Machine R, working alone at a constant rate

Machine R, working alone at a constant rate, produces x units of a product in 30 minutes, and machine S, working alone at a constant rate, produces x units of the product in 48 minutes, where x is a positive integer. Quantity A : The number of units of the product that machine R, working alone at its constant rate, produces in 3 hours Quantity B : The number of units of the product that machine S, working alone at its constant rate, produces in 4 hours Quantity A is greater., Quantity B is greater., The two quantities are equal., The relationship cannot be determined from the information given.

5 Explanations

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Meera Gandhi

Would it be OK to round 48 to 50 to make it easier? So 240/50 = 4.8 and so Option A is greater?

Feb 21, 2018 • Comment

Sam Kinsman

Hi Meera,

Yes, you could do that, and you'd still get the right answer. But you should be careful about rounding in quantitative comparison problems. If it is clear that the difference between the two quantities is very large, it is OK to round - but otherwise, I'd suggest that you avoid rounding, because if the two quantities are almost the same, rounding could make you get the wrong answer.

Mar 1, 2018 • Reply

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Vivek Venugopal

My method:
Machine R: x/30*(3*60) simplify and you get 6x
Machine S: x/48*(4*60) and we get 5x

therefore answer A.

Jul 5, 2017 • Comment

Sam Kinsman

That's correct, Vivek - good job, and thanks for sharing! :D

Jul 5, 2017 • Reply

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Samy Ishak-Boushaki

I think about it using proportions:

1) Convert x to a tangible number, like 1.
2) If machine R produces 1 unit in 30 minutes, and machine S produces 1 unit in 48 minutes, then notice that machine S needs 48/30 = 8/5 longer to make a unit than machine R.
3) If Quantity A is the amount that machine R can make in 3 hours, and Quantity B is the amount that machine S can make in 4 hours, then notice that machine S has 4/3 = 8/6 longer to make a unit than machine R.
4) Machine S needs 8/5 longer per unit, but only has 8/6 longer to work; 8/5 > 8/6, so machine S's extra time is not enough to counteract it's slower speed. Quantity A is greater.

May 6, 2016 • Comment

Cydney Seigerman, Magoosh Tutor

Thanks for sharing your solution! :D

May 6, 2016 • Reply

Hannah Taylor Brown

Hi Cydney! Why can we assume X is the same in both cases? Machine R could produce 1 in 30 minutes and machine S could produce let's say 20 in 48 minutes.... Making column B bigger. I figured this was a cannot be determined question

Jun 2, 2016 • Reply

Cydney Seigerman, Magoosh Tutor

Hi Hannah :)

Good question! In a given question, a variable is assigned to represent some unknown value. For each unknown value, we need a new variable. So, if the number of units being referred to were different, we would need to make that clear by assigning different variables (e.g. x and y).

Does that clear things up? If not, please let me know :)

Jun 3, 2016 • Reply

ABYN MATHEWS

Samy, How did you get the figure 48/40?

Jan 21, 2017 • Reply

Sam Kinsman

Samy noticed that if we plug in 1 for x, machine R produces 1 unit in 30 minutes, and machine S produces 1 unit in 48 minutes. So now, we can see that machine S takes longer to produce 1 unit than machine S does. More specifically, machine S takes 48 minutes, while machine R just takes 30 minutes. So we can say that machine S takes 48/30 times as long as machine R does.

Here's a simpler example that will help you see how this works. Let's say that it takes John 2 hours to paint a house, and that it takes Jessica just 1 hour to paint a house. So it takes John 2/1 times as long as it takes Jessica to paint 1 house. 2/1= 2, so it takes John 2 times as long as it takes Jessica to paint 1 house.

Jan 23, 2017 • Reply

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SAJA ABDULLAH AL MADINI

I did it differently as follows:

1) We change the Hour into Minutes, so:

3 H = 3 . 60 = 180 Min

4 H = 4 . 60 = 240 Min

180 / 30 = 6

240 / 48 = 5

So the Answer is: A is greater.

Jun 11, 2014 • Comment

That works too! :D Nice!