GreenlightTestPrep wrote:
If \(-2 < x \leq {5}\), then which of the following MUST be true?
A) \(-1 < x^2 < 16\)
B) \(4 < x^2 \leq {25}\)
C) \(0 \leq {x^2} \leq {16}\)
D) \(0 < x^2 \leq {25}\)
E) \(-4 \leq {x^2} < 36\)
Looks a lot easier than it is!
This question lends itself to
testing values, so let's see where that takes us...
If -2 < x
< 5, then it could be the case that
x = 5, in which case
x² = 25In other words, it's
possible that
x² = 25Check the answer choices...
Answer choice A says x² < 16. In other words, it says that x² can't equal 25. ELIMINATE A
Answer choice C says x²
< 16. In other words, it says that x² can't equal 25. ELIMINATE C
Also, if -2 < x
< 5, then it could be the case that that
x = 0, in which case
x² = 0In other words, it's
possible that
x² = 0When we check the remaining answer choices, we see that...
Answer choice B (4 < x²) says x² can't equal 0. ELIMINATE B
Answer choice D (0 < x²) says x² can't equal 0. ELIMINATE D
We're left with 1 answer choice...E
Cheers,
Brent
_________________
Brent Hanneson - founder of Greenlight Test Prep