Data Sufficiency

Que: If a certain machine produces toys at a constant rate, how many minutes will it take the machine to produce 1,200 toys?

(1) It takes the machine 75 minutes to produce 40 toys.
(2) It takes the machine 2.25 minutes to produce 2 toys.

Solution: To save time and improve accuracy on DS questions in GMAT, learn and apply the Variable Approach.

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

Visit https://www.mathrevolution.com/gmat/lesson for details.

Now we will solve this DS question using the Variable Approach.

DS question dealing with the work rate of one machine => rt = w

Let’s apply the 3 steps suggested previously.

Follow the first step of the Variable Approach by modifying and rechecking the original condition and the question.

We have to find the value of t – 1 machine rt = 1,200

Follow the second and the third step: From the original condition, we have 2 variables (r and t) and 1 equation (rt = 1,200). To match the number of variables with the number of equations, we need 1 more equation. Since conditions (1) and (2) will provide 1 equation each, D would most likely be the answer.

Recall 3- Principles and Choose D as the most likely answer. Let’s look at each condition separately.

[m]Condition (1) tells us that it takes the machine 75 minutes to produce 40 toys.[/m]

=> rt = w

=> r * 75 minutes = 40

=> Multiply by 30 on both sides

=> r * 75 minutes * 30 = 40 * 30

=> r * 1,350 minutes = 1,200

=> Machine makes 1,200 toys in 1,350 minutes

=> t = 1,350


The answer is unique, so condition (1) alone is sufficient, according to CMT 2 - there must be only one answer

Condition (2) tells us that it takes the machine 2.25 minutes to produce 2 toys.

=> rt = w

=> r * 2.25 minutes = 2

=> Multiply by 600 on both sides

=> r * 2.25 minutes * 600 = 2 * 600

=> r * 1,350 minutes = 1,200

=> Machine makes 1,200 toys in 1,350 minutes

=> t = 1,350

The answer is unique, so condition (2) alone is sufficient, according to CMT 2 - there must be one answer.

** Tip 1: When condition (1) = condition (2) => 95% likely that answer is D

Each condition alone is sufficient.

Therefore, D is the correct answer.

Answer: D