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

Question

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

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

aeon86 · Answer

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

generis · Answer

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

dave13 · Answer

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

ScottTargetTestPrep · Answer

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

dave13 · Answer

Congrats everyone on an international day of Freedom of speech

though i still dont agree with the inadequate wording of the problem above, here is my solution

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

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

quaes · Answer

300×(3)×(10/60)×(2/5) = 60

Gauriii · Answer

chetan2u  Sir, is it a rule that if time taken is 5/2 then rate will be 2/5? Can you pls tell me on this rule pls. Thanks in advance.

chetan2u · Answer

Yes, it is true. 
The reason is that distance =speed*time
1) If speed is s and time is t, so distance =s*t
2) say speed is 3 times or 3s and time is T, so distance =3s*T.

As distance is same s*t=3s*T.....T=t/3
So speed is thrice, time taken is 1/3

bumpbot · Answer

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

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