It Takes Printer A 4 Minute More than Printer B to Print 40 GMAT Problem Solving

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

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