It takes machine A x hours to manufacture a deck of cards that machine B can manufacture in y hours. If machine A operates alone for z hours and is then joined by machine B until 100 decks are finished, for how long will the two machines operate simultaneously?
a) (100xy – z)/(x+y)
b) y(100x – z)/(x+y)
c) (x+y)/(100xy – z)
d) xz(100y – z)/(x+y+z)
e) (x+y–z)/(100xy)
Let x = 1 hour.
Since A takes 1 hour to produce a deck, A's rate = 1 deck per hour.
Let y = 2 hours.
Let A complete the ENTIRE JOB.
Since A produces 1 deck per hour, the time for A to produce all 100 decks = 100 hours.
Thus, z=100.
The question stem asks for the time that A and B work together.
Since A completes the entire job, the number of hours that A and B work together = 0. This is our target.
Now plug x=1, y=2 and z=100 into the answers to see which yields our target of 0.
A quick scan reveals that only
B works:
y(100x – z)/(x+y) = 2(100*1 - 100)/(1+2) = 0.
The correct answer is
B.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at
[email protected].
Student Review #1
Student Review #2
Student Review #3
