9. If x is a number such that -2 ≤ x ≤ 2, which of the following has the largest possible absolute value?
0 3x - 1
0 x^2 + 1
0 3 â€“ x
0 x â€“ 3
0 x^2 â€“ x
I would like to know a shortcut on getting the answer to this question
This can be answered quickly using logic and knowledge of the "rules" of the GMAT.
First, E is the only tricky answers, so lets leave this for last.
Okay, since the interval is symmetric, and answers C and D are simply negatives of one another, they both have the same max value. Since there is only one answer we can immediately eliminate both choices.
A is a simple linear function that is monotonically increasing so we can quickly plugin 2 to get 5 as the max value. B is a simple function of x^2 so we simply plug in the greatest absolute value in the interval which is either 2 or -2 and we get 5 again. Once again, since there is only one answer, we can eliminate both A and B.
Hence, by POE, we can quickly narrow the choices down to E without the burden of figuring out what the maximum value of this function is in the interval.
Former Senior Instructor, Manhattan GMAT and VeritasPrep
Vice President, Midtown NYC Investment Bank, Structured Finance IT
MFE, Haas School of Business, UC Berkeley, Class of 2005
MBA, Anderson School of Management, UCLA, Class of 1993