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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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Brent Hanneson – Founder of gmatprepnow.com

Last edited by GMATPrepNow on 30 Nov 2016, 13:41, edited 1 time in total.

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

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19 Nov 2016, 07:25

GMATPrepNow wrote:

s1d1 wrote:

can anybody explain the answer?

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.

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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19 Nov 2016, 09:53

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.

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

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19 Nov 2016, 10:04

adamm412 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

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

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19 Nov 2016, 10:13

afarrukh786 wrote:

adamm412 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.

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

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20 Nov 2016, 00:54

1

This post was BOOKMARKED

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.

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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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.. So E is the answer
_________________

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.

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

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29 Nov 2017, 03:59

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