Question: How many liters of pure alcohol must be added to a 90-liter solution that is 20 percent alcohol in order to produce a solution that is 25 percent alcohol?

(A) 4.5
(B) 5.0
(C) 5.5
(D) 6.0
(E) 6.5

“How many liters of pure alcohol must be added to a 90-liter solution”- is a topic of the GMAT Quantitative reasoning section of GMAT. GMAT quant helps to improve the mathematical knowledge of the students. The student should pick the valid option by verifying with proper concepts on the basis of mathematical calculations. The students must possess better qualitative skills in order to solve GMAT Problem Solving questions. The GMAT Quant topic in the problem-solving part cites mathematical problems that can be decoded only by mathematical calculations. The candidates can brush up their knowledge by practising questions from the “GMAT Official Guide Quantitative Review”.

Solution and Explanation:

Approach Solution 1:

The problem statement suggests that

Given:

• 90-liter solution contains 20 percent alcohol

Find out:

• The quantity of pure alcohol to be added in order to make it 25 percent alcohol

As per the question, 90 liters of solution contains 20% alcohol.

Amount of water for 18 litres of alcohol = 72 liters

In order to make the solution to includes 25% alcohol, we have to add pure alcohol.
Let’s assume the quantity of pure alcohol added is x liters.

Therefore, we can say,
(18+x)/72 = 1/3
54 + 3x = 72
3x = 18

Therefore, x = 6

Thus, the amount of pure alcohol to be added to the solution will be 6 liters.

Hence, D is the correct answer.

Approach Solution 2:

The problem statement indicates that

Given:

• 90-liter solution contains 20 percent alcohol

Asked:

• To find the amount of pure alcohol to be added to make it 25 percent alcohol

The quantity of alcohol in the 90 liters solution is 90*1/5 =18 litres (since 20% alcohol is present in 90 liters solution, that is 20/100= 1/5)

We must add a certain amount of pure alcohol to the solution to make 25% of alcohol.

We can verify the question by using the answer choice D as it cites an easy number to consider the question.
From D, if 6 litres of alcohol is added to the solution, the quantity of alcohol will be = 18+6=24 litres

Therefore, the percent of alcohol will be = 24/(90+6) = 24/96 = 1/4 = 25%

Therefore, option D is the correct answer since it justifies the claim of the question.

Approach Solution 3:

The problem statement indicates that

Given:

• 90-liter solution contains 20 percent alcohol

Asked:

• To find the quantity of pure alcohol to be added to make it 25 percent alcohol

Let's assume the amount of alcohol to be added is x

20% alcohol is present in 90 liters of solution. A certain amount of pure alcohol needs to be added to the solution to make it 25% alcohol.
Therefore we can say,
(.20)90 + (1)x =.25(90+x)
=>18 + x = 22.5 +.25x
=>.75x = 4.5
=> 3/4 x= 9/2
=> x= 9/2 ∗ 4/3

Therefore the value of x will be 6.
Thus the amount of pure alcohol to be added to the solution will be 6 liters.

Hence, D is the correct answer.

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