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Machine A takes 20 minutes and B takes 15 minutes to warm up

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Machine A takes 20 minutes and B takes 15 minutes to warm up

by Max@Math Revolution » Wed Nov 07, 2018 12:37 am

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[Math Revolution GMAT math practice question]

Machine A takes 20 minutes and B takes 15 minutes to warm up. The machine A produces 300 pins per 1 minute and the machine B produces 200 parts per 1 minute. Including the time for warming up, is the number of pins produced by machine A smaller than the number of pins from the machine B?

1) The number of pins is greater than 3000
2) The number of pins is less than 4000
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Source: — Data Sufficiency |
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by Max@Math Revolution » Fri Nov 09, 2018 12:13 am

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=>

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.

The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question.

Let w be the number of pins.
20 + w / 300 is the time the machine A takes to produce w pins and 15 + w / 200. The question asks if 20 + w / 300 is less than 15 + w / 200.
20 + w / 300 < 15 + w / 200
=> 5 < w/200 - w/300
=> 5 < 3w/600 - 2w/600
=> 5 < w/600
=> 3000 < w

Since condition 1) is same as the question, condition 1) is sufficient.

Condition 2)
In inequality questions, the law "Question is King" tells us that if the solution set of the question includes the solution set of the condition, then the condition is sufficient
The solution set 3000 < w of the question does not include the solution set of condition 2) w < 400. Thus condition 2) is not sufficient.

Therefore, A is the answer.
Answer: A
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