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A tank of volume 432 cubic feet has one inlet pipe and 2 out [#permalink]

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02 Dec 2009, 00:14

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A tank of volume 432 cubic feet has one inlet pipe and 2 outlet pipes. The inlet pipe fills water into the tank at the rate of 4 cubic inches/min and the 2 outlet pipes empty it out at the rates of 14 cubic inches/min and 6 cubic inches/min respectively. If all 3 pipes are opened when the tank is full in how much time is it emptied?(1 foot = 12 inches)

A. 777.6 hrs B. 3 days C. 15 days D. 77.76 hrs E. 5 days

Eek I got all the way through and realized I only multiplied 432 \(ft^3\) by 12! When it should be 12*12*12 ... stupid mistake ... this is definitely a tough one in 2 mins

But I am surprised there was no "trap" answer as I got 5 hours 24 minutes because I divided 5,184 cubic inches (432*12) by 16. I would have thought that trap would have been there for me to fall into!

My first time through I did it the long, long way. When I did it again I decided against actually multiplying anything out and it seemed to go quicker. YMMV.

432 * 12^3 = 16t

Convert the 432 into 16 * 27

(16 * 27 * 12^3) / 16 = t

27 * 12^3 = t

Divide by 60 to convert seconds to hours

(27 * 12^3) / 60 = t

Convert one of the 12s into 2 * 6.

(27 * 2 * 6 * 12^2) / 60 = t

(27 * 2 * 12^2) / 10 = t

Multiply out 54 * 144 (much quicker than multiplying 432 * 1728) and divide by 10 for the answer: 777.6 hours.

On the other hand, given the wide range of the answer choices, what is everyone's opinion on simplifying the numbers and taking an estimate?

Also, is it reasonable to assume that the correct answer must be an exact answer because the question stem doesn't specifically ask for an approximate answer? If so, you could eliminate all the answers given in days once you find out that the answer in minutes isn't divisible by 60 (which is as soon as you set up the equation). If you can eliminate the "days" answer choices, the only other answer choices are an order of magnitude apart. Perfect candidates for estimation!

A tank of volume 432 cubic feet has one inlet pipe and 2 outlet pipes. The inlet pipe fills water into the tank at the rate of 4 cubic inches/min and the 2 outlet pipes empty it out at the rates of 14cubic inches/min and 6 cubic inches/min respectively. If all 3 pipes are opened when the tank is full in how much time is it emptied?(1 foot = 12 inches) A) 777.6 hrs B) 3 days C) 15 days D)77.76 hrs E)5 days

The options are such that you don't have to calculate a whole lot. 3 days is 72 hrs (think less than 100 if you will) 15 days is 360 hrs (10 days have 240 hrs so 5 days have 120 so overall, 15 days have 360 hrs)

Look at the question now:

The tank has one inlet pipe and 2 outlet pipes. When all 3 pipes are open, think what is happening in one minute.

4 \(in^3\) is flowing in the tank and (14+6) \(in^3\) is flowing out of the tank. So overall, in every one minute, 20-4 = 16 \(in^3\) is flowing out of the tank.

Now we have the volume of the full tank. In every minute, 16 \(in^3\) flows out of it. How long will it take to empty?

\(\frac{432*12*12*12 in^3}{16}\) minutes

We see that 16*27 = 432 (I wondered if 432 will directly go by 16. I saw that it does. It's good to know the multiplication tables)

Let's convert it to hours now: \(\frac{27*12*12*12 in^3}{60}\) hours = \(\frac{27*12*12 in^3}{5}\) hours

Now this is painful calculation so I will try to ballpark.

I say that 27/5 is more than 5. I know that 12*12 = 144 So answer will be more than 5 times 144 which has to be option (A).
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Re: A tank of volume 432 cubic feet has one inlet pipe and 2 out [#permalink]

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14 Sep 2013, 23:11

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: A tank of volume 432 cubic feet has one inlet pipe and 2 out [#permalink]

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12 Oct 2015, 09:11

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
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