Proportion

[silverflamein]

During a survey of company Y, Jay observes that the duration d, in which work gets completed in the company is inversely proportional to the sum of two quantities, the efficiency e of worker and the number of workerr,n. each of these two quantities is directly proportional to x.
It is also seen that e=1 n=10 and d=3 when x=2. Which of the following is a correct representation of d in terms of x?
A ) d = 3/{(x/2)+10}

B) d = 2x/{(1/2)+5x}

C) d = x/(x-5)

D) d = 6/x

E) d = 1/(1+x)

[rijul007]

d is inversely proportional to sum of e and n

d = k/(e+n)

e is directly proportional to x

e = px

n is also directly proportional to x

n = qx


when e=1, n=10, d=3, and x=2

d=k/(e+n)
3=k/11
k=33

e=px
1=2p
p=1/2

n=qx
10=2q
q=5

d=k/e+n = 33/(x/2 + 5x) = 33/(11x/2) = 6/x

Hence D is the correct option

[shankar.ashwin]

Since values of d and x are known to be 3 and 2.

Substituting them in the answer choices, only D satisfies.
All other equations do not satisfy

[saketk]

During a survey of company Y, Jay observes that the duration d, in which work gets completed in the company is inversely proportional to the sum of two quantities, the efficiency e of worker and the number of workerr,n. each of these two quantities is directly proportional to x.
It is also seen that e=1 n=10 and d=3 when x=2. Which of the following is a correct representation of d in terms of x?
A ) d = 3/{(x/2)+10}

B) d = 2x/{(1/2)+5x}

C) d = x/(x-5)

D) d = 6/x

E) d = 1/(1+x)

This question is pretty easy if you directly put values in options.

I started from the easiest one- OPTION D. given x =2 and d=3

You just need to prove LHS = RHS

Only D suffice. CORRECT answer.

ETA -- 45 seconds (including the reading part)

[neelgandham]

Lovely question! I liked the way the person who framed the question made it look so complicated. Questions like these are the ones which save you a minute or half of it OR make you spend an extra minute

Substitution is the mantra

D-> Answer, as it is the only equation which satisfies the condition d=3 when x=2

[rohit_gmat]

plugged in for x (x=2) and got D as the only choice that makes d=3

wats the source? it doesnt sound like a real gmat Q to me :S