x identical machines can make x widgets in x minutes. If each machine

Question

x identical machines can make x widgets in x minutes. If each machine works at the same constant rate, how many widgets can y identical machines make in y minutes, in terms of x and y?

A. x
B. y
C. y^2
D. x/y
E. y^2/x

rohit8865 · Accepted Answer

x machine-------x minutes---------x widgets

x machine-------1 minutes---------x /x widgets(=1 widget)

1 machine-------1 minutes---------1/x widgets (rate of x machine)

similarly 
let Y machine in y minutes make A widget. then

y machine-------y minutes---------A widgets

y machine-------1 minutes---------A/y widgets

1 machine-------1 minutes---------A/y^2 widgets (rate of y machine)

As rates are equal

A/y^2 = 1/x
A =y^2/x

Ans E

maheshaero20 · Answer

Number of Widgets is directly proportional to Number of machines and Time taken.

So we can write it as  W ∝T*N  ==>  W=K*T*N

Where
W= Number of Widgets
T= Time Taken
N= Number of Machine
K= Equation constant (Don't Worry about this :wink:)

From the given Problem

x=K*x*x

On Solving above equation  K=\frac{1}{x}

Wy= K*y*y

on substituting  K=\frac{1}{x}  ==>  Wy=\frac{y^2}{x}

Kudos +1

JeffTargetTestPrep · Answer

We are given that x identical machines can make x widgets in x minutes. Thus, the rate for the x machines is x/x or 1 widget per minute. Next we can determine the rate of y machines using the following proportion in which n is the rate for y machines:

x/1 = y/n

n = y/x

Since the rate for y machines is y/x and work = rate x time, y machines can produce (y/x)(y) = y^2/x widgets in y minutes.

Answer: E

ishaan.wares · Answer

x identical machines.......working x minutes......can make= x widgets
 
1 identical machines.......working 1 minutes......can make  = x/(x+x) widgets

y identical machines.......working y minutes......can make  = (x/(x+x))*(y*y) widgets
 = y^2 /x widgets

Answer: E

devlin · Answer

Lets say that R is the rate and W the number of widgets

X * R = \frac{X}{X}  
 R = \frac{1}{X}

(Replacing R)
 Y * R = \frac{W}{Y} 
 Y * \frac{1}{X} = \frac{W}{Y} 
 \frac{Y}{X} = \frac{W}{Y} 
 W = \frac{Y²}{X}

Option E

generis · Answer

Find the individual machine rate from scenario #1 (defined by  x ), then use that rate to find the number of widgets in scenario #2.

Scenario 1: x identical machines make x widgets in x minutes
  (# of workers) * R * T = W  
Plug in variables*
 x*R*x=x 
 Rate=\frac{x}{x^2}

At that rate . . .
Scenario 2: y identical machines in y minutes can make how many widgets? (= Work) 
  (# of workers) * R * T = W  
 y*\frac{x}{x^2}*y=W 
 W=\frac{y*x*y}{x2} 
 W=\frac{y^2}{x}

Answer E

*In other words, manipulate the equation exactly as RT=W is manipulated with one more variable (# of machines) on LHS. Scenario #1:
 R=\frac{W}{(No.Of.Machines*T)} 
Scenario #2:
 Work=(No.Of.Machines*R*T)

mdanieletto · Answer

NR.MACHINES-----------RATE-----------TIME-------------WORK
x-------------------------x/x=1----------x mins----------x widgets

Thus one single machine has rate equal to x/x=1 divided by x machines ------------> 1/x

Therefore,
NR.MACHINES-----------RATE-----------TIME-------------WORK
y-----------------------y*(1/x)=y/x-----y mins----------> rate*time=(y/x)*y=  (y^2)/x

asmba · Answer

Assume x = 10 then:
10 machines in 10 minutes can make 10 widgets i.e. 1 machine makes 1 widget in 10 mins
Assume y = 20 then:
20 machines in 20 minutes can make 40 widgets since machines and time both have doubled (and all machines are identical) 
If we check options, only (E) gives us 40 as an answer 
We can even assume y = 5 (lower value than x), only (E) will give us the correct answer

KarishmaB · Answer

x identical machines can make x widgets in x minutes. So 1 machine can make 1 widget in x mins. (and they are all working simultaneously)

Assume we still have 1 machine. In y minutes, how many widgets will it make?  \frac{y}{x}

Now if we have y machines, we will get  \frac{y}{x} * y = y^2/x  widgets

Answer (E)

Or as  asmba  has mentioned above - assume values
Say x = 10 and y = 20. The only thing is that we should refrain from calculating the actual value and then checking options.

10 machines............... 10 widgets............. 10 minutes
20 machines................ ?? ...........................20  minutes

Number of widgets =  10 * \frac{20}{10} * \frac{20}{10} = 20* \frac{20}{10} = \frac{y^2}{x}

HarshavardhanR · Answer

https://gmatclub.com/forum/download/file.php?id=85470 If x machines can make x widgets in x min, then 1 machine can make 1 widget in x min. Then, 1 machine can make 1/x widgets in 1 min. Then, 1 machine can make y/x widgets in y min. Then, y machines can make y^{2}/x widgets in y min. --- Harsha GMAT-Club-Forum-q1untf8s.png

PSKhore · Answer

Each machine makes 1/x widgets in 1 min.

In y minutes, it will make y/x widgets.

y machines will make  y^2/x  widgets in y min

x identical machines can make x widgets in x minutes. If each machine

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