TeamGMATIFY wrote:

Andy takes \(\sqrt{x}\) hours to till \(x\) acres of land while Bill takes 10 minutes to till each acre of land. If they work together, approximately how many hours will they take to till 72 acres of land?

A. 2.5

B. 3.5

C. 6

D. 8.5

E. 12

Lengthy Process : Algebraic approach Let x acre is tilled by Andy and 72-x acre is tilled by Bill.

So, time taken by Andy = \(\sqrt{x}\)

In this \(\sqrt{x}\) time Bill tilled 72-x acre of land.

Also to till 72-x acre of land Bill will take (72-x)*10/60 hours = (72-x)/6 hours.

So, \(\sqrt{x}\) = (72-x)/6

6*\(\sqrt{x}\) = (72-x)

36 x = 72^2 + x^2 -144x

x^2 -144 x -36x +72^2 = 0

x(x-144) -36(x-144) = 0

x= 144, 36

But x can't be greater than 72 . So, x = 36

\(\sqrt{x}\) = 6.

Shorter Process : GMAT ApproachStart putting options to check if the time taken by Bill matches with the both ways.

Option 1: time taken = 2.5

Land tilled by Andy = 6.25

Land tilled by Bill = 65.75 Time taken =65.75/6= approx 10+ =/=2.5

Option 2: time taken = 3.5

Land tilled by Andy = 12.25

Land tilled by Bill = 59.75 Time taken =59.75/6= approx 10- =/=3.5

Option 3: time taken = 6

Land tilled by Andy = 36

Land tilled by Bill = 36 Time taken = approx 36/6 =6 same as the option....

This is the answer...

All GMAT takers should learn to try this approach..

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