Lesson: Work Questions

Comment on Work Questions

I solved a slightly different way: B+40/40B=1/24. Then 24(B+40)=40B. And solved for B to get 60 minutes.
gmat-admin's picture

You're referring to the question at 6:20.
Good work!

Machines X and Y produced identical bottles at different constant rates. Machines X. operating alone of 4 hours, filled part of a production lot; then Machine Y, operating alone for 3 hours, filled the rest of this lot. How many hours would it have taken Machine X operating alone to fill the entire production lot?

1. Machine X produced 30 bottles per minute.
2. Machine X produced twice as many bottles in 4 hours as Machine Y produced in 3 hours.

My question concerns statement 2:
Machine “X” produced twice as many bottles in 4 hours as Machine “Y” produced in 3 hours.
4x = 2(3y)
4x = 6y
So, X=3/2y or Y=2/3x.

I understand that x = twice as many bottles as “Y” and that “Y” produces 2/3 as many bottles as “X” in the amount of time give (maybe I’m confused)

Here we go: using X=3/2y
If “Y” produced say 6 bottles then “x” should equal 18 bottles, right? But it equals 9.

9/9 +6 = 9/15 =3/5 not the 2/3

Brent, what is wrong with my thinking? I’m a bit frustrated here. I think I’m missing something somewhere with my reasoning. Please help. Thank you.
gmat-admin's picture

Question link: https://gmatclub.com/forum/machines-x-and-v-produced-identical-bottles-a...

When assigning variables, it's important to make sure you understand what each variable represents.

At the beginning of your solution, you have 4x = 2(3y)

What do x and y represent?

x = the Machine X's RATE (per hour)
y = the Machine Y's RATE (per hour)

So, in 4 hours, Machine X's OUTPUT = 4x
In 3 hours, Machine Y's OUTPUT = 3y

So, 4x + 3y = the OUTPUT for the entire job

In your solution, you noted that 2x=3y
So, let's take the above equation and replace 3y with 2x to get:
4x + 2x = the OUTPUT for the entire job
So, 6x = the OUTPUT for the entire job

In other words, working at a RATE of x "things" per hour, Machine X can complete the entire job in 6 hours.


Thanks Brent

I tend to over complicate and over think "Rate Problems'' more so than any other type of problem. They are definitely my weakest point and greatest frustration.


In 1/B=1/24-1/40, how were you able to quickly recognize the least common denominator was 120? What's a quick way to find a least common multiple or least common denominator?
gmat-admin's picture

Good question!

I started listing multiples of 24 until I found a multiple that's also a multiple of 40.

We get: 24 (no), 48 (no), 72 (no), 96 (no), 120...BINGO!

Alternatively, this video explains another way to find the least common multiple of two values: https://www.gmatprepnow.com/module/gmat-integer-properties/video/835


Awesome, thanks Brent!

Hi Brent, need your help with the below question:
At a certain department store present-wrapping counter, each clerk wraps presents at a minimum rate of 20 per hour and a maximum rate of 30 per hour. If 70 people are standing in line, will all of their presents be wrapped after one hour?

(1) Each person in line has at least one present to be wrapped by one of the six clerks at the counter.

(2) If each person in line had one more present to be wrapped, nine clerks would be required to guarantee that every present would be wrapped in one hour.
gmat-admin's picture


Here's my full solution: https://gmatclub.com/forum/at-a-certain-department-store-present-wrappin...


Hi Brent,

Need your help: https://gmatclub.com/forum/machine-a-operating-alone-at-its-constant-rate-produces-50-feet-of-285704.html
gmat-admin's picture

Dear Brent,

I thought I gave the correct answer to the 4th 650-800 question that you provided below the video. Unfortunately, I did not. Could you help me explain what went wrong? The question is as follows:

"Working alone, Printers X, Y, and Z can do a certain printing job, consisting of a large number of pages, in 12, 15, and 18 hours, respectively. What is the ratio of the time it takes Printer X to do the job, working alone at its rate, to the time it takes Printers Y and Z to do the job, working together at their individual rates?"
(A) 4/11
(B) 1/2
(C) 15/22
(D) 22/15
(E) 11/4

I Did:
X = 1/12 = 15/180
Y = 1/15 = 12/180
Z = 1/18 = 10/180
(Y + Z = 22/180)

Ratio X : Y&Z = 15/22 -> answer C
However, it was: 22/15 -> answer D

Could you explain to me what I did wrong?
Thanks a lot!

Kind regards,

gmat-admin's picture

You're approach is perfect. You just forgot what the numbers mean.

For example, X = 1/12 means that printer X can complete 1/12 of the job in ONE HOUR.

Likewise, Y + Z = 22/180 means that printers Y and Z can complete 22/180 of the job in ONE HOUR.

However, the question asks us for the ratio of the TIMES it takes to complete the ENTIRE JOB

If printer X can complete 1/12 of the job in ONE HOUR, then the time it takes to complete the ENTIRE JOB = 12/1 hours

Likewise, if printers Y and Z can complete 22/180 of the job in ONE HOUR, then the time it takes them to complete the ENTIRE JOB = 180/22 hours

So, the desired ratio = 12/(180/22) = (12)(22/180) = 22/15

By the way, here's my full solution: https://gmatclub.com/forum/working-alone-printers-x-y-and-z-can-do-a-cer...


The use of *ratios* to solve Work Problems seems very limited. In my case, I'd stick to the formulas since I'm not quite sure exactly when to use *ratios*.

gmat-admin's picture

If you're able to rephrase the question in the form, "for every X there are Y," then you can typically use ratios.
Having said that, when it comes to the GMAT, it's always best to work with your strengths.
So, if you find the formulas work best for you, then that's the best approach.

Question link: https://gmatclub.com/forum/machines-x-and-v-produced-identical-bottles-at-different-104208.html

Hi Brent, can you please share your solution for this problem?

Hi Brent,

Could you please provide an example of a question, where are given the rate say for 10 machines, for example. We are also given the output. We are required to find the time it takes for 5 machines to complete the job. In this case, would we take the rate for the 10 machines to complete the job and divide it by 10 to get the rate for 1 machine? After finding the rate for one machine, we would multiply it by 5 and then take the given output and divide it by the rate to find the time it takes for 5 machines to complete the job? I think there was a similar question on GMATCLUB, but I can't seem to find it anymore.

gmat-admin's picture

Here's an example for you to try:
If it takes 5 identical machines 5 days to make 5 widgets, then how many days will it take 7 machines to make 7 widgets?

Is it as follows:
1) 5 days to make 5 widgets--> 5 widgets/5days=1 widget per day--> rate for 5 machines
2) 1/5= rate for 1 machine
3) 1/5 * 7= 7/5 --> rate for 7 machines
4) to find how many days it takes for 7 machines to make 7 widgets: Output/rate= 7/ (7/5)= 5 days?
gmat-admin's picture

Perfectly reasoned!

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