Quant #3

[anirudhbhalotia]

This one I did a few calculations, I know its an easy one, but since I haven't touched elementary math in years, I am totally missing the fundamentals here.

The correct answer as far as I can recall is 2/5.

Can anyone explain?

[beat_gmat_09]

As you know that larger tank can fill in half hours two working together will take less than half hour only a and c remains
now total tank cannot be filled in 1/4 hours (try it) only c remains
hope that helps.
post your questions in problem solving /ds sections for quant

[anirudhbhalotia]

Oh ok....was not sure where to post it! Will keep in mind henceforth!

I get it that option d and e are ruled out.

but how do I decide between a, b and c.

I may be complicating myself....my way is that, for sure than it would take less than 0.5 hrs.

Now a is 0.25, b is 0.33 and c is 0.4.

So how do we further narrow down our options?

[beat_gmat_09]

Oh ok....was not sure where to post it! Will keep in mind henceforth!

I get it that option d and e are ruled out.

but how do I decide between a, b and c.

I may be complicating myself....my way is that, for sure than it would take less than 0.5 hrs.

Now a is 0.25, b is 0.33 and c is 0.4.

So how do we further narrow down our options?

Ok, first of all there is a formula for solving this problem

1/A + 1/B = 1/T
Where A is the time taken by Say Person x to perform a work individually and B is time taken by say person y to perform the same work individually and T is the time required to perform the same work when both person x and person y work together, obviously the combined effect will reduce the time, now lets plug our values in this formula
1/1/2 + 1/2 = 1/T

2+1/2 = 1/T
5/2 = 1/T
T = 2/5 = 0.4

other way to solve is logic -
Larger fills in 1/2 - full tank.
1/2 tank by larger in 1/4 hours
Smaller fills in 2 hours - full tank
in 1/2 hours it will fill 1/8 of the tank.
so total tank filled till now - 1/2+1/8 = 5/8, remaining is 3/8
in next 1/4 hour (working same as above) tank will fill to 5/8 + 5/8 = 10/8 approx = 1.2
so slightly less time (less than 1/2 hours) is needed to fill the tank.
1/3 is less, tank will still be left to fill so 2/5 = 0.4 is the answer.

[anirudhbhalotia]

Oh ok....was not sure where to post it! Will keep in mind henceforth!

I get it that option d and e are ruled out.

but how do I decide between a, b and c.

I may be complicating myself....my way is that, for sure than it would take less than 0.5 hrs.

Now a is 0.25, b is 0.33 and c is 0.4.

So how do we further narrow down our options?

Ok, first of all there is a formula for solving this problem

1/A + 1/B = 1/T
Where A is the time taken by Say Person x to perform a work individually and B is time taken by say person y to perform the same work individually and T is the time required to perform the same work when both person x and person y work together, obviously the combined effect will reduce the time, now lets plug our values in this formula
1/1/2 + 1/2 = 1/T

2+1/2 = 1/T
5/2 = 1/T
T = 2/5 = 0.4

other way to solve is logic -
Larger fills in 1/2 - full tank.
1/2 tank by larger in 1/4 hours
Smaller fills in 2 hours - full tank
in 1/2 hours it will fill 1/8 of the tank.
so total tank filled till now - 1/2+1/8 = 5/8, remaining is 3/8
in next 1/4 hour (working same as above) tank will fill to 5/8 + 5/8 = 10/8 approx = 1.2
so slightly less time (less than 1/2 hours) is needed to fill the tank.
1/3 is less, tank will still be left to fill so 2/5 = 0.4 is the answer.

Wonderful, the first method works like a charm!

2nd method seems complicated to me!