Multiple choice

Directions: This data sufficiency problem consists of a question and two statements labelled (1) and (2). You have to decide whether the data given in the statements is sufficient for answering the question. Find the quantity of milk in 180 L of mixture of milk and water. (1) If 24 L of mixture is replaced by equal quantity of water, then the ratio of milk and water in the mixture becomes 91 : 89. (2) If 12 L of mixture is replaced by equal quantity of milk, then the ratio of milk and water in the mixture becomes 11 : 7.

  1. Statement (1) alone is sufficient, but statement (2) alone is not sufficient.

  2. Statement (2) alone is sufficient, but statement (1) alone is not sufficient.

  3. Both statements (1) and (2) together are sufficient, but neither of them alone is sufficient.

  4. Both the statements alone are sufficient.

  5. Both statements (1) and (2) together are not sufficient.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Both statements provide enough information to set up equations for the initial amounts of milk and water in the 180L mixture. Statement 1 allows solving for the initial ratio, and Statement 2 also allows solving for the initial ratio. Thus, both are independently sufficient.

AI explanation

Let the initial amount of milk be x litres in the 180 litre mixture. Using statement (1), replacing 24 litres removes 24 times x over 180 litres of milk, so the remaining milk is x times the quantity 156 over 180, which equals 91 over 100 of the 180 litre total, giving x as 105 litres. Using statement (2), adding 12 litres of milk and removing 12 litres of the mixture means the final milk is x times 168 over 180 plus 12, which equals 11 over 18 of the 180 litre total, also resulting in x as 105 litres. Both statements independently provide a solvable linear equation for the exact milk quantity.

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