Bunuel wrote:
Water flows into an empty tank of 54 liters via 12 small pipes. The rate of flow in each pipe is 1 liter per hour. However, water also flows out of the tank via several large pipes at the rate of 1.5 liter per hour. If the tank is completely full after 12 hours, how many large pipes are there?
A. 2.5
B. 3
C. 4
D. 5
E. 6
An alternative approach - As I often like to do on Problem Solving questions, I took a more intuitive, logic-based approach to solving this one. With the answers staring us right in the face, why not reason our way to what
must be correct, leaving no room for error? The first step is to eliminate choice (A), on the grounds that there cannot be half a pipe. (What would that mean? Half as long? Sawed in half to leave only a semicircle?) With four choices remaining, we can choose one of those in the middle to use as a gauge. For the sake of illustration, let us assume we chose (C), 4, first.
1) If there were 4 "out" pipes,
each flowing at 1.5 L/h, then 4 x 1.5 = 6 L/h of outflow.
2) Since we know the inflow is 12 (pipes) x 1 (L/h), or 12 L/h, we can make quick work of the net inflow by subtracting our calculated outflow from the last step: 12 - 6 = 6 L/h.
3) To fill a 54 L tank, an inflow of 6 L/h would take 9 hours (from 54 divided by 6). This does
not corroborate our known information--it should take 12 hours instead--but importantly, we can see that we need to slow the rate of inflow to drag out the total time it will take to fill the tank. Hence, (B) makes no sense, and the answer will have to be (D) or (E).
Since I am not as fond of decimals as I am whole numbers, I might try (E), 6, next. Repeating the same process from before, we get the following:
1) 6 x 1.5 = 9 L/h of outflow.
2) 12 - 9 = 3 L/h of net inflow.
3) 54/3 = 18 h.
We have overshot the target, so one more adjustment is needed, and without doing the math, we know the answer
has to be (D), the only sensible choice remaining. If you were curious about proving (D) (even though I would not bother on the actual test):
1) 5 x 1.5 = 7.5 L/h of outflow.
2) 12 - 7.5 = 4.5 L/h of net inflow.
3) 54/4.5 (understanding that 4.5 is half of 9, so the answer will be double that of 54/9) = 12 h, the very number we are given.
Such a Goldilocks approach should not be overlooked or written off if it gets you the correct answer in a time-efficient manner. Better than feeling stuck during the test and fishing around for a formula you are sure you have forgotten.
- Andrew