A bartender mixes drink A with drink B. If drink A contains 24 percent alcohol, what percentage of the mixture of drink A and B is alcohol?

(1) The ratio of drink A and drink B is 1:4 (2) The alcohol concentration of drink B is 1.5 times greater than the alcohol concentration of drink A.

A .Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not. B. Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not. C. Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient. D. Either statement BY ITSELF is sufficient to answer the question. E. Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, meaning that further information would be needed to answer the question.

(C) Statement (1) gives us the quantity of each of the drinks in the new cocktail. Statement (2) gives us the connection between the alcohol concentration of Drink B and the mixed cocktail. To solve this question, try using the statements and see what happens.

Let us use the statement (1) by itself. If the ratio of A to B is 1:4, then there is one part A to 4 parts B. This means if there are five parts total, one part is A and 4 parts are B, or 1/5 is A and 4/5 is B. A = .2 and B = .8. This information doesn’t tell us enough to solve the question because we don’t know the alcohol concentration of drink B. Statement (1) is not sufficient (meaning choices A and D can be ruled out). Let us use the statement (2) by itself. It tells us the concentration in drink B. It is 1.5 times greater than drink A. The concentration is drink A is 24%, therefore the concentration in drink B = .24 × 1.5 = .36 (36%) alcohol. This information doesn’t tell us enough to solve the question because we don’t know the quantity of each drink in the new cocktail. Statement (2) is not sufficient (meaning choice B can be ruled out). If we use the both statements together, we can set up an equation for this, using the following amounts: Suppose the new mixture is 1. Then Alcohol in Drink A = .24 × .2, Alcohol in Drink B = .36 × .8. We can get the percentage of alcohol in the new mixture: (.048 + .288) / 1 = .336 (33.6%). Since we required both statements to answer this question, the correct answer is (C). ----------

Can you send the steps to the answer for this question?

In brief, we use the general method for solving data sufficiency questions:

1. Use statement (1) alone. Analyse. Is it sufficient BY ITSELF? 2. Use statement (2) alone. Analyse. Is it sufficient BY ITSELF? Are the BOTH statements sufficient? If no, then the third step: 3. Use the both statements combined. Analyse. Are they sufficient together? CONCLUDE.

There are two shortcuts along the way: 1. The fastest way to prove (to be sure) that some data is insufficient is to provide (construct) 2 options that comply with data but yield different results. ("different" - in means of answering a given question).

2. In order to see that data is sufficient you do NOT need to solve the question all the way, but you need to be 100% sure that the question can be answered unambiguously.

The analysis of this particular question is the following:

1. What information does the basic statement tell us? drink A contains 24 percent alcohol

2. Let's try using statement (1) by itself. (1) The ratio of drink A and drink B is 1:4 If we denote the volume of drink A in the mixture by x, then there are 4x units of drink B in the mixutre. Suppose, the concentration of alcohol in the drink B is b, then the concentration in the mixture is: (0.24x + b × 4x) / (5x) = (0.24 + 4b) / 5 Different values of b yield different values of alcohol concentration in the mixture, etc. If b = 24%, then the mixture contains 24% as well. If b = 4%, then the mixture contains 8% alcohol. So the first statement by itself is NOT sufficient.

3. Let's try using statement (2) by itself. (2) The alcohol concentration of drink B is 1.5 times greater than the alcohol concentration of drink A. Therefore the alcohol concentration of drink B is 24% × 1.5 = 36%. Let's denote the volume of drink A in the mixture by x and the volume of drink B in the mixture by y. Then the concentration in the mixture is the following: (0.24x + 0.36y) / (x + y) = 0.24(x + y) / (x + y) + 0.12y / (x + y) = 0.24 + 0.12 × y/(x + y) Different values of y/(x + y) yield different values of alcohol concentration in the mix, etc. If x = y = 1, then the mixture contains 30% alcohol. If x = 1, y = 3, then the mixture contains 27% alcohol. So statement (2) by itself is NOT sufficient.

4. Let's try the both statements together. The first one implies that the concentration in the mixture is: (0.24 + 4b) / 5 The second one implies that b = 36%. So the concentration is: (0.24 + 4 × 0.36)/5 This is some DEFINITE value, that we do NOT need to calculate. Therefore the both statements used together are sufficient. The correct answer is C.

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