• NEW! FREE Beat The GMAT Quizzes
Hundreds of Questions Highly Detailed Reporting Expert Explanations
• 7 CATs FREE!
If you earn 100 Forum Points

Engage in the Beat The GMAT forums to earn
100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## Work/Rate tagged by: BTGmoderatorRO ##### This topic has 3 expert replies and 0 member replies ## Work/Rate It takes printer A 4 more minutes more than printer B to print 40 pages. Working together, the two printers can print 50 pages in 6 minutes. How long will it take Printer A to print 80 pages? A. 12 B. 18 C. 20 D. 24 E. 30 OA is D This question is confusing me.C an expert explain why D is the answer? ### GMAT/MBA Expert Legendary Member Joined 14 Jan 2015 Posted: 2667 messages Followed by: 122 members Upvotes: 1153 GMAT Score: 770 Roland2rule wrote: It takes printer A 4 more minutes more than printer B to print 40 pages. Working together, the two printers can print 50 pages in 6 minutes. How long will it take Printer A to print 80 pages? A. 12 B. 18 C. 20 D. 24 E. 30 OA is D This question is confusing me.C an expert explain why D is the answer? Not a bad one to back-solve. Test B: If A can do 80 pages in 18 minutes, then we know it can do 40 pages in 9 minutes. If it takes B 4 fewer minutes to do 40 pages, then B can do 40 pages in 5 minutes. A's rate: 40/9 = 4 4/9 = About 4.4 pages per minute. B's rate: 40/5 = 8 pages per minute Combined rate = About 4.4+ 8 = 12.4 pages per minute. So in 6 minutes, the two could do 12.4 * 6 pages which is greater than 70. But they should be able to do 50 pages in this time, meaning they must be working slower. If they're working slower, it must have taken A more time to do 80 pages. Eliminate A and B. Test D: If A can do 80 pages in 24 minutes, then we know it can do 40 pages in 12 minutes. If it takes B 4 fewer minutes to do 40 pages, then B can do 40 pages in 8 minutes. A's rate: 40/12 = 10/3 pages per minute. B's rate: 40/8 = 5 = 15/3 pages per minute Combined rate = 10/3 + 15/3 = 25/3 pages per minute. In 6 minutes, the two would produce 6 * (25/3) = 2*25 = 50 pages. Bingo! D is our answer. _________________ Veritas Prep | GMAT Instructor Veritas Prep Reviews Save$100 off any live Veritas Prep GMAT Course

Enroll in a Veritas Prep GMAT class completely for FREE. Wondering if a GMAT course is right for you? Attend the first class session of an actual GMAT course, either in-person or live online, and see for yourself why so many students choose to work with Veritas Prep. Find a class now!

### GMAT/MBA Expert

GMAT Instructor
Joined
04 Oct 2017
Posted:
551 messages
Followed by:
11 members
180
Quote:
It takes printer A 4 more minutes more than printer B to print 40 pages. Working together, the two printers can print 50 pages in 6 minutes. How long will it take Printer A to print 80 pages?

A. 12
B. 18
C. 20
D. 24
E. 30

OA is D
This question is confusing me.C an expert explain why D is the answer?
Hi Roland2rule,
Let's take a look at your question.

If printer B takes 'x' minutes to print 40 pages, then printer A will take 'x+4' minutes to print 40 pages.
$$\text{Rate of Printer A}=\frac{40}{x+4}$$
$$\text{Rate of Printer B}=\frac{40}{x}$$

$$\text{Combined Rate of Printer A and B}=\frac{40}{x+4}+\frac{40}{x} ... (i)$$

The question states, "Working together, the two printers can print 50 pages in 6 minutes".
$$\text{Combined Rate of Printer A and B}=\frac{50}{6} ... (ii)$$

Equating Eq(i) and (ii)
$$\frac{40}{x+4}+\frac{40}{x} =\frac{50}{6}$$
$$\frac{40x+40\left(x+4\right)}{x\left(x+4\right)}=\frac{50}{6}$$
$$\frac{40x+40x+160}{x\left(x+4\right)}=\frac{25}{3}$$
$$40x+40x+160=\frac{25x\left(x+4\right)}{3}$$
$$80x+160=\frac{25x\left(x+4\right)}{3}$$
$$3\left(80x+160\right)=25x\left(x+4\right)$$
$$240x+480=25x^2+100x$$
$$25x^2+100x-240x-480=0$$
$$25x^2-140x-480=0$$
$$5x^2-28x-96=0$$
$$5x^2-40x+12x-96=0$$
$$5x\left(x-8\right)+12\left(x-8\right)=0$$
$$\left(5x+12\right)\left(x-8\right)=0$$
$$Either\ \left(5x+12\right)=0,\ or\ \left(x-8\right)=0$$
$$Either\ x=-\frac{12}{5},\ or\ x=8$$

Since 'x' represents the number of minutes Printer B takes to print 40 pages,so it can not be negative. Therefore we will only consider x = 8.

To print 40 pages Printer A takes = x + 4 = 8 + 4 = 24

We are asked to find the number of minutes Printer A will take to print 80 pages .
= 2 * (Number of minutes Printer A will take to print 40 pages) = 2 * ( 12) = 24 minutes

Therefore, Option D is correct.

Hope it helps.
I am available if you'd like any follow up.

_________________
GMAT Prep From The Economist
We offer 70+ point score improvement money back guarantee.
Our average student improves 98 points.

Free 7-Day Test Prep with Economist GMAT Tutor - Receive free access to the top-rated GMAT prep course including a 1-on-1 strategy session, 2 full-length tests, and 5 ask-a-tutor messages. Get started now.

### GMAT/MBA Expert

GMAT Instructor
Joined
22 Aug 2016
Posted:
1979 messages
Followed by:
30 members
470
Roland2rule wrote:
It takes printer A 4 more minutes more than printer B to print 40 pages. Working together, the two printers can print 50 pages in 6 minutes. How long will it take Printer A to print 80 pages?

A. 12
B. 18
C. 20
D. 24
E. 30

OA is D
This question is confusing me.C an expert explain why D is the answer?
Say printer B takes x minutes to print 40 pages, thus printer A would take (x + 4) minutes to print 40 pages.

We know that printer A and B together worked for 6 minutes and printed 50 pages, so let's compute the number of pages printer A and printer B would print in 6 minutes.

The number of pages printer A would print in 6 minutes = [40/(x + 4)]*6 = 240/(x + 4);
The number of pages printer B would print in 6 minutes = [40/x]*6 = 240/x

The number of pages printer A and B together would print in 6 minutes = 240/(x + 4) + 240/x

240/(x + 4) + 240/x = 50 pages (given)

=> 5x^2 - 28x - 96 = 0.

Instead of solving the unfamiliar linear equation, let's do the plug-in from the option values.

The option values are given for the time taken for printer A to print 80 pages. Since we assumed that printer A takes (x +4) minutes to print 40 pages, thus, it would take 2*(x + 4) minutes to print 80 pages. So the option values, in fact, are equal to 2(x + 4). Let's get the value of x from the options, and plug-in the equation 5x^2 - 28x - 96 = 0. If the RHS = the LHS, that option is the correct option.

A. 12: 2(x + 4) = 12 => x = 2. At x = 2, we have 5x^2 - 28x - 96 = 5*2^2 - 28*2 - 96 = 20 - 56 - 96 â‰  0. Eliminated!
B. 18: 2(x + 4) = 18 => x = 5. At x = 5, we have 5x^2 - 28x - 96 = 5*5^2 - 28*5 - 96 = 125 - 140 - 96 â‰  0. Eliminated!
C. 20: 2(x + 4) = 20 => x = 2. At x = 6, we have 5x^2 - 28x - 96 = 5*6^2 - 28*6 - 96 = 180 - 168 - 96 â‰  0. Eliminated!
D. 24: 2(x + 4) = 24 => x = 2. At x = 8, we have 5x^2 - 28x - 96 = 5*8^2 - 28*8 - 96 = 320 - 224 - 96 = 320 - 320 = 0. Correct
E. 30: No need to check!

Hope this helps!

-Jay
_________________
Manhattan Review GMAT Prep

Locations: Pasadena | Warsaw | Cairo | Kuala Lumpur | and many more...

• FREE GMAT Exam
Know how you'd score today for $0 Available with Beat the GMAT members only code • Award-winning private GMAT tutoring Register now and save up to$200

Available with Beat the GMAT members only code

• Free Veritas GMAT Class
Experience Lesson 1 Live Free

Available with Beat the GMAT members only code

• Magoosh
Study with Magoosh GMAT prep

Available with Beat the GMAT members only code

• Get 300+ Practice Questions

Available with Beat the GMAT members only code

• Free Practice Test & Review
How would you score if you took the GMAT

Available with Beat the GMAT members only code

• 1 Hour Free
BEAT THE GMAT EXCLUSIVE

Available with Beat the GMAT members only code

• 5-Day Free Trial
5-day free, full-access trial TTP Quant

Available with Beat the GMAT members only code

• Free Trial & Practice Exam
BEAT THE GMAT EXCLUSIVE

Available with Beat the GMAT members only code

• 5 Day FREE Trial
Study Smarter, Not Harder

Available with Beat the GMAT members only code

### Top First Responders*

1 Ian Stewart 53 first replies
2 Brent@GMATPrepNow 36 first replies
3 Jay@ManhattanReview 29 first replies
4 GMATGuruNY 25 first replies
5 ceilidh.erickson 15 first replies
* Only counts replies to topics started in last 30 days
See More Top Beat The GMAT Members

### Most Active Experts

1 Scott@TargetTestPrep

Target Test Prep

199 posts
2 Max@Math Revolution

Math Revolution

90 posts
3 Brent@GMATPrepNow

GMAT Prep Now Teacher

76 posts
4 Ian Stewart

GMATiX Teacher

62 posts
5 GMATGuruNY

The Princeton Review Teacher

44 posts
See More Top Beat The GMAT Experts