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## Official Guide Explanation:Problem Solving #173

Background

This is just one of hundreds of free explanations I've created to the quantitative questions in The Official Guide for GMAT Quantitative Review (2nd ed.). Click the links on the question number, difficulty level, and categories to find explanations for other problems.

These are the same explanations that are featured in my "Guides to the Official Guide" PDF booklets. However, because of the limitations of HTML and cross-browser compatibility, some mathematical concepts, such as fractions and roots, do not display as clearly online.

Question: 173
Page: 85
Difficulty: 7 (Very Difficult)
Category 1: Word Problems > Work Problems > 2 inputs
Category 2: Arithmetic > Ratio and Proportion >

Explanation: Focus on rates, using the formula amount equals rate times time. Machine X takes 2 days longer to produce w than does Machine Y. Call X's rate x, Y's rate y, and the time it takes X d days:

Machine X: w = xd

Machine Y: w = y(d - 2)

Their combined rate is x + y. Thus, if they can produce (5/4)w in 3 days, we have the equation:

(5/4)w = (x + y)(3)

Rewrite the first two equations so that they can be plugged into the third:

x = ((w)/(d))

y = ((w)/(d - 2))

Plug in:

(5/4)w = (((w)/(d)) + ((w)/(d - 2)))3

(5/12)w = w((1/(d)) + (1/(d - 2)))

(5/12) = (1/(d)) + (1/(d - 2))

Solving this will get messy. But there's a way out! d is the number of days it takes Machine X to produce w widgets. The answer choices are how many days it takes X to produce 2w widgets. So in terms of w widgets, the answer choices are 2, 3, 4, 5, and 6. Try each one of them in the equation we're left with:

(A)    (5/12) = (1/2) + (1/0) --- doesn't work

(B)    (5/12) = (1/3) + (1/1)--- much too big

(C)    (5/12) = (1/4) + (1/2)--- still too big

(D)    (5/12) = (1/5) + (1/3)--- still a bit too big

(E)    (5/12) = (1/6) + (1/4) = (2/12) + (3/12) = (5/12) --- that's it!

Choice (E) is correct.

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