Multiple choice

Directions: In this problem, a question is given followed by three statements numbered (I), (II) and (III). Read the statements carefully and determine which of them is/are sufficient/necessary to answer the question. In a solution of milk and water, what is the quantity of milk? I. Ratio of milk to water in the solution is 5 : 3. II. If we replace 40 L of solution with water, ratio of milk to water will become 5 : 11. III. Adding 10 L of milk and 10 L of water to the solution makes the ratio of milk to water 3 : 2.

  1. Only statements I and II

  2. Only statements II and III

  3. Any two of the statements

  4. All three statements

  5. Only statement I and either statement II or statement III
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

I gives the ratio. II allows setting up an equation with the 40L replacement to find the total volume. III allows setting up an equation with the additions to find the total volume. Any two statements are sufficient to solve for the specific quantity of milk.

AI explanation

We can solve this using any two of the three statements because each pair of statements provides exactly two independent equations with two variables. For example, if we let milk be 5x and water be 3x based on statement I, statement III gives the equation (5x plus 10) divided by (3x plus 10) equals 3/2, which solves to x equals 10 and yields the milk quantity. Similarly, combining statement I and statement II gives the equation (5x minus 25) divided by (3x minus 15 plus 40) equals 5/11, which also solves to x equals 10. Even combining II and III sets up two linear equations that uniquely determine the initial milk and water volumes.

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