Mastering the Combined Work Formula for GMAT Success

When dealing with more than two workers in a combined work question, which formula should be used?

• A. 1/T = 1/A + 1/B
• B. 1/T = 1/A + 1/B + 1/C + ...
• C. T = (A * B * C)/(A + B + C)
• D. T = A + B + C

Answer: (B)

In combined work problems involving multiple workers, the correct approach to determine the time taken by all workers to complete a task together is represented by the formula where the reciprocals of their individual work rates are summed. This formula is particularly powerful because it incorporates the contribution of each worker in terms of the fraction of the work they complete per unit of time. When using the formula, each individual’s rate of work is represented as 1/A for worker A, 1/B for worker B, and so forth for each additional worker, culminating in the sum of all these individual contributions. The total time T, needed to complete the work together, is thus found by taking the reciprocal of the sum of these individual rates, expressed as 1/T = 1/A + 1/B + 1/C + .... This means that if one worker can complete the job in A hours, another in B hours, and a third in C hours, the overall time T it would take for all three to complete the job when working together can be calculated accurately using the summation of these individual rates. This formula is foundational in work rate problems and allows you to constructively analyze the combined efficiency of multiple workers collaborating on a task. The other options provided do not adequately

When studying for the Graduate Management Admission Test (GMAT), you’ll encounter various challenging problems that test your mathematical aptitude and critical thinking. One such area involves combined work questions, a classic opportunity to shine as it showcases how effectively each worker contributes to a shared task. But wait—do you know the right formula to use when more than two workers are involved? Let’s break it down.

In these scenarios, the correct approach is laid out in the formula: 1/T = 1/A + 1/B + 1/C + ... This nifty little equation helps calculate the time it takes for multiple workers to finish a task together. Think of it as a teamwork scorecard; it sums up the efficiency of each individual contributor.

But what do the letters mean? Okay, let’s clarify. In this equation:

• T stands for total time to complete the task.

• A, B, C represent the time taken by each worker to finish the job on their own.

So, if Worker A can complete the job in A hours, Worker B in B hours, and Worker C in C hours, you can predict the time T it will take them together. The real kicker here is that you’re summing up their individual rates of work, not merely adding their hours. Why is that important? Because each worker’s contribution isn't equal—they each have different speeds. It’s like running a relay race: some teammates may sprint while others jog, but together, they’ll cross the finish line faster than if they were to run alone.

Let’s unpack the formula a bit more. You’ve got individual work rates represented as:

• Worker A: 1/A

• Worker B: 1/B

• Worker C: 1/C

By finding the sum of these fractions, you’re effectively calculating how much of the work is done per unit of time when they’re all hustling together. The beauty of it is that when you take the reciprocal of that sum, you get the total time T—like flipping a light switch to see the room brighten; it's all about perspective, right?

Now, you might be wondering why other formulas like T = A + B + C or T = (A * B * C)/(A + B + C) don’t quite cut it. Well, that's because these expressions overlook how each worker's unique pace contributes to the task's overall completion rate. They simply don’t capture the essence of teamwork quite like our shining star, 1/T = 1/A + 1/B + 1/C + ... does.

Practicing this formula not only helps you score well on multiple-choice questions, but it also hones your analytical skills—skills essential for succeeding in any business environment. Speaking of which, as you prep for the GMAT, remember that these concepts often mirror real-life teamwork scenarios in the corporate world. Being able to assess the value each individual brings to a group dynamically is a crucial skill in leadership roles.

So, as you sharpen your GMAT skills, remember this powerful formula. Whether you’re juggling numbers or managing a team project, understanding efficiency in collaborative situations will take you a long way. Who knew that a simple equation could illuminate so many paths to success? So go ahead, embrace it! You might just find that conquering this topic can boost your confidence and improve your overall performance on test day.