Source: Official Guide Revised GRE 1st Ed. Part 6; Set 2; #1

14

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.

4 Explanations

1

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, Magoosh Tutor

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

Jul 5, 2017 • Reply

1

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, Magoosh Tutor

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

4

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

2)

180 / 30 = 6

240 / 48 = 5

So the Answer is: A is greater.

Jun 11, 2014 • Comment

Kevin Rocci, Magoosh Tutor

That works too! :D Nice!

Jun 17, 2014 • Reply

5

Gravatar Chris Lele, Magoosh Tutor

Oct 7, 2012 • Comment

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