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13 Oct 2020, 10:41
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
52% (02:31) correct
48%
(03:15)
wrong
based on 179
sessions
History
Date
Time
Result
Not Attempted Yet
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
A. 7 gallons
B. 14 gallons
C. 21 gallons
D. 28 gallons
E. 35 gallons
14 Oct 2020, 03:15
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tanu11
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
14 Oct 2020, 09:22
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tanu11
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.
