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Machine A produces parts twice as fast as machine B does. Machine B pr

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Machine A produces parts twice as fast as machine B does. Machine B pr  [#permalink]

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New post 01 Jul 2017, 02:38
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Machine A produces parts twice as fast as machine B does. Machine B produces 100 parts of product X in 40 minutes. If each machine produces parts at a constant rate, how many parts of product Y does machine A produce in 6 minutes, if each part of product Y takes 3/2 times of the time taken to produce each part of product X?

(A) 45
(B) 30
(C) 25
(D) 20
(E) 15

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Re: Machine A produces parts twice as fast as machine B does. Machine B pr  [#permalink]

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New post 01 Jul 2017, 02:39
Bunuel wrote:
Machine A produces parts twice as fast as machine B does. Machine B produces 100 parts of product X in 40 minutes. If each machine produces parts at a constant rate, how many parts of product Y does machine A produce in 6 minutes, if each part of product Y takes 3/2 times of the time taken to produce each part of product X?

(A) 45
(B) 30
(C) 25
(D) 20
(E) 15


This is a modified question of the the following OG question: https://gmatclub.com/forum/machine-a-pr ... 67872.html
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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Machine A produces parts twice as fast as machine B does. Machine B pr  [#permalink]

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New post 01 Jul 2017, 02:50
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Given data:
Machine B produces 100 parts in 40 minutes(1 part in 24 seconds) Machine A produces twice as fast
as machine B. So in essence, machine A produces 100 parts in 20 minutes(1 part in 12 seconds)

Now we need to produce another product using the same machines(at constant rates). However, each
product(takes 1.5 times the time, meaning it will need machine A 18 seconds to produce 1 product)

Since we have 6 minutes or 360 seconds, machine A makes 20 products(\(\frac{360s}{18s}\)) (Option D)
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Machine A produces parts twice as fast as machine B does. Machine B pr  [#permalink]

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New post 01 Jul 2017, 06:35
Bunuel wrote:
Machine A produces parts twice as fast as machine B does. Machine B produces 100 parts of product X in 40 minutes. If each machine produces parts at a constant rate, how many parts of product Y does machine A produce in 6 minutes, if each part of product Y takes 3/2 times of the time taken to produce each part of product X?

(A) 45
(B) 30
(C) 25
(D) 20
(E) 15

1. Find rates of Machines B and A in hours.

Machine B rate: B makes 100 parts in 40 minutes. 40 minutes is \(\frac{2}{3}\) of one hour.

B's rate = \(\frac{100}{(\frac{2}{3})}\) =

\(\frac{100}{1} * \frac{3}{2}\) =

\(\frac{300}{2}\) or 150 parts in 1 hour. B = \(\frac{150}{1}\)

A's rate for product X: A produces parts twice as fast as B does.

In one hour Machine A will produce \(\frac{150}{1}\) * 2 = 300 parts of product X in 1 hour --> \(\frac{300}{1}\)

2. Find rate of Machine A for product Y.

To produce each part of Y takes \(\frac{3}{2}\) times as long as it does to produce each part of product X.

Machine A produces 300 parts in one hour for product X. \(\frac{3}{2}\) times as long means 1.5 hours for the same amount of parts.

A's rate for product Y is \(\frac{300}{1.5} = \frac{3000}{15}\) = 200 Y parts in one hour =\(\frac{200}{1}\)

3. Find how many parts of Product Y that Machine A can make in 6 minutes.

Time in hours: \(\frac{6 min}{60 min}\) = \(\frac{1}{10}\) hour

A's rate for producing Y is \(\frac{200}{1}\) parts per hour

R*T = W --- >\(\frac{200}{1}\) * \(\frac{1}{10}\) = 20 parts

Answer D
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Re: Machine A produces parts twice as fast as machine B does. Machine B pr  [#permalink]

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New post 01 Jul 2017, 07:16
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1
Bunuel wrote:
Machine A produces parts twice as fast as machine B does. Machine B produces 100 parts of product X in 40 minutes. If each machine produces parts at a constant rate, how many parts of product Y does machine A produce in 6 minutes, if each part of product Y takes 3/2 times of the time taken to produce each part of product X?

(A) 45
(B) 30
(C) 25
(D) 20
(E) 15



B's rate = 100 of X parts / 40 mints =100/40

thus A's rate = 2*100/40= 200/40 = 1/5
i.e A can produce 1 of x product in 5 minutes..

now we have product Y which takes 3/2 of time it takes to produce product X

so now A will take 1/5 *3/2 = 3/10 minutes to produce 1 of Y product
A's rate = 10/3
with similar rate if A works for 6 minutes , A produces = 10*6/3 = 20 products of Y

Ans D
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Re: Machine A produces parts twice as fast as machine B does. Machine B pr  [#permalink]

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New post 01 Jul 2017, 07:45
100 products of X in 40 min for Machine B
200 Products of X in 40 min for Machine A (because machine A has double the speed of B)
200/40 = 5 products of X a min for Machine A
In 6 min - 30 products of X
For Y - It takes 50% extra time (3/2 in percentage terms is 50% extra), which means productivity will reduce by 33.33% (which is 1/3 in fractional form)
So, Machine A, which could make 30 products of X and now make only 20 products of Y (1/3rd reduction in productivity)
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Re: Machine A produces parts twice as fast as machine B does. Machine B pr  [#permalink]

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New post 01 Jul 2017, 07:47
Given in the question
Machine A produces parts twice as fast as machine B does
AND
Machine B produces 100 parts of product X in 40 minutes
so according to the question
Machine A produces 100 parts of product X in 20 minutes

Also given in the question..
each part of product Y takes 3/2 times of the time taken to produce each part of product X

so
Machine A produces 100 parts of product Y in 20x3/2 minutes i.e 30minutes
so. if in 30 mins Machine A produces 100 parts of product Y
then in 6 minutes Machine A will produce 100x6/30 parts of product Y i.e 20 parts of product Y D
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Re: Machine A produces parts twice as fast as machine B does. Machine B pr  [#permalink]

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New post 06 Jul 2018, 11:56
1
Bunuel wrote:
Machine A produces parts twice as fast as machine B does. Machine B produces 100 parts of product X in 40 minutes. If each machine produces parts at a constant rate, how many parts of product Y does machine A produce in 6 minutes, if each part of product Y takes 3/2 times of the time taken to produce each part of product X?

(A) 45
(B) 30
(C) 25
(D) 20
(E) 15


Since each part of Y takes 3/2 as long as each part of X -- and B takes 40 minutes to produce 100 parts of X -- the time for B to produce 100 parts of Y = \(\frac{3}{2} * 40 = 60\) minutes.
Since A is twice as fast as B -- and B produces 100 parts of Y in 60 minutes -- A produces 200 parts of Y in 60 minutes.
Since in 60 minutes A produces 200 parts of Y, in 6 minutes A produces 20 parts of Y.


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