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tanu11
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Raman steals four gallons of liquid soap kept in a train compartment
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13 Oct 2020, 09:41
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Difficulty:

95% (hard)

Question Stats:

51% (02:32) correct 49% (03:10) wrong based on 194 sessions

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Raman steals four gallons of liquid soap kept in a train compartment bathroom from a container that is full of liquid soap. He then fills it with water to avoid detection. unable to resist his temptation he steals 4 gallon of the mixture again. When the liquid soap is check at the station it is found that the ratio of liquid soap now left in the container to that of the water is 36:13. What was the initial amount of liquid soap in the container if it is know that the liquid is neither used nor augmented by anybody else during the entire period ?

A. 7 gallons

B. 14 gallons

C. 21 gallons

D. 28 gallons

E. 35 gallons
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Raman steals four gallons of liquid soap kept in a train compartment
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14 Oct 2020, 02:15
tanu11
Raman steals four gallons of liquid soap kept in a train compartment bathroom from a container that is full of liquid soap. He then fills it with water to avoid detection.
unable to resist his temptation he steals 4 gallon of the mixture again. When the liquid soap is check at the station it is found that the ratio of liquid soap now left in the container to that of the water is 36:13. What was the initial amount of liquid soap in the container if it is know that the liquid is neither used nor augmented by anybody else during the entire period ?

A. 7 gallons
B. 14 gallons
C. 21 gallons
D. 28 gallons
E. 35 gallons
Show more



Let us use the Equation for removal and replacement.

\(\frac{Final \space Quantity}{Initial \space Quantity}= (1 - \frac{Volume \space replaced}{Final \space Volume \space after \space replacement})^n\)


Final quantity and initial quantity is for that component who's concentration is reducing.


n is the number of times the process is repeated. The other terms are self explanatory.


Let the initial quantity of the liquid soap = x

Final quantity = \(\frac{36}{49} * x\) (Since the final ratio is 36 : 13)


Therefore \(\frac{\frac{36x}{49}}{x} = (1 - \frac{4}{x})^2\)


Taking the square root on both sides

\(\frac{6}{7}= 1 - \frac{4}{x}\)

\(\frac{4}{x}= 1 - \frac{6}{7}= \frac{1}{7}\)

x = 28 gallons


Option D

Arun Kumar
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Raman steals four gallons of liquid soap kept in a train compartment
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14 Oct 2020, 08:22
tanu11
Raman steals four gallons of liquid soap kept in a train compartment bathroom from a container that is full of liquid soap. He then fills it with water to avoid detection.
unable to resist his temptation he steals 4 gallon of the mixture again. When the liquid soap is check at the station it is found that the ratio of liquid soap now left in the container to that of the water is 36:13. What was the initial amount of liquid soap in the container if it is know that the liquid is neither used nor augmented by anybody else during the entire period ?

A. 7 gallons
B. 14 gallons
C. 21 gallons
D. 28 gallons
E. 35 gallons
Show more

What is the source? You can instantly tell it's not credible once it says "unable to resist his temptation". GMAT questions don't provide character motivations; they aren't writing novels. There are several other issues with the language I won't bother to mention.

But I will mention the disastrous problem with the wording, highlighted above: the question doesn't bother to tell us that Raman refills the soap dispenser with water the second time he takes soap. That's what the question intends, but it would be patently incorrect to assume that Raman refills the soap dispenser twice if the question only says he does it once. So interpreting the question as it's actually written, when he steals soap mixture the second time, he won't change the ratio of soap to water. So 36 to 13 is thus the ratio of soap to water after he replaces soap with water the first time. Since he actually introduced 4 gallons of water, the actual numbers here are 4/13 as big as the numbers in the ratio, and since we have 36+13 = 49 parts in total in our ratio, the actual total quantity in the dispenser must be (4/13)(49), or roughly 15 gallons.

From the answer choices, that's clearly not what the question designer had in mind. The question means to say that Raman replaced the soap he removed with water each time. Especially with these numbers, that's not a GMAT question, and you'd certainly never need to know a formula to answer that kind of problem. You can work out how the concentration of pure soap changes conceptually, but there's no reason for GMAT test takers to bother thinking about that since it won't ever be relevant on the test. Here I'd probably just estimate: the final mixture is still mostly soap. We've introduced nearly 8 gallons of water into it (4 gallons of pure water the first time, and nearly 4 gallons the second time, since the second time some of what is removed is water). If the ratio of soap to water at the end in 36 to 13, then the ratio of the total amount to water is 49 to 13. So the total amount is (49/13) times the amount of water. If the amount of water is a bit less than 8, the total amount is a bit less than (49/13)(8), which is roughly 30, so 28 is the only plausible answer.

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tanu11
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Raman steals four gallons of liquid soap kept in a train compartment
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14 Oct 2020, 08:25
IanStewart
tanu11
Raman steals four gallons of liquid soap kept in a train compartment bathroom from a container that is full of liquid soap. He then fills it with water to avoid detection.
unable to resist his temptation he steals 4 gallon of the mixture again. When the liquid soap is check at the station it is found that the ratio of liquid soap now left in the container to that of the water is 36:13. What was the initial amount of liquid soap in the container if it is know that the liquid is neither used nor augmented by anybody else during the entire period ?

A. 7 gallons
B. 14 gallons
C. 21 gallons
D. 28 gallons
E. 35 gallons

What is the source? You can instantly tell it's not credible once it says "unable to resist his temptation". GMAT questions don't provide character motivations; they aren't writing novels. There are several other issues with the language I won't bother to mention.

But I will mention the disastrous problem with the wording, highlighted above: the question doesn't bother to tell us that Raman refills the soap dispenser with water the second time he takes soap. That's what the question intends, but it would be patently incorrect to assume that Raman refills the soap dispenser twice if the question only says he does it once. So interpreting the question as it's actually written, when he steals soap mixture the second time, he won't change the ratio of soap to water. So 36 to 13 is thus the ratio of soap to water after he replaces soap with water the first time. Since he actually introduced 4 gallons of water, the actual numbers here are 4/13 as big as the numbers in the ratio, and since we have 36+13 = 49 parts in total in our ratio, the actual total quantity in the dispenser must be (4/13)(49), or roughly 15 gallons.

From the answer choices, that's clearly not what the question designer had in mind. The question means to say that Raman replaced the soap he removed with water each time. Especially with these numbers, that's not a GMAT question, and you'd certainly never need to know a formula to answer that kind of problem. You can work out how the concentration of pure soap changes conceptually, but there's no reason for GMAT test takers to bother thinking about that since it won't ever be relevant on the test. Here I'd probably just estimate: the final mixture is still mostly soap. We've introduced nearly 8 gallons of water into it (4 gallons of pure water the first time, and nearly 4 gallons the second time, since the second time some of what is removed is water). If the ratio of soap to water at the end in 36 to 13, then the ratio of the total amount to water is 49 to 13. So the total amount is (49/13) times the amount of water. If the amount of water is a bit less than 8, the total amount is a bit less than (49/13)(8), which is roughly 30, so 28 is the only plausible answer.
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it is from Mc Graw hill
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Raman steals four gallons of liquid soap kept in a train compartment
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07 Dec 2024, 08:13
ow i
CrackverbalGMAT
tanu11
Raman steals four gallons of liquid soap kept in a train compartment bathroom from a container that is full of liquid soap. He then fills it with water to avoid detection.
unable to resist his temptation he steals 4 gallon of the mixture again. When the liquid soap is check at the station it is found that the ratio of liquid soap now left in the container to that of the water is 36:13. What was the initial amount of liquid soap in the container if it is know that the liquid is neither used nor augmented by anybody else during the entire period ?

A. 7 gallons
B. 14 gallons
C. 21 gallons
D. 28 gallons
E. 35 gallons



Let us use the Equation for removal and replacement.

\(\frac{Final \space Quantity}{Initial \space Quantity}= (1 - \frac{Volume \space replaced}{Final \space Volume \space after \space replacement})^n\)


Final quantity and initial quantity is for that component who's concentration is reducing.


n is the number of times the process is repeated. The other terms are self explanatory.


Let the initial quantity of the liquid soap = x

Final quantity = \(\frac{36}{49} * x\) (Since the final ratio is 36 : 13)


Therefore \(\frac{\frac{36x}{49}}{x} = (1 - \frac{4}{x})^2\)


Taking the square root on both sides

\(\frac{6}{7}= 1 - \frac{4}{x}\)

\(\frac{4}{x}= 1 - \frac{6}{7}= \frac{1}{7}\)

x = 28 gallons


Option D

Arun Kumar
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how is
Final Volume after replacement x shouldn't it be 36/49
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Raman steals four gallons of liquid soap kept in a train compartment
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07 Dec 2024, 08:16
Poojashah1012
I am unable to understand solution. how did we arrive at 36/49 ratio
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the ratio at the end is 36:13 36 parts is soap and 13 parts being water therefore the total is 36+13 =49 parts
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Raman steals four gallons of liquid soap kept in a train compartment
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19 Jun 2025, 22:41
CrackverbalGMAT
tanu11
Raman steals four gallons of liquid soap kept in a train compartment bathroom from a container that is full of liquid soap. He then fills it with water to avoid detection.
unable to resist his temptation he steals 4 gallon of the mixture again. When the liquid soap is check at the station it is found that the ratio of liquid soap now left in the container to that of the water is 36:13. What was the initial amount of liquid soap in the container if it is know that the liquid is neither used nor augmented by anybody else during the entire period ?

A. 7 gallons
B. 14 gallons
C. 21 gallons
D. 28 gallons
E. 35 gallons



Let us use the Equation for removal and replacement.

\(\frac{Final \space Quantity}{Initial \space Quantity}= (1 - \frac{Volume \space replaced}{Final \space Volume \space after \space replacement})^n\)


Final quantity and initial quantity is for that component who's concentration is reducing.


n is the number of times the process is repeated. The other terms are self explanatory.


Let the initial quantity of the liquid soap = x

Final quantity = \(\frac{36}{49} * x\) (Since the final ratio is 36 : 13)


Therefore \(\frac{\frac{36x}{49}}{x} = (1 - \frac{4}{x})^2\)


Taking the square root on both sides

\(\frac{6}{7}= 1 - \frac{4}{x}\)

\(\frac{4}{x}= 1 - \frac{6}{7}= \frac{1}{7}\)

x = 28 gallons


Option D

Arun Kumar
Show more
I agree the question is poorly written, but still lets understand that the replacement happened twice.
Now where do I exactly go wrong when I say let the final quantity of soap be 36x and hence the initial quantity 49x.

The equation on the left hand side remains same 36/49 but on the right hand side it changes to [1-(4/49x)]^2

Please help HarshavardhanR
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Raman steals four gallons of liquid soap kept in a train compartment
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19 Jun 2025, 23:52
Hey Rohit,

Sure. I can help with this.

Between what you have done and the solution you have highlighted, the only difference is the definition of "x".

Short Answer: Your method also works, if done correctly. I will show you how!


In the highlighted solution ->

Initial quantity of soap = x
Final quantity of soap after 2 rounds of replacement = (36/49) * x (because the final mixture contains soap/water in 36:13 ratio)

Using the formula (hope you are clear about why it works!)

(x)*(1 - 4/x)^2 = (36/49)*x

=> x = initial quantity = 28 gallons.

Using your definition of x ->

x -> multiplication factor for the ratio 36:13

So,

Final volume of soap = 36x
Final total volume = 49x = initial volume of soap.

Using the same formula

(49x)*(1 - 4/49x)^2 = 36x

=> (1 - 4/49x) = 6/7
=> 4/49x = 1/7
=> x = 4/7

This x is your multiplication factor.

So, what is the initial quantity of soap?

49x = 49 x 4/7 = 7 x 4 = 28 gallons.

Hope this helps.

---
Harsha



Rohit_842
CrackverbalGMAT
tanu11
Raman steals four gallons of liquid soap kept in a train compartment bathroom from a container that is full of liquid soap. He then fills it with water to avoid detection.
unable to resist his temptation he steals 4 gallon of the mixture again. When the liquid soap is check at the station it is found that the ratio of liquid soap now left in the container to that of the water is 36:13. What was the initial amount of liquid soap in the container if it is know that the liquid is neither used nor augmented by anybody else during the entire period ?

A. 7 gallons
B. 14 gallons
C. 21 gallons
D. 28 gallons
E. 35 gallons



Let us use the Equation for removal and replacement.

\(\frac{Final \space Quantity}{Initial \space Quantity}= (1 - \frac{Volume \space replaced}{Final \space Volume \space after \space replacement})^n\)


Final quantity and initial quantity is for that component who's concentration is reducing.


n is the number of times the process is repeated. The other terms are self explanatory.


Let the initial quantity of the liquid soap = x

Final quantity = \(\frac{36}{49} * x\) (Since the final ratio is 36 : 13)


Therefore \(\frac{\frac{36x}{49}}{x} = (1 - \frac{4}{x})^2\)


Taking the square root on both sides

\(\frac{6}{7}= 1 - \frac{4}{x}\)

\(\frac{4}{x}= 1 - \frac{6}{7}= \frac{1}{7}\)

x = 28 gallons


Option D

Arun Kumar
I agree the question is poorly written, but still lets understand that the replacement happened twice.
Now where do I exactly go wrong when I say let the final quantity of soap be 36x and hence the initial quantity 49x.

The equation on the left hand side remains same 36/49 but on the right hand side it changes to [1-(4/49x)]^2

Please help HarshavardhanR
Show more

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