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A tank containing water started to leak. Did the tank contai

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A tank containing water started to leak. Did the tank contai [#permalink]

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New post 23 Feb 2011, 04:12
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A tank containing water started to leak. Did the tank contain more than 30 gallons of water when it started to leak? (Note: 1 gallon = 128 ounces)

(1) The water leaked from the tank at a constant rate of 6.4 ounces per minute.
(2) The tank became empty less than 12 hours after it started to leak.
[Reveal] Spoiler: OA

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Last edited by Bunuel on 12 Jan 2014, 06:18, edited 1 time in total.
Added the OA.

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Re: Water [#permalink]

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New post 23 Feb 2011, 06:11
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(1 alone) Does not tell you anything about the size of the tank. OUT

(2 alone) Does not tell you anything about the rate of leakage. OUT

(1 & 2) Lets do some simple math to begin.

30 gallons = 3840 oz
6.4 oz/min = 384 oz/hr

Ah, nice! 3840 and 384 are easy numbers to work with. It should be pretty clear that...

10 hours to drain => 30 gallons
less than 10 hours to drain => less than 30 gallons
more than 10 hours to drain => more than 30 gallons

However, (2) does not help us out in this category, as the time could be either 1 or 11. OUT

(1 or 2) OUT

(Neither Sufficient) CORRECT

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Re: Water [#permalink]

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New post 12 Mar 2011, 18:22
Good question. My answer is E too.

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Re: A tank containing water started to leak. Did the tank [#permalink]

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New post 12 Jan 2014, 06:12
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E as well.
1 is clearly not sufficient.
2 Without knowing rate of leakage nothing can be said. - not sufficient.

1+2 at 6.4 ounce per min in 12 hours 36 gallons will be leaked so if tank leaks in 11:59 hrs tank must have > 30 gallons initially. This case yields "yes" answer. but if the tank is empty in 2 hours then tank has 6 gallons which is < 30. This case yields "no" answer. NOT SUFFICIENT.
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Re: A tank containing water started to leak. Did the tank contai [#permalink]

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New post 01 Dec 2015, 18:10
oh damn...I thought 1 gallon = 1280 oz...dumb me..

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Re: A tank containing water started to leak. Did the tank contai [#permalink]

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Baten80 wrote:
A tank containing water started to leak. Did the tank contain more than 30 gallons of water when it started to leak? (Note: 1 gallon = 128 ounces)

(1) The water leaked from the tank at a constant rate of 6.4 ounces per minute.
(2) The tank became empty less than 12 hours after it started to leak.


ok...30gallons * 128 = 1280x3 = 3840 ounces
the question is - did the tank contain more than 3840 ounces when it started to leak?

1. we know the rate of the leakage..but we do not know for how long it leaked..
2. tells that time is less than 12 hours..but we do not know the rate of the leakage..+ we do not know the exact time..

1+2.
6.4/min = 64*6=384 ounces/hour
if the tank leaked for > 10 hours, then it contained more than 30 gallons
if the tank leaked for less than 10 hours, then it contained fewer than 30 gallons.

since 2 alone tells that it is less than 12 hours..it can be either 11 or 9. 11-> over 30 gallons and 9-> less than 30 gallons.

E

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Re: A tank containing water started to leak. Did the tank contai [#permalink]

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New post 02 Apr 2016, 11:44
A tank containing water started to leak. Did the tank contain more than 30 gallons of water when it started to leak? (Note: 1 gallon = 128 ounces)

(1) The water leaked from the tank at a constant rate of 6.4 ounces per minute.
(2) The tank became empty less than 12 hours after it started to leak.

Individually statements are not sufficient.
lets t is the time taken to drain out completely as per statement 2. (t<12). X be the no of gallons.
from both the statements 6.4 = 128x/t*60
solving x=3t (t <12). So we can not get any single value.

Hence E

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Re: A tank containing water started to leak. Did the tank contai [#permalink]

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Re: A tank containing water started to leak. Did the tank contai [#permalink]

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New post 17 Jul 2017, 15:44
All the post above do a great job of answering the question, but I'll include my own approach in case anyone finds it helpful.

I find these problems hard because of (1) the inequalities and (2) the immediate decision that needs to be made about what numbers to convert. I'll try and illustrate how I triage these questions.

A tank containing water started to leak. Did the tank contain more than 30 gallons of water when it started to leak? (Note: 1 gallon = 128 ounces).

(1) The water leaked from the tank at a constant rate of 6.4 ounces per minute.
(2) The tank became empty less than 12 hours after it started to leak.

Ok, at first glance I have a decision to be made about ounces vs. gallons. Without even doing anything else, I make the call that I'm going to convert 6.4 ounces to gallons because 6.4 oz/min is already a decimal, and making it a smaller decimal doesn't seem appealing. Therefore, convert the question (often an overlooked asset) to a ounces.

30 gallons = 30*(128) ounces = 3840 oz.

So the restated question is: Volume > 3840 oz. ?

At this point I can also see (as other posters have pointed out) that the answer is either C or E as neither statement is going to be sufficient on its own. Knowing that, I reach the second decision point: minutes vs hours?

I either convert the first statement into oz/hr or the second statement into minutes. Quickly eyeball your choices as either 6.4*60 or 12*60. In this case, it actually doesn't matter. Sometimes the numbers are easier going down one road, but here they look equally fine. I guess if pushed, it'd rather take advantage of 6.4*60 eliminating that decimal and take that one.

6.4*60 = 64*6 = 384 oz/hr

The tricky thing with statement 2 is that it's an inequality not a raw number. In order to remind myself of that, I actually include the inequality when I start combining stuff. It looks like this:

(384 oz/hr)*(<12 hrs) > 3840 oz ?

Now we can see the units will cancel we get a leaned down:

(384)*(<12) > 3840 ? --> remove the factor of 10 from the RHS
(384)*(<12) > (384)*(10) ? --> cancel common factors

We are then left with:

(<12) > 10 ?

Now this, although it might have seemed silly before, is very clear. Can the range of numbers less than 12 exceed 10? Yes of course it can (i.e. 11). Can it be less than 10? Yes of course (1, 2, 4, 7 etc).

Therefore, (E).

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Re: A tank containing water started to leak. Did the tank contai   [#permalink] 17 Jul 2017, 15:44
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