Hi swerve,
While this question might look 'scary', it can be solved in a couple of different ways (and it's based on a few Number Property rules which you can use to avoid doing much of the math altogether).
To start, we're asked to find the SMALLEST fraction - since all 5 answers have a '1' in the numerator, whichever one has the LARGEST denominator will be the smallest fraction. Thus, we have to compare denominators to determine which will give us the biggest denominator.
To start, here are 2 rules worth knowing:
1) Squaring a positive number that is less that 1 will make that number SMALLER. Squaring a number greater than 1 will make that number BIGGER.
2) Square-rooting a positive number that is less than 1 will make that number BIGGER (although it will still be less than 1). Square-rooting a number greater than 1 will make that number SMALLER.
Now we can compare answers to one another:
-Answer B will have a bigger denominator than Answer A. Eliminate Answer A.
-Answer D will give us a square root that is BIGGER than 1 (and that will be BIGGER than Answer B). Eliminate Answer B.
-Squaring (P+1) will make the result BIGGER. Square-rooting (P+1) will make the number SMALLER. Eliminate Answer D.
Between Answers C and E, you can TEST VALUES (choose a number for P and plug it in). You'll find that Answer E has the LARGER denominator.
Final Answer: E
GMAT assassins aren't born, they're made,
Rich
