Question: It takes printer A 4 minute more than printer B to print 40 pages. If working together, the two printers can print 50 pages in 6 minutes, how long will it take printer A to print 80 pages?

1. 12
2. 18
3. 20
4. 24
5. 30

“It takes printer A 4 minute more than printer B to print 40 pages. If working together, the two printers can print 50 pages in 6 minutes, how long will it take printer A to print 80 pages?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide Quantitative Review”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.

Answer:

Approach Solution 1:

Let the time needed to print 40 pages for printer A be a minutes, so for printer B, it would be a-4 minutes

The rate of A would be \(rate=\frac{job}{time}=\frac{40}{a}\) pages per minute and the rate of B \(rate=\frac{job}{time}=\frac{40}{a-4}\) pages per minute.

Their combined rate would be  \(\frac{40}{a}+\frac{40}{a-4}\) pages per minute. Also as “two printers can print 50 pages in 6 minutes” then their combined rate is, \(rate=\frac{job}{time}=\frac{50}{6}, \frac{40}{a}+\frac{40}{a-4}=\frac{50}{6}\)

Divide it by 40, we will get: \(\frac{1}{a}+\frac{1}{a+4}=\frac{5}{24}\)

At this point we can either try to substitute the values from answer choices or solve quadratic equation. Remember as we are asked to find the time needed for printer A to print 80 pages, then the answer would be 2a (as a is the time needed to print 40 pages).

Correct option: D

Approach Solution 2:

It is easy to solve this question in terms of printer B

Time it takes printer A to do 40 pages, A{40}, = B + 4 minutes

Thus, to do 80 pages as question asks, A{80}, = 2 (B + 4) minutes

Next \(R_A+R_B=\frac{25}{3}\Rightarrow \frac{40}{B+4}+\frac{40}{B}=\frac{25}{3}\)

At this point, eyeballing is useful: B = 10 or B = 5 are clearly out and a little mental stretching suggests only B = 8 fit the quadratic

If B = 8, then A{80} = 2(8 + 4) = 24 minutes

Correct option: D

Suggested GMAT Problem Solving Questions

• A Truck Travelling At 70 Kilometres Per Hour Uses 30% More Diesel To GMAT Problem Solving
• If The Area Of A Rectangle Is Equal To The Area Of A Square, Then The GMAT Problem Solving
• The rectangles shown above are similar and the ratio of the area of GMAT Problem Solving
• A School has Set Different Minimum Qualifying Marks in an Exam GMAT Problem Solving
• The Temperature of Delhi and Lucknow were in the Ratio 3:5 in July GMAT Problem Solving
• When a Certain Tree was First Planted, it was 4 feet Tall and the Height GMAT Problem Solving
• When a Number A is Divided by 6, the Remainder is 3 and When Another GMAT Problem Solving
• Which of the Following is the Correct Ordering of 2√13, 4√3, 5√2 and 3√6 ? GMAT Problem Solving
• If the mean of set S does not exceed mean of the subset of set S, which GMAT Problem Solving
• A Milkman Sells Milk after Adding Some Water in it GMAT Problem Solving
• It Was Observed by National Geographic that Equinox Happened GMAT Problem Solving
• Paracelsus University has Two Kinds of Professors, Academic Professors GMAT Problem Solving
• What is the Smallest Prime Factor of 5^8+10^6–50^3? GMAT Problem Solving
• In A Locality, There Are Ten Houses In A Row. On A Particular Night GMAT Problem Solving
• The “Connection” Between Any Two Positive Integers a And b GMAT Problem Solving
• Find the least positive integers which must be added to 15,463 so that the result GMAT Problem Solving
• Mayank Buys Some Candies for $15 a dozen and An Equal Number of Different GMAT Problem Solving
• If John Throws a Coin Until a Series of Three Consecutive Heads GMAT Problem Solving
• In the Diagram Above, ABCD is a Parallelogram and the Areas of Yellow GMAT Problem Solving
• On certain road 10% of the motorists exceed the posted speed limit GMAT Problem Solving