The correct answer is C.See the question again >
Is x negative?
- x < y
- x + y = 0
|(A)||Statement (1) ALONE is sufficient, but statement (2) is not sufficient to answer the question asked.|
|(B)||Statement (2) ALONE is sufficient, but statement (1) is not sufficient to answer the question asked.|
|(C)||BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient.|
|(D)||EACH statement ALONE is sufficient to answer the question asked.|
|(E)||Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the question are needed.|
We have a particular method that we use for all Data Sufficiency questions, and then some methods that we use for specific types of Data Sufficiency question. We won't cover the methods fully here, but we'll show you how to use them.
We see that this question asks whether X is negative. We also train ourselves to distinguish questions that are formulated as Yes or No, which we dub "Yes/No" questions. The exact answer to this yes-or-no question isn't necessarily important, although it will be nice to have; what the question is really asking is if it is possible to answer that question. If we know the answer will always be the same, then we have sufficient answer to answer the question—if the answer could be "yes" but also could be "no," then we do not have sufficient information.
There's a particular logic to evaluating the statements in a Data Sufficiency question. For example, you don't always need to evaluate the statements to gether, but you do always need to evaluate them individually. Again, we won't go into it all here (it takes a couple hours in the course to go over this fully), but we'll evaluate the statements separately.
- The first statement, x < y, leaves the question unanswered. x and y could both be positive or both be negative. It does not answer the question.
- To evaluate the second statement, we must banish the first statement from our mind and look at it alone. It tells us that x + y = 0, or in other words, that x = -y. By itself, this tells us that x and y have opposite signs (or are both equal to zero). Since x could be positive, negative, or zero, we cannot answer the question.
Once both statements are shown to be insufficient, we can rule out choices (A), (B), and (D). With practice, you'll be crossing off answer choices as you go without any second-guessing. (We actually use a mnemonic specific to Data Sufficiency to talk about the answer choices, but for this question we'll say the letters A, B, etc.) The only two remaining choices are that either the statements can answer the questions when they are combined, or they cannot answer even if combined. So, we treat the two statements as one long statement and see what we have.
Indeed, we now can answer the question. If x = -y as in statement 2), but x must be less than y according to statement 1), then together, we can definitively say that x is negative. Since we can answer the question, the answer is Together—answer choice (C)—both statements together are sufficient, even though neither is sufficient alone.
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