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# A consulting firm uses a Trenchard score to help companies determine

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Math Expert
Joined: 02 Sep 2009
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A consulting firm uses a Trenchard score to help companies determine  [#permalink]

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25 Jul 2017, 22:38
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55% (hard)

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63% (01:03) correct 37% (01:15) wrong based on 70 sessions

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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. ab/(a−b)

C. ab/(b−a)

D. (a−b)/(ab)

E. (b−a)/(ab)

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A consulting firm uses a Trenchard score to help companies determine  [#permalink]

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25 Jul 2017, 22:51
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Trenchard score : Reciprocal of the difference of the reciprocals of times taken to complete a task

If we have time taken as T1 and T2,

Trechard score can be calculated as follows :
Step 1 : Difference in reciprocal of their times : $$\frac{1}{T1} - \frac{1}{T2}$$
Hence the difference will be $$\frac{(T2 - T1)}{(T1*T2)}$$
Step 2 : Reciprocal of difference in reciprocal of times : $$\frac{(T1*T2)}{(T2 - T1)}$$

Given data : Tasks take a and b nanoseconds respectively, with b>a
Substituting these values into the formula,
we will get Trenchard score : $$\frac{a*b}{b-a}$$ (Option C)
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Re: A consulting firm uses a Trenchard score to help companies determine  [#permalink]

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08 Sep 2017, 02:32
Ans is C:

a nano secs and b nano secs

so first difference between the reciprocals

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

Reciprocal of difference = R = 1/D => ab/(b-a)

Trenchard Score is Reciprocal = ab/(b-a)
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Re: A consulting firm uses a Trenchard score to help companies determine  [#permalink]

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11 Sep 2017, 16:00
Bunuel wrote:
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. ab/(a−b)

C. ab/(b−a)

D. (a−b)/(ab)

E. (b−a)/(ab)

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)

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Re: A consulting firm uses a Trenchard score to help companies determine  [#permalink]

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12 Sep 2017, 03:47
Trenchard score = reciprocal of the difference of the reciprocals of two times
Given that two times are 'a' and 'b' where b>a

Hence, 1/a > 1/b
---> Reciprocal(1/a - 1/b) = Reciprocal{(b-a)/ab} = ab/(b-a)
Re: A consulting firm uses a Trenchard score to help companies determine &nbs [#permalink] 12 Sep 2017, 03:47
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