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# From a full tank containing 729 liters of honey, we pour off "a" litre

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Intern
Joined: 01 Jan 2016
Posts: 28
From a full tank containing 729 liters of honey, we pour off "a" litre  [#permalink]

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11 Jun 2017, 06:23
1
8
00:00

Difficulty:

75% (hard)

Question Stats:

50% (02:07) correct 50% (02:38) wrong based on 64 sessions

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From a full tank containing 729 liters of honey, we pour off "a" litres and add water to fill up the tank. After stirring the solution thoroughly, we pour off "a" liters of the solution and again add water to fill up the tank. After the procedure is repeated for a total of 6 times, the solution contains 64 liters of honey. Find "a"

A) 243 liters
B) 81 liters
C) 2.7 liters
D) 90 liters
Intern
Joined: 05 Apr 2017
Posts: 7
Re: From a full tank containing 729 liters of honey, we pour off "a" litre  [#permalink]

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11 Jun 2017, 08:07
1
Suppose a container contains x units of a liquid from which y units are taken out and replaced by water. After n operations, quantity of pure liquid =
x(1−y/x)^n (which in this case = 64)

In this case x = 729
y = a
n = 6

By checking option A. Replace a with 243, equate further, and LHS will match RHS viz. 64.

(This is a CAT question, don't worry. You won't encounter such questions on the GMAT)
Senior Manager
Joined: 28 May 2017
Posts: 285
Concentration: Finance, General Management
Re: From a full tank containing 729 liters of honey, we pour off "a" litre  [#permalink]

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11 Jun 2017, 08:57
1
smitsharma wrote:
Suppose a container contains x units of a liquid from which y units are taken out and replaced by water. After n operations, quantity of pure liquid =
x(1−y/x)^n (which in this case = 64)

In this case x = 729
y = a
n = 6

By checking option A. Replace a with 243, equate further, and LHS will match RHS viz. 64.

(This is a CAT question, don't worry. You won't encounter such questions on the GMAT)

nice n crisp explanation
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Intern
Joined: 23 May 2016
Posts: 7
Location: India
GPA: 3.04
WE: Analyst (Retail)
Re: From a full tank containing 729 liters of honey, we pour off "a" litre  [#permalink]

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11 Jun 2017, 09:20
smitsharma wrote:
Suppose a container contains x units of a liquid from which y units are taken out and replaced by water. After n operations, quantity of pure liquid =
x(1−y/x)^n (which in this case = 64)

In this case x = 729
y = a
n = 6

By checking option A. Replace a with 243, equate further, and LHS will match RHS viz. 64.

(This is a CAT question, don't worry. You won't encounter such questions on the GMAT)

I see this formula is related to the compound interest formula. But i am not able to relate how is formula applied here? Any help?
Manager
Joined: 03 Feb 2017
Posts: 75
Location: Australia
GMAT 1: 720 Q48 V40
Re: From a full tank containing 729 liters of honey, we pour off "a" litre  [#permalink]

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12 Jun 2017, 06:04
I did not know the formula as well.

However, I was able to answer this quite simply by working backwards from answer choices.

First, I took choice D, which gives 'a' = 90 litres.

Now, if we remove 'a' litres 6 times, we will remove 6*90=540 litres of fluid.
Even if we assume 540 litres as entirely honey (which it is not), then the amount of honey remaining after 6 attempts will be 729-540=189 litres

However, the question says that amount of honey that should remain is only 64 litres, so going by this, the amount being removed has to be far greater than 90 litres.

Conveniently, answer choice A = 243 litres is the only one larger than D, so A is the answer

In case you are wondering, how much honey we will actually remove when we use choice D, here is how to work it:

Step 1:
From choice D, a = 90, so we remove 90 from 729 = 639 litres of honey remain

Step 2:
We add a=90 litres of water and remove a=90 litres of mixture.
However, this time, only a fraction of the mixture removed is honey, so we need to calculate amount of honey removed.

Amount of honey in 90 litres of mixture = 90 * Fraction of money in total mixture = 90*$$\frac{639}{729}$$ $$\approx{80}$$
Amount of honey remaining = 639-80 = 559 litres

Step 3:
We again add a=90 litres of water and remove a=90 litres of mixture

Now, the fraction of honey in the 90 litres, will now be even less than 80, so if we were to remove it for 3 more steps, the actual of honey removed will get lower and lower, so no need to even do this calculation.
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8678
Location: Pune, India
Re: From a full tank containing 729 liters of honey, we pour off "a" litre  [#permalink]

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12 Jun 2017, 07:26
2
1
theperfectgentleman wrote:
From a full tank containing 729 liters of honey, we pour off "a" litres and add water to fill up the tank. After stirring the solution thoroughly, we pour off "a" liters of the solution and again add water to fill up the tank. After the procedure is repeated for a total of 6 times, the solution contains 64 liters of honey. Find "a"

A) 243 liters
B) 81 liters
C) 2.7 liters
D) 90 liters

For a quick and easy method of dealing with removal and replacement, check: https://www.veritasprep.com/blog/2012/0 ... -mixtures/

$$Cfinal = Cf1 * [\frac{(729 - a)}{729}]^6$$

$$64/729 = 1 * [\frac{(729 - a)}{729}]^6$$

$$(\frac{2}{3})^6 = [\frac{(729 - a)}{729}]^6$$

$$\frac{2}{3} = \frac{(729 - a)}{729}$$

$$2*243 = 729 - a$$

$$a = 243$$
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Re: From a full tank containing 729 liters of honey, we pour off "a" litre  [#permalink]

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25 Nov 2018, 23:08
Hello from the GMAT Club BumpBot!

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Re: From a full tank containing 729 liters of honey, we pour off "a" litre &nbs [#permalink] 25 Nov 2018, 23:08
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