GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 15 Jul 2018, 12:05

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# If -2 < x <= 5, then which of the following MUST be true?

Author Message
TAGS:

### Hide Tags

CEO
Joined: 12 Sep 2015
Posts: 2630
If -2 < x <= 5, then which of the following MUST be true? [#permalink]

### Show Tags

06 Oct 2016, 10:53
2
Top Contributor
22
00:00

Difficulty:

95% (hard)

Question Stats:

26% (01:03) correct 74% (00:55) wrong based on 463 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) $$-4 \leq {x^2} < 36$$

_________________

Brent Hanneson – Founder of gmatprepnow.com

SC Moderator
Joined: 13 Apr 2015
Posts: 1712
Location: India
Concentration: Strategy, General Management
GMAT 1: 200 Q1 V1
GPA: 4
WE: Analyst (Retail)
Re: If -2 < x <= 5, then which of the following MUST be true? [#permalink]

### Show Tags

06 Oct 2016, 11:30
4
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.

CEO
Joined: 12 Sep 2015
Posts: 2630
If -2 < x <= 5, then which of the following MUST be true? [#permalink]

### Show Tags

Updated on: 30 Nov 2016, 14:41
2
Top Contributor
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
_________________

Brent Hanneson – Founder of gmatprepnow.com

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]

### Show Tags

19 Nov 2016, 08:25
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
Joined: 02 Sep 2009
Posts: 46991
Re: If -2 < x <= 5, then which of the following MUST be true? [#permalink]

### Show Tags

19 Nov 2016, 08:30
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.
_________________
Intern
Joined: 07 Oct 2015
Posts: 6
Re: If -2 < x <= 5, then which of the following MUST be true? [#permalink]

### Show Tags

19 Nov 2016, 09:40
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
Posts: 20
Re: If -2 < x <= 5, then which of the following MUST be true? [#permalink]

### Show Tags

19 Nov 2016, 10:11
1
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.

Sent from my A1601 using GMAT Club Forum mobile app
Intern
Joined: 24 Oct 2016
Posts: 8
Location: United States
GMAT 1: 750 Q48 V44
GPA: 3.2
Re: If -2 < x <= 5, then which of the following MUST be true? [#permalink]

### Show Tags

19 Nov 2016, 10:53
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.
Intern
Joined: 07 Oct 2015
Posts: 6
Re: If -2 < x <= 5, then which of the following MUST be true? [#permalink]

### Show Tags

19 Nov 2016, 11:04
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
Intern
Joined: 24 Oct 2016
Posts: 8
Location: United States
GMAT 1: 750 Q48 V44
GPA: 3.2
Re: If -2 < x <= 5, then which of the following MUST be true? [#permalink]

### Show Tags

19 Nov 2016, 11:13
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.
Senior Manager
Joined: 06 Jun 2016
Posts: 263
Location: India
Concentration: Operations, Strategy
Schools: ISB '18 (D)
GMAT 1: 600 Q49 V23
GMAT 2: 680 Q49 V34
GPA: 3.9
Re: If -2 < x <= 5, then which of the following MUST be true? [#permalink]

### Show Tags

20 Nov 2016, 01:54
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
Joined: 02 Sep 2009
Posts: 46991
Re: If -2 < x <= 5, then which of the following MUST be true? [#permalink]

### Show Tags

20 Nov 2016, 03:28
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.
_________________
Math Expert
Joined: 02 Aug 2009
Posts: 6196
Re: If -2 < x <= 5, then which of the following MUST be true? [#permalink]

### Show Tags

20 Nov 2016, 05:09
2
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..
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

GMAT online Tutor

CEO
Joined: 12 Sep 2015
Posts: 2630
Re: If -2 < x <= 5, then which of the following MUST be true? [#permalink]

### Show Tags

20 Nov 2016, 06:35
1
Top Contributor
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
_________________

Brent Hanneson – Founder of gmatprepnow.com

Non-Human User
Joined: 09 Sep 2013
Posts: 7241
Re: If -2 < x <= 5, then which of the following MUST be true? [#permalink]

### Show Tags

29 Nov 2017, 04:59
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: If -2 < x <= 5, then which of the following MUST be true?   [#permalink] 29 Nov 2017, 04:59
Display posts from previous: Sort by

# Events & Promotions

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.