A consulting firm uses a Trenchard score to help companies determine

Question

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)

A. a−b

B. ab/(a−b)
 
C. ab/(b−a)
 
D. (a−b)/(ab)
 
E. (b−a)/(ab)

pushpitkc · Answer

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} = \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, the Trenchard score is  \frac{a*b}{b-a}   (Option C)

sahilvijay · Answer

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)

ScottTargetTestPrep · Answer

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/  = (ab)/(b - a)
 
Answer: C

devanshu92 · Answer

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)

gmat800live · Answer

Hello! Where is it mentioned that the score can't be negative? I mean, couldn't the Trenchard score be a negative value? Although I did it instinctively I really don't understand why we need to perform the calculations on that order... If anyone could help I'd be grateful!

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A consulting firm uses a Trenchard score to help companies determine

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