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) 100y(x-z)/x+y
D) x+y/100xy-z
E) x+y-z/100xy
OAB
Hi Experts ,
Please explain.
Thanks,
SJ
5-Day Free Trial
5-day free, full-access trial TTP
Available with Beat the GMAT members only code
MORE DETAILS
deck of cards
This topic has expert replies
GMAT/MBA Expert
-
[email protected]
- Elite Legendary Member
- Posts: 10392
- Joined: Sun Jun 23, 2013 6:38 pm
- Location: Palo Alto, CA
- Thanked: 2867 times
- Followed by:511 members
- GMAT Score:800
Hi jain2016,
This question can be solved by TESTing VALUES.
Machine A takes X hours to make a deck of cards.
Machine B takes Y hours to make a deck of cards.
Since the answers are suitably complex-looking, let's choose really small, easy numbers to work with:
X = 1
Y = 2
So...
Machine A takes 1 hour to make a deck of cards
Machine B takes 2 hours to make a deck of cards
When both machines work together for 2 total hours, 3 decks of cards are made.
The question goes on to state that Machine A will work alone for Z hours, then be joined by Machine B until 100 decks are made.
Z = 1
In that first hour, Machine A will produce 1 deck of cards, leaving 99 decks to go. Since the two machines together can produce 3 decks every 2 hours, the remaining 99 decks will take...
2 hours x 33 sets = 66 hours.
We're looking for the answer that equals 66 when we plug in X=1, Y=2 and Z=1 into the answer choices.
While it "looks like" there's a lot of math to be done, most of the answers are way too small to be 66 (and it shouldn't take too long to figure that out). Only one answer equals 66
Final Answer: B
GMAT assassins aren't born, they're made,
Rich
This question can be solved by TESTing VALUES.
Machine A takes X hours to make a deck of cards.
Machine B takes Y hours to make a deck of cards.
Since the answers are suitably complex-looking, let's choose really small, easy numbers to work with:
X = 1
Y = 2
So...
Machine A takes 1 hour to make a deck of cards
Machine B takes 2 hours to make a deck of cards
When both machines work together for 2 total hours, 3 decks of cards are made.
The question goes on to state that Machine A will work alone for Z hours, then be joined by Machine B until 100 decks are made.
Z = 1
In that first hour, Machine A will produce 1 deck of cards, leaving 99 decks to go. Since the two machines together can produce 3 decks every 2 hours, the remaining 99 decks will take...
2 hours x 33 sets = 66 hours.
We're looking for the answer that equals 66 when we plug in X=1, Y=2 and Z=1 into the answer choices.
While it "looks like" there's a lot of math to be done, most of the answers are way too small to be 66 (and it shouldn't take too long to figure that out). Only one answer equals 66
Final Answer: B
GMAT assassins aren't born, they're made,
Rich
-
GMATGuruNY
- GMAT Instructor
- Posts: 15539
- Joined: Tue May 25, 2010 12:04 pm
- Location: New York, NY
- Thanked: 13060 times
- Followed by:1906 members
- GMAT Score:790
Let x = 1 hour.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)
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
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
-
Matt@VeritasPrep
- GMAT Instructor
- Posts: 2630
- Joined: Wed Sep 12, 2012 3:32 pm
- Location: East Bay all the way
- Thanked: 625 times
- Followed by:119 members
- GMAT Score:780
We could also just use a rate-time equation here: Work = R * T.
Since we're making one deck of cards, Work = 1. That means that our equations are:
Machine A:
1 = R * x
1/x = R
Machine B:
1 = R * y
1/y = R
So the machines' rates are 1/x and 1/y of the job per hour, respectively.
In z hours, Machine A will do
z * (1/x) of the job, or (z/x) of the job. That means we have (100 - z/x) left to do. One more work equation gives
Work = R * T
(100 - z/x) = (1/x + 1/y) * T
We want to solve for T, so we just divide both sides by (1/x + 1/y), and we're done!
(100 - z/x) / (1/x + 1/y) = T
(100 - z/x) / (x + y)/xy = T
xy * (100 - z/x) / (x + y) = T
(100xy - zy) / (x + y) = T
Since we're making one deck of cards, Work = 1. That means that our equations are:
Machine A:
1 = R * x
1/x = R
Machine B:
1 = R * y
1/y = R
So the machines' rates are 1/x and 1/y of the job per hour, respectively.
In z hours, Machine A will do
z * (1/x) of the job, or (z/x) of the job. That means we have (100 - z/x) left to do. One more work equation gives
Work = R * T
(100 - z/x) = (1/x + 1/y) * T
We want to solve for T, so we just divide both sides by (1/x + 1/y), and we're done!
(100 - z/x) / (1/x + 1/y) = T
(100 - z/x) / (x + y)/xy = T
xy * (100 - z/x) / (x + y) = T
(100xy - zy) / (x + y) = T
Hi GMATGuruNY ,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.
Thanks for your reply.
Just a quick question if x=1 hour and y=2 hours , then A and B work together will be 3. So why A and B work together =0 ?
Please explain.
Many thanks in advance.
SJ
Hi Rich ,In that first hour, Machine A will produce 1 deck of cards, leaving 99 decks to go. Since the two machines together can produce 3 decks every 2 hours, the remaining 99 decks will take...
2 hours x 33 sets = 66 hours.
Can you please explain the above part? How come 66 hours?
Many thanks in advance.
SJ
GMAT/MBA Expert
-
[email protected]
- Elite Legendary Member
- Posts: 10392
- Joined: Sun Jun 23, 2013 6:38 pm
- Location: Palo Alto, CA
- Thanked: 2867 times
- Followed by:511 members
- GMAT Score:800
Hi jain2016,
Using the VALUES I chose...
Machine A takes 1 hour to make a deck of cards
Machine B takes 2 hours to make a deck of cards
When both machines work together for 2 total hours, Machine A makes 2 decks and Machine B makes 1 deck... for a total of 3 decks every 2 hours.
Since we get 3 decks every 2 hours
(3 decks)(33) = 99 decks
(2 hours)(33) = 66 hours
GMAT assassins aren't born, they're made,
Rich
Using the VALUES I chose...
Machine A takes 1 hour to make a deck of cards
Machine B takes 2 hours to make a deck of cards
When both machines work together for 2 total hours, Machine A makes 2 decks and Machine B makes 1 deck... for a total of 3 decks every 2 hours.
Since we get 3 decks every 2 hours
(3 decks)(33) = 99 decks
(2 hours)(33) = 66 hours
GMAT assassins aren't born, they're made,
Rich
-
Matt@VeritasPrep
- GMAT Instructor
- Posts: 2630
- Joined: Wed Sep 12, 2012 3:32 pm
- Location: East Bay all the way
- Thanked: 625 times
- Followed by:119 members
- GMAT Score:780
These are just hypothetical numbers that seem to have been chosen to lead to a convenient answer. y = 2 is the time it WOULD take B on its own if B were forced to work alone, but since A's rate was fast enough to complete the job solo, B didn't have to work at all.jain2016 wrote:Hi GMATGuruNY ,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.
Thanks for your reply.
Just a quick question if x=1 hour and y=2 hours , then A and B work together will be 3. So why A and B work together =0 ?
Please explain.
Many thanks in advance.
SJ
