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Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
If [m]-2 < x \leq {5}[/m], then which of the following MUST
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30 Nov 2016, 13:40
30 Nov 2016, 13:40
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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) \(-4 \leq {x^2} < 36\)
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) \(-4 \leq {x^2} < 36\)
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: If [m]-2 < x \leq {5}[/m], then which of the following MUST
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30 Nov 2016, 13:42
30 Nov 2016, 13:42
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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) \(-4 \leq {x^2} < 36\)
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 = 25
In other words, it's possible that x² = 25
Check 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 = 0
In other words, it's possible that x² = 0
When 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
General Discussion
Re: If [m]-2 < x \leq {5}[/m], then which of the following MUST
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03 Dec 2016, 08:05
03 Dec 2016, 08:05
Brent-
I understand your reasoning in your explanation, but I still don't see how x^2 could be a negative number? or exceed 25?
I can see that answer E is still technically valid even though it might not explicitly define the boundaries of x, but if the actual range is 0 <= x <= 25, this still falls within the bounds defined by E. Is this the correct reasoning?
I understand your reasoning in your explanation, but I still don't see how x^2 could be a negative number? or exceed 25?
I can see that answer E is still technically valid even though it might not explicitly define the boundaries of x, but if the actual range is 0 <= x <= 25, this still falls within the bounds defined by E. Is this the correct reasoning?
