A consulting firm uses a Trenchard score to help companies determine which computer tasks work best together in parallel

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Wed Sep 30, 2020 6:47 am

A consulting firm uses a Trenchard score to help companies determine which computer tasks work best together in parallel. The Trenchard score is calculated by determining the number of nanoseconds a task takes for each of two processes, then calculating the difference between the reciprocals of those times. The reciprocal of that difference is the Trenchard score. What would be the Trenchard score for tasks that take \(a\) and \(b\) nanoseconds, respectively, where \(b>a?\)

A. \(a-b\)

B. \(\dfrac{ab}{a-b}\)

C. \(\dfrac{ab}{b-a}\)

D. \(\dfrac{a-b}{ab}\)

E. \(\dfrac{b-a}{ab}\)

Answer: C

Solution:

First, let’s calculate the difference between the reciprocals of the times:

1/a - 1/b = b/(ab) - a/(ab) = (b - a)/(ab)

Notice that since b > a, 1/a > 1/b (so we use 1/a - 1/b instead of 1/b - 1/a). Next, we can calculate the Trenchard score as follows:

1 / [(b - a)/(ab)] = (ab) / (b - a)

Answer: C


Source: Veritas Prep