GMAT Math : Data-Sufficiency Questions

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Example Question #3441 : Gmat Quantitative Reasoning

A bake sale sells only individual cupcakes and boxes of cookies. If cupcakes sell for $2 each, and a box of cookies sells for $15, how many boxes of cookies did Kevin buy?

(1) Kevin spent $27
(2) Kevin bought 6 cupcakes

Possible Answers:

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked

EACH statement ALONE is sufficient to answer the question asked

Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked

Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed

Both statements (1) and (2) TOGETHER are sufficient to answer the question asked; but NEITHER statement ALONE is sufficient

Correct answer:

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked

Explanation:

Because this is a "what is the value" data sufficiency problem, for a statement to be sufficient it must yield one and only one value for the number of boxes of cookies Kevin bought. Any time you have a data sufficiency problem couched in real-world terms, think about what the implications of the set up are. In this case, Keven can only buy whole numbers of cupcakes and boxes of cookies. This is important since it limits the number of combinations within the problem.

According to the question stem, you know that Kevin bought an unknown number of cupcakes and boxes of cookies for $2 and $15 each, respectively.

Statement 1 tells you that Kevin spent $27 total. Cupcakes sell for an even dollar amount, and a box of cookies sells for an odd dollar amount. Kevin cannot have purchased ONLY cupcakes and still have an odd total, since an even number plus an even number will always be even. That means that he must have bought at least one box of cookies.

If he bought one box of cookies for $15, he would have had $12 left over to buy 6 total cupcakes.

However, could he have bought more than one box of cookies? Assume that Kevin bought two boxes of cookies for $15 each and spent $30. There are two problems. First, the number is even, not odd. However, second (and most importantly) the question stem states that Kevin only spent $27, so he can't have spent $30 on two boxes of cookies!

Because there is therefore only one valid combination of cookies and cupcakes, we can determine that he purchased exactly ONE box of cookies. Statement 1 is therefore sufficient. Eliminate "Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked", "Both statements (1) and (2) TOGETHER are sufficient to answer the question asked; but NEITHER statement ALONE is sufficient", and "Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed".

Statement 2 gives that Kevin purchased 6 cupcakes. However, without any information about how much money spent in total, this statement is insufficient. Keven could have bought six cupcakes and 1 box of cookies, as in statement 1, but he also could have bought any other number of boxes of cookies. Statement 2 is therefore insufficient, eliminating "EACH statement ALONE is sufficient to answer the question asked" and leaving you with correct answer "Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked".

Consider, however, why the testmaker included Statement (2). If you didn't take the time to either consider that there could only be a whole-number number of cupcakes and boxes of cookies sold or you didn't take the time to actually test numbers for statement (1), you may have assumed that statement (1) was insufficient and that you needed to know the value of the number of cupcakes. This would have led you to incorrectly pick "Both statements (1) and (2) TOGETHER are sufficient to answer the question asked; but NEITHER statement ALONE is sufficient". Remember to always leverage your assets to see if you can "move up" the Data Sufficiency ladder if you are tempted to pick "Both statements (1) and (2) TOGETHER are sufficient to answer the question asked; but NEITHER statement ALONE is sufficient" without putting the work in first.

Answer is "Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked".

 

 

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