Multiple choice

Directions: The following problem consists of a question followed by three statements (I), (II) and (III). You have to determine which statement(s) is/are sufficient/necessary to answer the question. A solution contains alcohol and water. What is the quantity of water in the solution? I. The ratio of alcohol to water in the solution is 1 : 2. II. If 150 ml of solution is replaced with alcohol, then the ratio of alcohol to water becomes 2 : 1. III. If 100 ml of soda is added to the solution, then the ratio of alcohol to solution becomes 1 : 4.

  1. Only I and II

  2. Only I and either II or III

  3. Only II and either I or III

  4. Any two statements

  5. All three statements
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Statement I gives the ratio, but not the total quantity. Statement II allows calculating the total quantity by setting up an equation with the change in ratio. Statement III also allows calculating the total quantity. Thus, I and either II or III are sufficient.

AI explanation

Statement I provides the initial ratio, and either statement II or III provides a second condition that can be solved to find the absolute quantities. For example, using I and II, if the initial quantities are x and 2x, removing 150 ml of solution removes 50 ml of alcohol and 100 ml of water. Adding 150 ml of alcohol makes the new ratio (x - 50 + 150) to (2x - 100) equal to 2:1, which yields x = 150 and the quantity of water as 300 ml. Statement III similarly introduces a fixed volume change that allows solving for x. Therefore, the quantity of water can be found using Only I and either II or III.

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