Test: Min/Max Problems - GMAT MCQ

Statement (1): There are 50 grams of the 35%-solution. This statement provides information about the initial amount of the 35%-solution. We know the concentration (35%) and the quantity (50 grams). From this information, we can calculate the amount of acid in the solution (35% of 50 grams) and determine the amount of water in the solution (100% - 35% of 50 grams). With this information, we can calculate how much water should be added to obtain a 10%-solution.

Statement (2): In the 35%-solution, the ratio of acid to water is 7:13. This statement provides information about the ratio of acid to water in the 35%-solution. However, it does not give us any information about the quantity or concentration of the solution. Without knowing the amount or concentration of the solution, we cannot determine the amount of water needed to obtain a 10%-solution.

When we consider both statements together, we know the initial amount of the 35%-solution (50 grams) from Statement (1) and the ratio of acid to water in the solution from Statement (2). With this information, we can calculate the amount of acid and water in the initial solution. However, we still don't have enough information to determine how much water should be added to obtain a 10%-solution. We need to know the desired quantity or final concentration of the solution.

Therefore, Statement (1) alone is sufficient to answer the question, but Statement (2) alone is not sufficient. The correct answer is option A: Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.

Statement (1): After the second drink is poured in, 40% of the entire beverage is juice.
This statement tells us the proportion of juice in the final mixture. Since we know the initial amounts of soda and juice in the first drink (7 oz. of soda and 3 oz. of juice), we can determine the total amount of liquid in the final mixture. If 40% of the final beverage is juice, then the remaining 60% must be soda. Therefore, the ratio of soda to juice in the final mixture is 60:40, which simplifies to 3:2. With this information, we can determine the amount of liquid poured into the first drink.

Statement (2): 30% of the second drink was soda.
This statement provides information about the composition of the second drink. However, it does not give us any information about the overall composition of the final mixture when it is poured into the first drink. Without knowing the proportions of soda and juice in the second drink, we cannot determine the amount of liquid poured in.

When we consider both statements together, we have information about the proportion of juice in the final mixture (40%) and the proportion of soda in the second drink (30%). Since both statements provide independent information about the composition of the final mixture and the second drink, we can use them together to determine the amount of liquid poured in.

Therefore, both statements together are sufficient to answer the question, but neither statement alone is sufficient. The correct answer is option C: BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient.

Statement (1) tells us that the recipe calls for a mixture that includes 60% brand A. Since the pitcher is currently filled with equal amounts of brands A and B, it means that each brand currently constitutes 50% of the mixture. To conform to the recipe, we need to add more brand A to reach a 60% concentration. Since we know the initial volume of the pitcher is 30 ounces, we can calculate the additional amount of brand A needed.

Statement (1) alone is sufficient to answer the question.

Statement (2) tells us that when filled to capacity, the pitcher contains 12 ounces of brand B. However, this statement does not provide any information about brand A or the proportions between the two brands. Therefore, statement (2) alone is not sufficient to answer the question.

When we consider both statements together, we have information about the target concentration of brand A (60%) and the volume of brand B in the pitcher (12 ounces). With this information, we can determine the amount of brand A required to achieve the desired mixture. Therefore, both statements together are sufficient to answer the question.

Hence, the correct answer is (D) EACH statement ALONE is sufficient to answer the question asked.

Statement (1) tells us that before adding more vinegar, vinegar made up 20% of the mixture. However, it does not provide any information about the initial amount of the mixture or the amount of vinegar added. Therefore, statement (1) alone is not sufficient to answer the question.

Statement (2) tells us that after adding more vinegar, vinegar made up 35% of the mixture. Again, this statement does not give us any information about the initial amount of the mixture or the amount of vinegar added. Hence, statement (2) alone is also not sufficient to answer the question.

When we consider both statements together, we still do not have enough information to determine the amount of vinegar added. We need additional data about the initial amount of the mixture or the specific quantities involved. Therefore, when considering both statements together, they are still not sufficient to answer the question.

Therefore, the correct answer is (E) Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.

Statement (1) alone: After adding water, water made up fifteen percent of the mixture.

Statement (1) tells us the proportion of water in the mixture after adding water, which is fifteen percent. However, it doesn't provide any information about the initial composition of the mixture or the amount of water originally present. Without knowing the initial composition, we cannot determine the amount of water added to the mixture. Therefore, statement (1) alone is not sufficient to answer the question.

Statement (2) alone: Before adding water, water made up ten percent of the mixture.

Statement (2) provides information about the proportion of water in the mixture before adding water, which is ten percent. However, it doesn't give us any information about the final composition or the amount of water added. Without knowing the change in composition or the specific quantities involved, we cannot determine the amount of water added to the mixture. Therefore, statement (2) alone is not sufficient to answer the question.

Combining both statements:

By combining the statements, we know that before adding water, water made up ten percent of the mixture (statement 2), and after adding water, water made up fifteen percent of the mixture (statement 1). However, this information alone does not provide enough information to determine the amount of water added to the mixture. We need additional data such as the total volume or quantity of the mixture to make that determination.

Since statements (1) and (2) together are not sufficient to answer the question and additional data are needed, the correct answer is (E): Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.

Given
Jar 1 - 30% Nitric acid & 70% water
Jar 2 - 60% Nitric acid & 40% water.
Quantity of Jar 2 = 100ml
Quantity of Jar 1 = X ml
No info in prompt about intended solution S.
Lets look at St.1 Alone
Intended Solution S = 40% Nitric acid & 60% water.
Quantity of Solution S = (100+X) ml
Hence Quantity of Nitric acid = Quantity of Nitric acid in Jar 1 + Quantity of Nitric acid in Jar 2
40%*(100+X) = 30% of X + 60% of 100
Equation in single unknown, solving which we can deduce Quantity of Jar 1 hence, statement 1 is Sufficient.
Statement 2 Alone
When similar quantities of Solution S & Jar 1 are taken, the Nitric acid quantity in Solution 4/3 times of Nitric acid in Jar 1.
which means, if 100 ml of Solution S & Jar 1 are taken,
Quantity of Nitric acid in Jar 1 is 30% of 100 ml = 30ml
Therefore, Quantity of Nitric acid in Solution S = 4/3*(30) = 40 ml
Hence Solution S contains 40% Nitric acid & 60% water.
Which is similar to info provided in St.1, solving which we can deduce Quantity of Jar 1. Statement 2 is Sufficient.
Statement 1 & Statement alone are Sufficient.

Statement (1) alone: It will take 300 quarts of paint to cover the house.

Statement (1) provides information about the total amount of paint required to cover the house, which is 300 quarts. However, it doesn't give us any specific information about the composition or proportions of the turquoise color. Without knowing the proportions or quantities of the primer and the blue base coat, we cannot determine how many quarts of the blue base coat should be mixed. Therefore, statement (1) alone is not sufficient to answer the question.

Statement (2) alone: The blue base coat is made up of 90% pure-white color.

Statement (2) gives us information about the composition of the blue base coat, stating that it is made up of 90% pure-white color. However, it doesn't provide any information about the proportion of the blue base coat to be mixed with the primer or the resulting color composition. Without knowing the proportion of the blue base coat in the mixture or the desired percentage of pure-white color in the turquoise, we cannot determine the number of quarts needed. Therefore, statement (2) alone is not sufficient to answer the question.

Combining both statements:

Together, we know that it will take 300 quarts of paint to cover the house (statement 1) and that the blue base coat is made up of 90% pure-white color (statement 2). However, we still don't have enough information to determine the number of quarts from the blue base coat that should be mixed to make enough turquoise to paint the house. We need information about the composition of the primer and the specific proportion of the blue base coat to be mixed.

Since neither statement alone is sufficient to answer the question, but together they provide some useful information, 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) alone: The mixture originally has 40% beans and 60% pulses.

Statement (1) provides the initial composition of the mixture, stating that it contains 40% beans and 60% pulses. However, it does not give any information about the quantity or size of the mixture. Therefore, statement (1) alone is not sufficient to answer the question.

Statement (2) alone: The total quantity of the mixture is 20 lb.

Statement (2) gives us the total quantity of the mixture, which is 20 lb. However, it doesn't provide any information about the composition or percentage of beans and pulses in the mixture. Without knowing the initial composition, we cannot determine the required percentage of the mixture to be replaced with pulses. Therefore, statement (2) alone is not sufficient to answer the question.

Combining both statements:

Together, we know that the mixture originally has 40% beans and 60% pulses, and the total quantity of the mixture is 20 lb. However, we still don't have enough information to determine the exact percentage of the mixture that needs to be replaced with pulses to achieve 20% beans. We need to know the current quantity of beans and pulses in the mixture to make this determination.

Since neither statement alone is sufficient to answer the question, but together they provide some useful information, the correct answer is (C): BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient.

Let's analyze the statements:

Statement (1) alone: X = Y

If X = Y, it means that an equal volume of solution is taken from bottles A and B. Since bottle A has a 1:3 alcohol-water ratio and bottle B has a 4:1 ratio, the resulting mixture will have equal amounts of alcohol and water. Therefore, the percentage of alcohol in the resultant solution will be 50%.

Statement (1) alone is sufficient to answer the question.

Statement (2) alone: Total 10 liters of solutions from bottles A and B are mixed.

From statement (2) alone, we know the total volume of the mixture is 10 liters. However, we don't have any information about the specific volumes of solution X and Y taken from bottles A and B. Without knowing the individual quantities mixed, we cannot determine the percentage of alcohol in the resultant solution.

Statement (2) alone is not sufficient to answer the question.

Combining both statements:

From statement (1), we know that X = Y. However, we still don't have any information about the specific values of X and Y.

From statement (2), we know the total volume of the mixture is 10 liters.

Even when considering both statements together, we still don't have enough information to determine the values of X and Y or the respective quantities of alcohol and water in the resultant solution. Therefore, statements (1) and (2) together are not sufficient to answer the question.

The correct answer is (A): Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.

Statement (1) says that on combining bonds of type A and type C, the average value per bond is $4000.

Statement (2) says that on combining bonds of type B and type C, the average value per bond is $5200.

Let's examine each statement individually:

Statement (1) alone: If we combine bonds of type A and type C to achieve an average value per bond of $4000, it implies that the number of type A bonds is equal to the number of type C bonds. However, this statement doesn't provide any information about type B bonds, so it alone is not sufficient to answer the question.

Statement (2) alone: If we combine bonds of type B and type C to achieve an average value per bond of $5200, it doesn't provide any information about type A bonds. Therefore, this statement alone is not sufficient to answer the question.

Since neither statement alone is sufficient, let's consider both statements together:

Combining both statements, we know that the average value per bond when combining A and C is $4000, and the average value per bond when combining B and C is $5200. However, we still don't have enough information to determine the exact number of each type of bond. Therefore, both statements together are not sufficient to answer the question.

Based on the analysis above, the correct answer is:

E: Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.