Test: Mixture Problems - GMAT MCQ

Statement (1): There are a total of 15 cups in the mixture.
From this statement alone, we cannot determine the specific amounts of flaxseed and cornmeal in the mixture. It only provides the total quantity, but not the ratio or specific amounts of each ingredient. Statement (1) alone is not sufficient.

Statement (2): The ratio of the number of cups of flaxseed to the total number of cups in the mixture is 1 to 5.
From this statement alone, we know that the ratio of flaxseed to the total mixture is 1:5. However, we still don't have the specific total quantity of the mixture. Without knowing the total cups in the mixture, we cannot determine the exact amount of flaxseed. Statement (2) alone is not sufficient.

Combining both statements, we have the following information:

• The total quantity is 15 cups (Statement 1).
• The ratio of flaxseed to the total mixture is 1:5 (Statement 2).

Using this information, we can determine the amounts of flaxseed and cornmeal in the mixture. Since the ratio of flaxseed to the total mixture is 1:5, we can calculate that the amount of flaxseed is (1/6) * 15 = 2.5 cups. Therefore, both statements together are sufficient to answer the question.

Hence, the correct answer is (C) BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient.

Statement (1): When 2 liters of milk is added to the mixture, the resultant mixture has equal quantities of milk and water.
From this statement alone, we know that when 2 liters of milk is added, the resulting mixture has equal quantities of milk and water. However, we don't have any information about the initial quantities or proportions of milk and water in the mixture. Statement (1) alone is not sufficient.

Statement (2): The initial mixture had 2 parts of water to 1 part milk.
From this statement alone, we know the initial ratio of water to milk in the mixture. However, we don't have any information about the actual volumes or quantities of the mixture. Statement (2) alone is not sufficient.

Combining both statements, we have the following information:

When 2 liters of milk is added, the resulting mixture has equal quantities of milk and water (Statement 1).
The initial mixture had a ratio of 2 parts water to 1 part milk (Statement 2).
Using this information, we can determine the volume of milk in the mixture. Since the resultant mixture has equal quantities of milk and water when 2 liters of milk is added, we can infer that the initial mixture had 2 liters of water and 1 liter of milk. Therefore, the volume of milk in the mixture is 1 liter.

Hence, the correct answer is (C) BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient.

Statement (1): The granola mixture is packaged in one-pound bags.
From this statement alone, we know that the granola mixture is packaged in one-pound bags. However, we don't have any information about the proportion or ratio of oats to raisins in the mixture or the total weight of the mixture. Statement (1) alone is not sufficient.

Statement (2): Oats cost $1.00 per pound.
From this statement alone, we know the cost per pound of oats. Since we are told that the granola mixture costs $2.00 per pound, and the raisins cost $3.50 per pound, we can deduce that the oats constitute the difference in cost between the granola mixture and the raisins. Therefore, for every pound of oats added, the cost of the mixture decreases by $1.50 per pound. With this information, we can calculate the number of pounds of oats needed to balance the cost.

Since 10 pounds of raisins are used and the cost difference is $1.50 per pound, the total cost difference for the 10 pounds of raisins is $1.50 * 10 = $15.00. Since oats cost $1.00 per pound, the number of pounds of oats needed to balance the cost is $15.00 / $1.00 = 15 pounds.

Hence, statement (2) alone is sufficient to answer the question, but statement (1) alone is not sufficient. Therefore, the correct answer is (B).

Statement (1): Brand X cat food consists of 35 percent fat.
Statement (2): Brand Y cat food consists of 11 percent fat.

From Statement (1), we know the fat content of Brand X cat food. From Statement (2), we know the fat content of Brand Y cat food. In order to determine the amount of Brand X cat food in the mixture, we need to consider the fat content and weight of both brands.

Let's assume that Sergio feeds x grams of Brand X cat food and y grams of Brand Y cat food. We are given that the total mixture weighs 500 grams and contains 103 grams of fat.

From Statement (1), we can write the equation: 0.35x = (35/100)x grams of fat from Brand X cat food.
From Statement (2), we can write the equation: 0.11y = (11/100)y grams of fat from Brand Y cat food.

Since the cat consumes 103 grams of fat per day, we have the equation: (35/100)x + (11/100)y = 103.

Combining these equations, we have a system of two equations with two variables:
(35/100)x + (11/100)y = 103,
x + y = 500.

With these equations, we can solve for x, the amount of Brand X cat food in grams.

Therefore, BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient.