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If -2 < x [u]<[/u] 5, then which of the following MUST

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If -2 < x [u]<[/u] 5, then which of the following MUST

by Brent@GMATPrepNow » Thu Oct 06, 2016 9:54 am
If -2 < x < 5, then which of the following MUST be true?

A) -1 < x² < 16
B) 4 < x² < 25
C) 0 < x² < 16
D) 0 < x² < 25
E) -4 < x² < 36

Answer: E
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by regor60 » Thu Oct 06, 2016 10:42 am
I think D not E
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by Brent@GMATPrepNow » Thu Oct 06, 2016 10:51 am
regor60 wrote:I think D not E
If -2 < x < 5, then it's possible that x = 0, which means x² = 0
However, answer choice D says that 0 < x² (x² is greater than 0)

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by regor60 » Thu Oct 06, 2016 11:32 am
Brent@GMATPrepNow wrote:
regor60 wrote:I think D not E
If -2 < x < 5, then it's possible that x = 0, which means x² = 0
However, answer choice D says that 0 < x² (x² is greater than 0)

Cheers,
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Yes I see missed the left side <
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by Brent@GMATPrepNow » Fri Oct 07, 2016 7:26 am
Brent@GMATPrepNow wrote:If -2 < x < 5, then which of the following MUST be true?

A) -1 < x² < 16
B) 4 < x² < 25
C) 0 < x² < 16
D) 0 < x² < 25
E) -4 < x² < 36

Answer: E
Here's one approach:

If -2 < x < 5, then it's possible that x = 5, in which case x² = 25
In other words, it's possible that x² = 25
When we check the answer choices, we see that...
Answer choice A says that x² < 16. In other words, it says that x² cannot equal 25. ELIMINATE A
Answer choice C says that x² < 16. In other words, it says that x² cannot equal 25. ELIMINATE C

Also, if -2 < x < 5, then it's possible 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 says that 4 < x². In other words, it says that x² cannot equal 0. ELIMINATE B
Answer choice D says that 0 < x². In other words, it says that x² cannot equal 0. ELIMINATE D

We're left with 1 answer choice...E

Cheers,
Brent
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