Que: Machine A and machine B produce toys at their constant rates, respectively. In how many hours.....

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Que: Machine A and machine B produce toys at their constant rates, respectively. In how many hours does machine A produce the total number of toys?

(1) Machine B produces 1,000 toys in 8 hours.
(2) The total number of toys that machine A must produce is 2,000.

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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.

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 \(t_1\) =>(2 machines: \(r_1\cdot t_1 = w_1\) and \(r_2\cdot t_2 = w_2\))

Follow the second and the third step: From the original condition, we have 6 variables ( \(r_1,\ t_1\ ,\ w_1,\ r_2,\ t_2\ and\ \ w_2\ \)) and 2 Equations (\(r_1\cdot t_1 = w_1\) and \(r_2\cdot t_2 = w_2\)). To match the number of variables with the number of equations, we need 4 more equations. Since conditions (1) and (2) will provide 1 equation each, E would most likely be the answer.

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

Condition (1) tells us that Machine B produces 1,000 toys in 8 hours => \(r_2\cdot8=1,000\ \) => \(r_2=125\)

Condition (2) tells us that the total number of toys that machine A must produce is 2,000 => \(r_1\cdot t_1=w_1=2,000\)

Thus, the Work rate of Machine A is unknown => Cannot determine the unique value of \(t_1\).

The answer is not unique, so the conditions combined are not sufficient, according to CMT 2 - there must be one answer.

Both conditions together are not sufficient.

Therefore, E is the correct answer.

Answer: E