Working simultaneously and independently at an identical con

Hi All,

We're told that working simultaneously and independently at an identical constant rate, 4 machines of a certain type can produce a total of X units of product P in 6 days. We're asked for the number of machines that would be needed, working simultaneously and independently at this constant rate, to produce a total of 3X units of product P in 4 days?

When dealing with these types of 'work' questions, it's usually easiest to think in terms of the TOTAL amount of work needed to complete a job. If it takes 4 machines 6 days EACH to produce X units, then it takes...
(4 machines)(6 days each) = 24 machine-days of work to produce X units

Thus, 1 machine would need 24 days to produce X units
2 machines would need 12 days each to produce X units
3 machines would need 8 days each to produce X unites
Etc.

Now that we know how much work it takes to create X units, we know it takes 3(24) = 72 machine-days of work to produce 3X units. With a limit of just 4 days....
(Z machines)(4 days each) = 72 machine-days of work
Z = 72/4 = 18 machines needed to complete the job.

Final Answer: B

GMAT assassins aren't born, they're made,
Rich

mitzwillrockgmat wrote:Working simultaneously and independently at an identical constant rate, 4 machines of a
certain type can produce a total of x units of product P in 6 days. How many of these
machines, working simultaneously and independently at this constant rate, can produce a
total of 3x units of product P in 4 days?

A. 24
B. 18
C. 16
D. 12
E. 8

We are given that 4 machines can complete x units in 6 days. Thus, the rate of the 4 machines is x/6.

Now, we need to determine the number of machines needed to produce a rate of 3x/4. To calculate that number of machines, we can use the following proportion in which the value in each numerator is the number of machines and the value in each denominator is the corresponding rate of those machines. We can let n = the number of machines needed:

4/(x/6) = n/(3x/4)

24/x = 4n/3x

72x = 4nx

18 = n

Answer: B

mitzwillrockgmat wrote:Working simultaneously and independently at an identical constant rate, 4 machines of a
certain type can produce a total of x units of product P in 6 days. How many of these
machines, working simultaneously and independently at this constant rate, can produce a
total of 3x units of product P in 4 days?

A. 24
B. 18
C. 16
D. 12
E. 8

Can someone break this down for me logically, in words. thanks

Let's assign a nice value to x (a value that will work well with all of the numbers 3, 4 and 6.

Let's say x = 24

GIVEN: 4 machines make x units in 6 days
This means 4 machines make 24 units in 6 days
So, 4 machines make 4 units in 1 day [if you divide the work time by 6, the output is also divided by 6]
So, 1 machine makes 1 unit in 1 day [if you divide the number of machines by 4, the output is also divided by 4]

From here, we can answer the question How many of these machines, working simultaneously and independently at this constant rate, can produce a total of 3x units of product P in 4 days?
If x = 24, 3x = 72
Our goal is to make 72 units in 4 days.

So, 1 machine makes 4 units in 4 days [if you multiply the work time by 4, the output is also multiplied by 4]
So, 18 machines make 72 units in 4 days [if you multiply the number of machines by 18, the output is also multiplied by 18]

Answer: B

Cheers,
Brent