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Re: If [m]-2 < x \leq {5}[/m], then which of the following MUST [#permalink]
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rsudhakar wrote:
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?


Hi rsudhakar,

Many students will assume that E is incorrect, because x² CANNOT equal -4. However, answer choice E doesn't suggest that x² can equal -4, it only states that x² must be GREATER THAN or equal to -4.

Here's a similar example: If Joe has more than 5 shirts, which of the following can we conclude with certainty?
A) Joe owns more than 6 shirts.
NO. We can't conclude this, because it's possible that Joe owns exactly 6 shirts, and 6 is not greater than 6.

B) Joe owns more than -3 shirts.
YES. If Joe owns more than 5 shirts, then he definitely owns more than -3 shirts
Does this mean that Joe COULD own -2 shirts? No. If just means that we can be certain that he owns more than -3 shirts.

Does that help?

Cheers,
Brent
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Re: If [m]-2 < x \leq {5}[/m], then which of the following MUST [#permalink]
Brent-

Thanks for the prompt response! Definitely makes sense now.
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Re: If [m]-2 < x \leq {5}[/m], then which of the following MUST [#permalink]
While this makes sense, it's a really nasty question. Answer E, while correct, deliberately presents a misleading boundary.
I guess like many other people, I answered D.
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Re: If [m]-2 < x \leq {5}[/m], then which of the following MUST [#permalink]
I got it correct. Choice D doesn't cover when x is 0.

Choice E looks out of boundary, but, it covers everything question asks.
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Re: If [m]-2 < x \leq {5}[/m], then which of the following MUST [#permalink]
can be easily done using POE and cleverly using values.

First we can take X=5 ( boundary value), A and C gets eliminated

then take X=0 B & D gets eliminated

Left with option E. and voila same is the ans
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Re: If [m]-2 < x \leq {5}[/m], then which of the following MUST [#permalink]
GreenlightTestPrep wrote:
rsudhakar wrote:
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?


Hi rsudhakar,

Many students will assume that E is incorrect, because x² CANNOT equal -4. However, answer choice E doesn't suggest that x² can equal -4, it only states that x² must be GREATER THAN or equal to -4.

Here's a similar example: If Joe has more than 5 shirts, which of the following can we conclude with certainty?
A) Joe owns more than 6 shirts.
NO. We can't conclude this, because it's possible that Joe owns exactly 6 shirts, and 6 is not greater than 6.

B) Joe owns more than -3 shirts.
YES. If Joe owns more than 5 shirts, then he definitely owns more than -3 shirts
Does this mean that Joe COULD own -2 shirts? No. If just means that we can be certain that he owns more than -3 shirts.

Does that help?

Cheers,
Brent
_________


Hello there,

I see your point, but from a mathematical perspective answer E keeps being troublesome for some reason. The phrasing "\( -4 \leq{x^2} \)" suggests that \(x^2\) CAN also be -4, which is not within what GRE actually tests. Complex number are not tested here... so, how comes?
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Re: If [m]-2 < x \leq {5}[/m], then which of the following MUST [#permalink]
reynolds wrote:
Hello there,

I see your point, but from a mathematical perspective answer E keeps being troublesome for some reason. The phrasing "\( -4 \leq{x^2} \)" suggests that \(x^2\) CAN also be -4, which is not within what GRE actually tests. Complex number are not tested here... so, how comes?


I'm not saying \(x^2\) can equal -4. I'm just identifying what must be true about the value of \(x^2\)

Consider this analogous question: Joe, a living human, is x inches tall. If Joe is taller than 50 inchers, which of the following must be true?
A) x > -10
B) x is prime
C) x > 60
D) x is even
E) x is odd

I think we'd agree that the correct answer here is A.
Does this mean Joe could be -8 inches tall?
No, it just means that x (Joe's height in inches) must lie to the right of -10 on the number line.

Similarly, If \(-2 < x \leq {5}\), then we can be certain of that \(x^2\) is greater than or equal to \(0\).
In other words it must be the case that either \(x^2 = 0\) or \(x^2\) lies to the right of zero on the number line.
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Re: If [m]-2 < x \leq {5}[/m], then which of the following MUST [#permalink]
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GreenlightTestPrep wrote:
reynolds wrote:
Hello there,

I see your point, but from a mathematical perspective answer E keeps being troublesome for some reason. The phrasing "\( -4 \leq{x^2} \)" suggests that \(x^2\) CAN also be -4, which is not within what GRE actually tests. Complex number are not tested here... so, how comes?


I'm not saying \(x^2\) can equal -4. I'm just identifying what must be true about the value of \(x^2\)

Consider this analogous question: Joe, a living human, is x inches tall. If Joe is taller than 50 inchers, which of the following must be true?
A) x > -10
B) x is prime
C) x > 60
D) x is even
E) x is odd

I think we'd agree that the correct answer here is A.
Does this mean Joe could be -8 inches tall?
No, it just means that x (Joe's height in inches) must lie to the right of -10 on the number line.

Similarly, If \(-2 < x \leq {5}\), then we can be certain of that \(x^2\) is greater than or equal to \(0\).
In other words it must be the case that either \(x^2 = 0\) or \(x^2\) lies to the right of zero on the number line.


Great point GreenlightTestPrep
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Re: If [m]-2 < x \leq {5}[/m], then which of the following MUST [#permalink]
X² Cant be equal to -4 therefore there is no solution to the question.
But the only way to get your score is to chose E or to file an appeal.
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