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

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Math Expert
Joined: 02 Sep 2009
Posts: 46267
x identical machines can make x widgets in x minutes. If each machine [#permalink]

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24 Apr 2017, 04:25
1
5
00:00

Difficulty:

25% (medium)

Question Stats:

67% (00:57) correct 33% (01:42) wrong based on 90 sessions

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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

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Director
Joined: 05 Mar 2015
Posts: 971
x identical machines can make x widgets in x minutes. If each machine [#permalink]

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24 Apr 2017, 11:31
1
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
Intern
Joined: 28 Oct 2014
Posts: 35
Location: India
GMAT 1: 640 Q50 V27
GMAT 2: 680 Q50 V30
GPA: 3.89
WE: Engineering (Aerospace and Defense)
x identical machines can make x widgets in x minutes. If each machine [#permalink]

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24 Apr 2017, 11:57
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

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
Target Test Prep Representative
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2570
Re: x identical machines can make x widgets in x minutes. If each machine [#permalink]

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27 Apr 2017, 17:11
1
1
Bunuel wrote:
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

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.

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Jeffery Miller

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Joined: 14 May 2015
Posts: 52
Re: x identical machines can make x widgets in x minutes. If each machine [#permalink]

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02 May 2017, 15:29
1
x identical machines.......working x minutes......can make= x widgets

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

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

Re: x identical machines can make x widgets in x minutes. If each machine   [#permalink] 02 May 2017, 15:29
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