I often equate data sufficiency with determining whether the competition is stealing from you. If you are sure they are not, then everything is fine and you are competing in a fair and balanced environment. Similarly, if you have definitive proof that they are hijacking your million dollar idea, then you can pursue legal action to remedy the situation.
The real problem in such a predicament is if you don’t know for certain whether you’re being ripped off. If all you’ve got is hearsay and conjecture, then you may toss and turn at night wondering what is actually going on. Having a definitive answer is always better than living with uncertainty, but assurance is not always easy to obtain. In the real world, it usually costs time, money or both. On the GMAT, it costs additional resources, such as using both statements when only one was necessary. This is tantamount to overpaying and should be avoided on the GMAT.
The most common mistake in data sufficiency is choosing answer choice C when in fact it was A, B or even D. Putting all the information together usually looks like the best option, and indeed sometimes it is. Before galloping to that answer, however, you must ensure that it is the correct choice and not overpay for the answer.
Consider the following question:
Is x * y < 0?
(1) x^2 * y^3 < 0 (2) x * y^2 > 0
(A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. (B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. (C) BOTH statements TOGETHER are sufficient, but NEITHER statement alone is sufficient. (D) EACH statement ALONE is sufficient. (E) Statements (1) and (2) TOGETHER are NOT sufficient.
The first thing to do is to make certain that you understand the question being asked, which often means paraphrasing it. Asking whether x*y is less than zero is like asking whether x*y is negative. Another way to phrase this question would be: Are x and y different signs? It’s interesting to note that, had the question been whether x and y are the same sign, the answer would still have been the same. This is due to the fact that, in data sufficiency, always no and always yes mean that you are sure, and therefore you have sufficient information.
Getting back to the question at hand, we must determine the sign of both x and y given the two statements provided. The first one indicates that x^2 * y^3 is less than zero. What do we know about this equation? Well, x^2 will necessarily be positive, as any number with an even exponent will be. Thus, regardless of the sign of x, x^2 will be positive. Moreover, the value of y^3 must be negative for this equation to hold, so we know that y is negative. Statement one thus tells us about the sign of y while telling us nothing about the sign of x. Insufficient.
Statement 2 tells us that x * y^2 > 0. On its own, we can view this in much the same way as statement 1, in that y could be either positive or negative and y^2 would necessarily be positive. This means that x must be positive in order for the entire equation to be positive as well. So we know the sign of x but don’t know anything about y. Insufficient again.
The third and final step is to consider these statements together. The first statement guarantees that y is negative, and the second guarantees that x is positive. If you consider them together, x * y must necessarily be less than 0. This means that answer choice C is the correct option here, as neither statement on their own will provide a conclusive answer, but both of them together precludes any other option.
As I mentioned before, the most common incorrect answer in Data Sufficiency is C, but that doesn’t mean that it is never the correct answer. You simply have to have enough information to ensure that the question asked has only one answer. If the two statements together had still been insufficient to be 100% certain, then you could not say that answer choice C is correct. Data sufficiency questions tend to be more difficult than problem solving questions because every answer choice is a realistic possibility. The key is to evaluate the statements objectively and logically to come to one unquestionable conclusion: I have enough information to say this with confidence.
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