A can contains a mixture of two liquids A and B in proportion 3:5. Whe GMAT Problem-Solving

Question: A can contains a mixture of two liquids A and B in proportion 3:5. When 16 L of mixture is drawn off and the same quantity of B is added, then the proportion of A and B becomes 1 : 2. How many litres of liquid A was contained by the can initially?

(A) 25 L
(B) 38 L
(C) 45 L
(D) 54 L
(E) 108 L

Answer: D

Solution and Explanation:

Approach Solution 1:
Apply the information in the question to the GMAT question at hand. These problems apply to numerous disciplines of mathematics. This question has to do with basic mathematics. It is challenging to select the best option because of the way the options are presented. Candidates must be able to comprehend the appropriate approach to eliciting the desired response. Out of the five possible answers, there is only one that is correct.
A) Mixture is homogenous throughout the entire replacement process, it should be noted (as its all liquid). Old Blend: - A/B = 3/5
New combination = A/B = half
Old concentration therefore: A=3/8,B=5/8, Volume = 8x
B) Amount of A is unchanged (constant); hence, 3/8 in 8x will become 1/3 once 16 L of B are switched out for pure, melted chocolate.
C) The amount of B is changing (B is being added to change the concentration)
As a result, using the replacement formula, we must use A. (constant)
Ci*Vi = Cf*Vf
3/8 (8x - 16) =1/3 8x
x=144/8
x=18
Initial Volume: 18 * 3 = 54L
Correct option: D

Approach Solution 2:
Apply the information in the question to the GMAT question at hand. These problems apply to numerous disciplines of mathematics. This question has to do with fundamental math. It is challenging to select the best option because of the way the options are presented. Candidates must be able to comprehend the appropriate approach to eliciting the desired response. Out of the five possible answers, there is only one that is correct.
This can be done in a variety of ways. Let's talk about 2 such techniques:
Method 1 (more logical): When the mixture is taken out, the ratio of A to B stays the same. We still have A: B = 3: 5 as a result.
When we now include B, the ratio becomes 1: 2.
But, since we did not alter A while adding B, we must maintain the value for A as is.
As a result, we rewrite the new A: B ratio as 3: 6.
As a result, we can observe that B has grown by 1. Nonetheless, we are aware that this "1" truly stands for 16L.
As a result, A: B = 3: 5 suggests that A Plus B was "8," but in reality, this is 16 x 8 = 128L.
This is after the mixture was drained by 16L.
The initial volume was 128 + 16 = 144L as a result.
Hence, the volume of A is equal to 3/(3+5)*144 = 3*18 = 54L.
Correct option: D

Approach Solution 3:
Apply the information in the question to the GMAT question at hand. These problems apply to numerous disciplines of mathematics. This question has to do with fundamental math. It is challenging to select the best option because of the way the options are presented. Candidates must be able to comprehend the appropriate approach to eliciting the desired response. Out of the five possible answers, there is only one that is correct.
Let initial total = xL
We need to find out 3x/8
After the substitution of 16L,
remaining A = 3(x-16)/8
remaining B = 5(x-16)/8 + 16
the ratio of remaining A and remaining B = ½
Solving for x, x=144
So 3x/8 = 54
Correct option: D

“A can contains a mixture of two liquids A and B in proportion 3:5. Whe" - is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been borrowed from the book “GMAT Official Guide Quantitative Review”.

To understand GMAT Problem Solving questions, applicants must possess fundamental qualitative skills. Quant tests a candidate's aptitude in reasoning and mathematics. The GMAT Quantitative test's problem-solving phase consists of a question and a list of possible responses. By using mathematics to answer the question, the candidate must select the appropriate response. The problem-solving section of the GMAT Quant topic is made up of very complicated math problems that must be solved by using the right math facts.

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