Quantitative

Given: The 3 pumps A, B and C are available for filling a swimming pool. Pump A creates a liter per minute. The pump B creates b liters per minute. The pump C creates c liters per minute. If A and B pump together, the pool will fill up in 1592 minutes. If A and C pump together, the pool will fill up in 1250 minutes. If B and C pump together, the pool will fill up in 995 minutes. The pool has a volume of less than 3000 cubic meters. The values ​​a, b, and c are integers.

Asked: We are looking for the product of a, b and c

Let the size of the swimming pool be x litres

If A and B pump together, the pool will fill up in 1592 minutes.
x = 1592(a + b)
If A and C pump together, the pool will fill up in 1250 minutes.
x = 1250(a + c)
If B and C pump together, the pool will fill up in 995 minutes.
x = 995(b+c)

x = 1592 (a+b) = 1250 (a+c) = 995 (b+c) <= 3000000 litres

1592 = 2^3*199
1250 = 2*5^4
995 = 5*199

2(a + b + c) = x (1/1592 + 1/1250 + 1/995) = x/2^3*5^4*199 (5^4 + 2^2*199 + 2^3*5^3) = x/2^3*5^4*199 (625 + 796 + 1000) = 2421x/995000 =
a + b + c = 2421x/1990000

1990000 = 199*2^4*5^4

c = 2421x/1990000 - x/1592 = x/1990000 (2421 - 2*5^4) = x/1990000 (2421 - 1250) = 1171x/1990000
b = 2421x/1990000 - x/1250 = x/1990000 (2421 - 2^3*199) = x/1990000 (2421 - 1592) = 829x/1990000
a = 2421x/1990000 - x/995 = x/1990000 (2421 - 2^4*5^3) = x/1990000 (2421 - 2000) = 421x/1990000

Let x = 1990000 <= 3000000 litres

a = 421
b = 829
c = 1171
a*b*c = 421*829*1171 = 408689539

Hello, rishimarde. This question does not look even remotely GMAT™-like to me, and seeing the solution posted above by Kinshook only strengthens my view. The exam tests the ability to apply sound reasoning to a problem, not work through needlessly large numbers. Furthermore, I am not sure whether to take the second sentence at face value or to consider it a typo:

If pump A does indeed create a liter per minute, then the value of a is 1. If liter is supposed to say liters instead, then the problem will produce different values for the three unknowns. I would advise you to abandon such a poorly phrased and thought out question. I think GmatTutorKnight pointed you in the right direction. If you need to read more theory on Work/Rate problems, I would suggest you check out the main page of the Quantitative thread under the Announcements subsection.

Good luck with your studies.

- Andrew