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Machine P produces parts thrice as fast as machine Q does. Machine Q p

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Machine P produces parts thrice as fast as machine Q does. Machine Q p  [#permalink]

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New post 26 Sep 2018, 05:15
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Machine P produces parts thrice as fast as machine Q does. Machine Q produces 300 parts of product R in 60 minutes. If each machine produces parts at a constant rate, how many parts of product S does machine P produce in 10 minutes, if each part of product S takes 5/2 times of the time taken to produce each part of product R?

(A) 30
(B) 40
(C) 50
(D) 60
(E) 75

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Re: Machine P produces parts thrice as fast as machine Q does. Machine Q p  [#permalink]

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New post 28 Sep 2018, 06:21
if machine P is 3x as fast as machine Q it would be capable of producing 900 parts of product R in 60 minutes

however every part of product S takes 5/2 the time to produce of a part of product R as such we have to divide 900 by 5/2

900/(5/2) = 900 x 2/5 = 180 x 2 = 360

so machine P is capable of making 360 parts of product S in 60 minutes

the question asks for number of parts in 10 minutes so
360/6 = 60 ==> D
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Machine P produces parts thrice as fast as machine Q does. Machine Q p  [#permalink]

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New post 28 Sep 2018, 18:06
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Bunuel wrote:
Machine P produces parts thrice as fast as machine Q does. Machine Q produces 300 parts of product R in 60 minutes. If each machine produces parts at a constant rate, how many parts of product S does machine P produce in 10 minutes, if each part of product S takes 5/2 times of the time taken to produce each part of product R?

(A) 30
(B) 40
(C) 50
(D) 60
(E) 75

Machine Q's rate for R: \(\frac{300R}{60min}=\frac{5R}{1min}\)

Machine P's rate for R is 3 times that of Q, so \((3*\frac{5R}{1min})=\frac{15R}{1min}\)

Machine P's rate for S?
Producing S takes \(\frac{5}{2}\) times of the time needed to produce R.

We have P's rate for R for 1 minute.
Multiply 1 minute by \(\frac{5}{2}\)

P's rate for S: \(\frac{15}{(\frac{5}{2}*1min)}=\frac{15}{(\frac{5}{2}min)}=(15*\frac{2}{5}min)=\frac{6S}{1 min}\)

In 10 minutes P will make how many parts of product S? RT = W: \(\frac{6S}{1min}*10min=60S\)

Answer D
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Machine P produces parts thrice as fast as machine Q does. Machine Q p  [#permalink]

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New post 29 Sep 2018, 03:23
Bunuel wrote:
Machine P produces parts thrice as fast as machine Q does. Machine Q produces 300 parts of product R in 60 minutes. If each machine produces parts at a constant rate, how many parts of product S does machine P produce in 10 minutes, if each part of product S takes 5/2 times of the time taken to produce each part of product R?

(A) 30
(B) 40
(C) 50
(D) 60
(E) 75



Hello Bunuel - GMAT club Quant Infinity - i couldnt understad what infinity is until i started following your posts :)

i have a frank question to you :) just keep it secret please only between you and me :) what is your opinon about the wording of this word problem ? :)


the wording is quite VAGUE because the question is :

If each machine produces parts at a constant rate, how many parts of product S does machine P produce in 10 minutes, if each part of product S takes 5/2 times of the time taken to produce each part of product R?

it says to produce EACH PART.

so based on the above question if Q produces 300/60 = 5 parts a minutes and P`s rate 900/60= 15 parts a minute , THEN HOW SHOULD I FIND, HOW MANY MINUTES/ SECONDS DOES IT TAKE TO PRODUCE EACH PART , because the question mentiones "5/2 times of the time taken to produce each part of product R?" it mentiones the word EACH PART.

so following such logic to find the time of P to produce EACH part i divided 15 parts by 60 SECONDS , because it takes 1 minute to produce 15 parts. Am i not correct ? if not, pls explain :)



p.s.
gmat quant preparation and division by zero have something in common i think …. that moment when i am infinite...indeed :lol:
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Re: Machine P produces parts thrice as fast as machine Q does. Machine Q p  [#permalink]

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New post 29 Sep 2018, 18:04
Bunuel wrote:
Machine P produces parts thrice as fast as machine Q does. Machine Q produces 300 parts of product R in 60 minutes. If each machine produces parts at a constant rate, how many parts of product S does machine P produce in 10 minutes, if each part of product S takes 5/2 times of the time taken to produce each part of product R?

(A) 30
(B) 40
(C) 50
(D) 60
(E) 75


Since machine Q produces 300 parts of product R in 60 minutes, it can produce 300/60 = 5 parts of product R per minute. Since machine P is thrice as fast as machine Q, machine P can produce 15 parts of product R per minute.

Since each part of product S takes 5/2 times of the time taken to produce each part of product R, machine P can produce 15/(5/2) = 15 x 2/5 = 6 parts of product S per minute. So in 10 minutes, machine P can produce 10 x 6 = 60 parts of product S.

Answer: D
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Machine P produces parts thrice as fast as machine Q does. Machine Q p  [#permalink]

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New post 30 Sep 2018, 03:44
Bunuel wrote:
Machine P produces parts thrice as fast as machine Q does. Machine Q produces 300 parts of product R in 60 minutes. If each machine produces parts at a constant rate, how many parts of product S does machine P produce in 10 minutes, if each part of product S takes 5/2 times of the time taken to produce each part of product R?

(A) 30
(B) 40
(C) 50
(D) 60
(E) 75



Congrats everyone on an international day of Freedom of speech :lol: though i still dont agree with the inadequate wording of the problem above, here is my solution :)

:cool:
Machine Q rate X
Machine P rate 3x

If Q`s rate \(\frac{300}{60}\) \(= 5\) parts produced a minute, then P`s rate is \(3x\) i.e \(15\)parts a minute


here comes the Question, vague and ambiguous, like political world :lol:

P Machine ---> # of parts S in 10 min, if S takes \(\frac{5}{2}\) of the time taken to produce part R


\(\frac{900}{(\frac{60}{1} *\frac{5}{2})}= \frac{900}{150}= 6\) --> it takes machine P to produce 6 parts of S in a minute


Hence in 10 minutes: 6*10 = 60
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Machine P produces parts thrice as fast as machine Q does. Machine Q p   [#permalink] 30 Sep 2018, 03:44
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