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GMAT Official Guide 2019 Machine R and machine S work

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by BTGmoderatorDC » Wed Jul 04, 2018 3:31 pm

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Answers

A

B

C

D

E

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Difficulty—

Machine R and machine S work at their respective constant rates. How much time does it take machine R, working alone, to complete a certain job?

(1) The amount of time that it takes machine S, working alone, to complete the job is 3/4 the amount of time that it takes machine R, working alone, to complete the job.
(2) Machine R and machine S, working together, take 12 minutes to complete the job.
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by Jay@ManhattanReview » Fri Jul 06, 2018 11:31 pm
BTGmoderatorDC wrote:Machine R and machine S work at their respective constant rates. How much time does it take machine R, working alone, to complete a certain job?

(1) The amount of time that it takes machine S, working alone, to complete the job is 3/4 the amount of time that it takes machine R, working alone, to complete the job.
(2) Machine R and machine S, working together, take 12 minutes to complete the job.
Given: Machine R and machine S work at their respective constant rates

To find: Time taken by machine R, working alone, to complete a certain job

Let's take each statement one by one.

(1) The amount of time that it takes machine S, working alone, to complete the job is 3/4 the amount of time that it takes machine R, working alone, to complete the job.

=> Time taken by Machine S : Time taken by Machine R : : 3 : 4

This is a ratio, we can't get the unique value. Insufficient.

(2) Machine R and machine S, working together, take 12 minutes to complete the job.

Can't get the value of the amount of time taken by machine R. Insufficient.

(1) and (2) together

With the help of the ratio value and the total combined time taken by Machine R and machine S, we can get the unique value of the amount of time taken by machine R. Sufficient.

The correct answer: C

Hope this helps!

-Jay
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Re: GMAT Official Guide 2019 Machine R and machine S work

by Scott@TargetTestPrep » Sat May 08, 2021 9:48 am
BTGmoderatorDC wrote: ↑
Wed Jul 04, 2018 3:31 pm
 Machine R and machine S work at their respective constant rates. How much time does it take machine R, working alone, to complete a certain job?

(1) The amount of time that it takes machine S, working alone, to complete the job is 3/4 the amount of time that it takes machine R, working alone, to complete the job.
(2) Machine R and machine S, working together, take 12 minutes to complete the job.
Solution:

Question Stem Analysis:

We need to determine the amount of time it takes machine R to complete a certain job alone.

Statement One Alone:

From statement one, we see that machine R takes 4/3 the amount of time of machine S to complete the job alone. However, without knowing the amount of time it takes machine S to complete the job alone, we can’t determine the amount of time it takes marchine R to complete the job alone. Statement one alone is not sufficient.

Statement Two Alone:

Knowing that it takes 12 minutes for machine R and machine S, combined, to complete the job is not sufficient to ascertain the amount of time it takes for machine R to complete the job alone. Statement two alone is not sufficient.

Statements One and Two Together:

If we let x be the amount of time (in minutes) it takes machine R to complete the job alone, then its rate is 1/x. We know it takes machine S4/3 the time it takes machine R, so its time is 4x/3 minutes, and its rate is 1/(4x/3). Since it takes them 12 minutes to complete the job when working together, we can create the rate equation:

1/x + 1/(4x/3) = 1/12

Without actually solving the equation, we see that we can determine a value for x. The two statements together are sufficient.

Answer: C

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Re: GMAT Official Guide 2019 Machine R and machine S work

by Scott@TargetTestPrep » Sat May 08, 2021 9:49 am
BTGmoderatorDC wrote: ↑
Wed Jul 04, 2018 3:31 pm
 Machine R and machine S work at their respective constant rates. How much time does it take machine R, working alone, to complete a certain job?

(1) The amount of time that it takes machine S, working alone, to complete the job is 3/4 the amount of time that it takes machine R, working alone, to complete the job.
(2) Machine R and machine S, working together, take 12 minutes to complete the job.
Solution:

Question Stem Analysis:

We need to determine the amount of time it takes machine R to complete a certain job alone.

Statement One Alone:

From statement one, we see that machine R takes 4/3 the amount of time of machine S to complete the job alone. However, without knowing the amount of time it takes machine S to complete the job alone, we can’t determine the amount of time it takes marchine R to complete the job alone. Statement one alone is not sufficient.

Statement Two Alone:

Knowing that it takes 12 minutes for machine R and machine S, combined, to complete the job is not sufficient to ascertain the amount of time it takes for machine R to complete the job alone. Statement two alone is not sufficient.

Statements One and Two Together:

If we let x be the amount of time (in minutes) it takes machine R to complete the job alone, then its rate is 1/x. We know it takes machine S4/3 the time it takes machine R, so its time is 4x/3 minutes, and its rate is 1/(4x/3). Since it takes them 12 minutes to complete the job when working together, we can create the rate equation:

1/x + 1/(4x/3) = 1/12

Without actually solving the equation, we see that we can determine a value for x. The two statements together are sufficient.

Answer: C

Scott Woodbury-Stewart
Founder and CEO
[email protected]

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