Data Sufficiency Gmat
GMAT: Data Sufficiency 3
Family GMAT ... Those who know the GMAT data sufficiency?
Heres the problem is x less than x ^ 2? statements 1. x ^ 2 is less than 1 but greater than 0 2. x ^ 3 is less than x ^ 2 options a. Statement 1 is sufficient by itself same, but the statement 2 is not b. statement 2 is sufficient by itself, but the statement of 1 is C. Statements 1 and 2 must be taken together to be sufficient but each is not sufficient per se d. well served by itself is enough e. Statements 1 and 2, together, are not sufficient requireing more data, thanks guys, hope you understand what is being asked and thanks in advance for all your help
I'm not sure what your notation is. It means that "less is x to x to square? "I assume so. A good way to start with this is the obvious - we usually think of x and square to be larger than x. However, it should be clear that not always the case. If it is not always true, then the answer would be too obvious. So first I review cases in which x-squared, it would greater than x. Remember that this could include x-square equals X. This would happen if x 1 or 0. Now let's consider the other "odd" numbers - numbers acting differently from the positive integers greater than 1. Weird numbers include positive fractions (between 0 and 1), 1, 0, negative numbers, fractions, negative. We have already dealt with what happens when x is 1 or 0. If x is negative 1, x squared is still larger than X. If x is a fraction (eg 1 / 2) squaring gives a number smaller (1 / 4), so for fractions, x squared is less than x. For all the negative numbers of the square will be greater than x, since the square is x is positive and negative. So far we have reviewed all of the different cases. Now for the statement 1. We say that x is a fraction squared. That means that x must be a fraction. We have already determined in this case the square of x must be less than x. So we have enough information to answer the question. The answer is "No". x is not less than x squared. The catch here is that even if you realize that stmt 1 tells us that x squared is less than x, there is a tendency to think that Stmt 1 does not work, because the original question, is not true. But all we need is a definitive answer to the question. No matter if the answer is yes or no. At this point, and Stmt 1 worker that the only possible answers are A or D. Why? For Stmt 2 we have to figure out what this says. In what cases is less than x to the third x squared? In dealing with the weird numbers, we see that Stmt 2 could occur if x is a positive fraction, or if x is a negative number. However, in the first if x not be less than x squared, but in the second case would be. Therefore Stmt 2 is not sufficient to answer the question, but sometimes gives a "yes" and sometimes not. For more information on deeper patterns of the GMAT, please see: http://www.cuttsreviews.com/jcutts/gmat/
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