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

Question

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

ganand · Accepted Answer

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.

GMATinsight · Answer

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

BillyZ · Answer

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

GMATinsight · Answer

Because we need to ensure that work is done in 20 Hours  which is a mentioned fact  which needs to be abide by

BillyZ · Answer

Dear  GMATinsight , However, the question is asking about greatest possible hours so that machine A & B can produce 88 units and not the remaining.

gracie · Answer

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

BillyZ · Answer

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

ishaan.wares · Answer

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

ShashankDave · Answer

Good question, bad wording. Agree?

Bunuel · Answer

Similar question to practice: https://gmatclub.com/forum/machine-a-pr ... 98123.html

premsmit · Answer

Should not the question be like--

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

Sejal16 · Answer

I am unsure of all the above solutions - question wants to maximize total hours of A&B such that they produce 88 units. Why not 88/7 = ~12 ? Why do we need to utilize all 20 hours ?

I initially interpreted the question in another manner - total machine hours should not exceed 20.

Please explain. This question appears super wierd

Kinshook · Answer

Given: 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.

Asked: 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?

Let us assume that machine A and machine B work together at their constant rates for 9 hours

Toys produced in 9 hours = 7*9 = 63 toys

Remaining toys = 88 - 63 = 25 toys

If Machine A is used for 10 hours and Machine B for 1 hours, toys produced in 11 hours = 5 + 20 = 25 toys

IMO E

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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

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