Maximizing Printer Efficiency: Solving the CCAT Challenge

How many additional printers are needed if six printers can complete a job in 12 hours and the goal is to reduce the time to 8 hours?

• A. 2
• B. 3
• C. 4
• D. 5

Answer: (B)

To solve this problem, we first need to determine the total amount of work that the six printers can do in 12 hours. We can express this work in terms of printer-hours. If six printers can complete the job in 12 hours, then the total work done is: Total Work = Number of Printers × Time Total Work = 6 printers × 12 hours = 72 printer-hours The goal is to complete the same amount of work, 72 printer-hours, in only 8 hours. To find out how many printers are required to achieve this, we divide the total work by the time allowed: Required Printers = Total Work / Time Required Printers = 72 printer-hours / 8 hours = 9 printers Now, we already have six printers, so we need to find out how many additional printers are necessary: Additional Printers = Required Printers - Existing Printers Additional Printers = 9 printers - 6 printers = 3 printers Thus, three additional printers are needed to complete the job in 8 hours. This reasoning clearly aligns with the choice that indicates three additional printers are necessary to meet the new target, demonstrating an understanding of the relationship between the number of printers,

Understanding how many additional printers are needed might seem like a straightforward question, but it can offer some valuable insights into problem-solving and efficiency—both key elements of the Criteria Cognitive Aptitude Test (CCAT). You may have faced similar challenges where you had to determine not just what’s required but how to achieve it within specific constraints. Let's break this down step by step.

So, here’s the scenario: Six printers can finish a job in twelve hours, but what if you need to slash that time down to just eight hours? Sounds daunting, right? But with a little math and practical reasoning, we can get to the answer.

First off, let’s calculate the total work done by those six printers. In a situation like this, we often look at work in terms of printer-hours. You know what I mean—if six printers are buzzing away for twelve hours, how much work is actually getting done?

Here’s the calculation:

Total Work = Number of Printers × Time

Total Work = 6 printers × 12 hours = 72 printer-hours

Now, to meet the new challenge of completing that same work, 72 printer-hours, in just eight hours, we need to figure out how many printers we're going to need. This is where some simple division comes into play—that isn’t so scary, right? Let’s break it down:

Required Printers = Total Work / Time

Required Printers = 72 printer-hours / 8 hours = 9 printers

Wow, there we go—nine printers are required to finish the job within that new time frame. But hold on—don’t forget we’ve already got six printers in operation. Here’s the crux of the matter:

How many additional printers do we need to maximize our efficiency? Here’s the equation we need:

Additional Printers = Required Printers - Existing Printers

Additional Printers = 9 printers - 6 printers = 3 printers

So, voilà! Three additional printers are required to meet that eight-hour goal. This reasoning not only clarifies the math but demonstrates how we can adjust resources to meet changing targets.

You know, this kind of logical reasoning isn’t just applicable in abstract scenarios like finding out how many printers we need. It’s a valuable skill in countless areas—from managing your study schedule for the CCAT to navigating time-sensitive projects in the workplace. Remember, it’s not just about finding the answer; it’s about understanding the process.

With the right approach, you can tackle even the trickiest of questions on the CCAT! Always keep the broader picture in mind and consider how each piece of information fits into the overall puzzle. Now, doesn’t that inspire you to look at challenges a little differently?