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M60-04

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Math Revolution GMAT Instructor
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M60-04  [#permalink]

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New post 11 Jun 2018, 02:35
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Difficulty:

  25% (medium)

Question Stats:

100% (01:12) correct 0% (00:00) wrong based on 6 sessions

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Working alone at its constant rate, machine A can produce 240 pins in \(x\) hours. Working alone at its constant rate, machine B can produce 240 pins in \(y\) hours. How many hours will it take machines A and B to produce 240 pins, when working together at their respective constant rates?



1) \(xy/(x+y)=4\)

2) \(x=20\)

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Math Revolution GMAT Instructor
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Re M60-04  [#permalink]

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New post 11 Jun 2018, 02:35
Official Solution:



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, and then recheck the question.

We have \(1/t = 1/x + 1/y = (x+y)/xy\) or \(t = xy/(x+y)\), where t is the time that machines A and B take to produce 240 pins, when working together. The question asks for \(xy / (x+y)\).

Thus, only condition 1) is sufficient. Condition 2) is not sufficient as it only gives us information about \(x\).

Therefore, the answer is A.



Answer: A
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Re M60-04  [#permalink]

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New post 13 Nov 2018, 01:26
I think this the explanation isn't clear enough, please elaborate.
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Re: M60-04  [#permalink]

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New post 22 Dec 2018, 14:29
1
It is a work rate problem, so it follows the generic set up for those questions:

total amount of work/total amount of time = total amount of work/time for x to complete that work + total amount of work/time for y to complete that work

240/T = 240/X + 240/Y

Can simplify this by dividing by 240

1/T = 1/X + 1/Y

We want a single denominator on the right

1/T = (Y/Y)1/X + (X/X)1/Y
1/T = Y/XY + X/XY
1/T = (Y+X)/XY

Get the reciprocal both sides of the equation

T=XY/(Y+X)

Statement 1) this is exactly what we need
Statement 2) doesn't provide anything about Y
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Re M60-04  [#permalink]

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New post 18 Jan 2019, 02:15
I think this is a high-quality question and I agree with explanation.
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Re M60-04   [#permalink] 18 Jan 2019, 02:15
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