Carcass wrote:
If -2 < x < 11, then which of the following must me true?
A. x > -1.9999999999
B. x < 10.999999999
C. x^3 > 0
D. x^2 < 100
E. -100 < x < 20
APPROACH #1: Number sense
If -2 < x < 11, then we can be certain that x is greater than -100, and can be certain that x is less than 20.
Answer: E
APPROACH #2: Process of elimination
If -2 < x < 11, then it could be the case that x = -1.9999999999999999999999999
Since -1.9999999999999999999999999 is NOT greater than -1.9999999999, we can eliminate choice A.
Similarly, if -2 < x < 11, then it could be the case that x = 10.99999999999999999999999
Since 10.99999999999999999999999 is NOT less than 10.999999999, we can eliminate choice B.
If -2 < x < 11, then it could be the case that x = -1
Since (-1)^3 is NOT greater than 0, we can eliminate choice C
If -2 < x < 11, then it could be the case that x = 10.5
Since (10.5)^2 is NOT less than 100, we can eliminate choice D
By the process of elimination, the correct answer must be E