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CEO  V
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If -2 < x <= 5, then which of the following MUST be true?  [#permalink]

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Question Stats: 27% (01:40) correct 73% (01:24) wrong based on 541 sessions

### HideShow timer Statistics 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) $$-4 \leq {x^2} < 36$$

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Re: If -2 < x <= 5, then which of the following MUST be true?  [#permalink]

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GMATPrepNow wrote:
If -2 < x < 5, then which of the following MUST be true?

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

Kudos for every correct solution.

Given: $$-2 < x \leq {5}$$
Value of $$x^2$$ can range from 0 to 25.
Only option E covers the above range

Alternate method:
Put x = 5 --> A and C can't be true
Put x = 0 --> B and D can't be true

Choice E works for all x between -2 and 5.

##### General Discussion
CEO  V
Joined: 12 Sep 2015
Posts: 3846
If -2 < x <= 5, then which of the following MUST be true?  [#permalink]

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s1d1 wrote:

Vyshak's solutions are great.
Let's examine his second 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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Originally posted by GMATPrepNow on 06 Oct 2016, 12:50.
Last edited by GMATPrepNow on 30 Nov 2016, 14:41, edited 1 time in total.
Intern  Joined: 07 Oct 2015
Posts: 6
Re: If -2 < x <= 5, then which of the following MUST be true?  [#permalink]

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GMATPrepNow wrote:
s1d1 wrote:

Vyshak's solutions are great.
Let's examine his second 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

Square of any number can never b negative, answer D is correct.
Math Expert V
Joined: 02 Sep 2009
Posts: 56235
Re: If -2 < x <= 5, then which of the following MUST be true?  [#permalink]

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afarrukh786 wrote:
GMATPrepNow wrote:
s1d1 wrote:

Vyshak's solutions are great.
Let's examine his second 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

Square of any number can never b negative, answer D is correct.

From the stem x CAN be 0, and if it is, then D is wrong. The correct answer is E. Please re-read the solutions above.
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Re: If -2 < x <= 5, then which of the following MUST be true?  [#permalink]

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From the stem x CAN be 0, and if it is, then D is wrong. The correct answer is E. Please re-read the solutions

D option does not say equal to zero, it says greater than zero, if you see option D, there is not a sign of equal to
Intern  Joined: 06 Oct 2016
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Re: If -2 < x <= 5, then which of the following MUST be true?  [#permalink]

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I could agree with all of you and eliminate abcd but what about e square of any number cannot be negative so how is option e true.

Can anyone tell why option E.

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Re: If -2 < x <= 5, then which of the following MUST be true?  [#permalink]

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ashishahujasham wrote:
I could agree with all of you and eliminate abcd but what about e square of any number cannot be negative so how is option e true.

Can anyone tell why option E.

This to me is a simple question that is complicated by GMAT trickery in the way the answer choices are presented. the smallest value for x^2 is 0, and 0 is always greater than -4, so option E still fulfills the demands of the question. It is always true that x^2 is greater than or equal to -4 because it is always greater than -4.
Intern  Joined: 07 Oct 2015
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Re: If -2 < x <= 5, then which of the following MUST be true?  [#permalink]

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ashishahujasham wrote:
I could agree with all of you and eliminate abcd but what about e square of any number cannot be negative so how is option e true.

Can anyone tell why option E.

This to me is a simple question that is complicated by GMAT trickery in the way the answer choices are presented. the smallest value for x^2 is 0, and 0 is always greater than -4, so option E still fulfills the demands of the question. It is always true that x^2 is greater than or equal to -4 because it is always greater than -4.

How can E be answer while it include negative numbers and zero also
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Re: If -2 < x <= 5, then which of the following MUST be true?  [#permalink]

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afarrukh786 wrote:
ashishahujasham wrote:
I could agree with all of you and eliminate abcd but what about e square of any number cannot be negative so how is option e true.

Can anyone tell why option E.

This to me is a simple question that is complicated by GMAT trickery in the way the answer choices are presented. the smallest value for x^2 is 0, and 0 is always greater than -4, so option E still fulfills the demands of the question. It is always true that x^2 is greater than or equal to -4 because it is always greater than -4.

How can E be answer while it include negative numbers and zero also

Again it comes down to the way the question is presented: "which of the following MUST be true". In theory, answer E could have been -1,000,000 ≤ x^2 < 1,000,000 and it would still be the only correct answer because it is the only solution offered that contains the actual possible values of x^2. notice the maximum value of x^2 is 25 but answer E allows for up to 36... we know x^2 cannot get that big, but the way the solution is presented means x^2 never actually needs to reach ~36 in order for it to still satisfy those constraints. This is the same idea on the negative lower bound of x^2.

Also, x^2 = 0 is a possible solution if x=0.
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Re: If -2 < x <= 5, then which of the following MUST be true?  [#permalink]

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1
1
GMATPrepNow 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) $$-4 \leq {x^2} < 36$$

Kudos for every correct solution.

Ok lets make it simpler. Given is $$-2 < x \leq {5}$$
which means x can have the following values -1, 0, 1, 2, 3, 4, 5 (for simplification purpose i'm using integers. x can have a decimal values also as question doesn't say x is an integer)
now see what all values can x^2 take. x^2 can take 0, 1, 4, 9, 16, 25. Yes?
with this knowledge approach the answer choice. Only option E gives you all the above values of x^2.
Math Expert V
Joined: 02 Sep 2009
Posts: 56235
Re: If -2 < x <= 5, then which of the following MUST be true?  [#permalink]

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afarrukh786 wrote:
ashishahujasham wrote:
I could agree with all of you and eliminate abcd but what about e square of any number cannot be negative so how is option e true.

Can anyone tell why option E.

This to me is a simple question that is complicated by GMAT trickery in the way the answer choices are presented. the smallest value for x^2 is 0, and 0 is always greater than -4, so option E still fulfills the demands of the question. It is always true that x^2 is greater than or equal to -4 because it is always greater than -4.

How can E be answer while it include negative numbers and zero also

I think you don't understand the logic of the question. The question asks: if $$-2 < x \leq {5}$$, then which of the following MUST be true? So, we KNOW that $$-2 < x \leq {5}$$ and should evaluate which of the options must be correct. If $$-2 < x \leq {5}$$, then only E must be true.
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Re: If -2 < x <= 5, then which of the following MUST be true?  [#permalink]

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GMATPrepNow 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) $$-4 \leq {x^2} < 36$$

Hi,
No calculations required, just logic on the choices given...

E has the widest range and contains ALL other choices, so if any of A to D is correct, E has to be correct....
But can we have TWO answers, No..
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Posts: 3846
Re: If -2 < x <= 5, then which of the following MUST be true?  [#permalink]

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GMATPrepNow 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) $$-4 \leq {x^2} < 36$$

Many students will assume that E is incorrect, because x² CANNOT equal -4. However, answer choice E does not 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 -2 < x <= 5, then which of the following MUST be true?  [#permalink]

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_________________ Re: If -2 < x <= 5, then which of the following MUST be true?   [#permalink] 23 Dec 2018, 00:58
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