GMAT Official Guide 2019 Machine R and machine S work

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

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