moderator
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Location: Malaysia
Machine A can produce toys at a constant rate of 2 units per hour and  [#permalink]

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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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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 $$y = 1$$

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

Thanks.
VP
Joined: 07 Dec 2014
Posts: 1223
Machine A can produce toys at a constant rate of 2 units per hour and  [#permalink]

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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
Senior SC Moderator
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Posts: 1348
Location: Malaysia
Machine A can produce toys at a constant rate of 2 units per hour and  [#permalink]

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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.

_________________
"Be challenged at EVERY MOMENT."

“Strength doesn’t come from what you can do. It comes from overcoming the things you once thought you couldn’t.”

"Each stage of the journey is crucial to attaining new heights of knowledge."

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Joined: 14 May 2015
Posts: 47
Re: Machine A can produce toys at a constant rate of 2 units per hour and  [#permalink]

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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
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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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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

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

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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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31 May 2017, 10:36
1
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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10 Aug 2018, 19:27
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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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