Quantitative

Question

I need a help with this question.

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

GmatKnightTutor · Answer

https://gmatclub.com/forum/pumps-a-b-an ... 91124.html

This question seems to be very similar to the one you posted. Consider trying to solve this one to understand the mechanics of the one in yours. Some of the solutions in the answer choices may help guide you.

nahid78 · Answer

From the information we can find that 1592 (a + b) < 3000000 ( 1 cubic meter equals 1000 liters) 
 and 1250 (b + c) < 3000000
 and 995 (a + c) < 3000000

Through estimation a+b<1800, b+c<2400, and a+c<3000
 2a + 2b+ 2c < 7200
 a + b + c < 3600

So, c < 1800
 a < 1200
 b < 600

I can calculate this far. Lets wait for the experts. 
However, I do not know whether it is a gmat like question.

Kinshook · Answer

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

AndrewN · Answer

Hello,  rishimarde . This question does not look even remotely GMATTM-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

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