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

 It is currently 18 Sep 2019, 21:31

### 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 5 ≥ |x| ≥ 0, which of the following must be true?

Author Message
TAGS:

### Hide Tags

SVP
Joined: 26 Mar 2013
Posts: 2326
Re: If 5 ≥ |x| ≥ 0, which of the following must be true?  [#permalink]

### Show Tags

12 Jun 2018, 02:18
EMPOWERgmatRichC wrote:
Hi All,

This question can be solved by TESTing VALUES. Notice the specific inequalities that we're given to work with - based on the information in the prompt, we know that X can be any value from -5 to +5 INCLUSIVE. We're asked which of the following MUST be true.

I. x ≥ 0
II. x > -5

For Roman Numerals 1 and 2, you could consider X = -5. With that value, neither of those two Roman Numerals is true.
Eliminate Answers B, D and E.

III. 25 ≥ x^2 ≥ -25

Roman Numeral 3 asks us to think about SQUARED terms. With the given range of values that we have to work with, the range of the squared terms would be 0 through +25, inclusive. Regardless of the exact value that you choose for X, X^2 will fall into the range provided by Roman Numeral 3 every time, so Roman Numeral 3 IS true.

GMAT assassins aren't born, they're made,
Rich

Hi Rich,

Based on your solution above, Can Roman II be correct if it says that x ≥ -5 ??
EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15023
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: If 5 ≥ |x| ≥ 0, which of the following must be true?  [#permalink]

### Show Tags

12 Jun 2018, 13:51
Hi sssjav,

From what you describe, the 'issue' seems to be about how you are interpreting the prompt. I'm going to rephrase the prompt a bit - but NOT change the meaning or the question that is asked.

Consider EVERY number from -5 to +5, inclusive (including negatives, 0, fractions, etc.). Those are the ONLY numbers to consider. Now, consider how each of those possible numbers would answer the three questions here:

I. Is EVERY number in that group greater than or equal to 0?

Of course not; none of the negative numbers are greater than 0.

II. Is EVERY number in that group GREATER than -5?

No. There is one value in the group that is NOT (re: -5).

III. When you square EACH number in that group, will you end up with a value that is between -25 and +25, inclusive?

YES. EVERY value in that group, when squared, will result in a number that is between 0 and +25, inclusive (thus, ALL of those results are between -25 and +25, inclusive).

Thus, the only statement that MUST be true is Roman Numeral 3.

GMAT assassins aren't born, they're made,
Rich
_________________
760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

*****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*****

# Rich Cohen

Co-Founder & GMAT Assassin

Special Offer: Save \$75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/
EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15023
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: If 5 ≥ |x| ≥ 0, which of the following must be true?  [#permalink]

### Show Tags

12 Jun 2018, 13:53
Hi Mo2men,

IF Roman Numeral 2 was changed to:

"II. x ≥ -5"

Then that statement would also always be true.

GMAT assassins aren't born, they're made,
Rich
_________________
760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

*****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*****

# Rich Cohen

Co-Founder & GMAT Assassin

Special Offer: Save \$75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/
SVP
Joined: 26 Mar 2013
Posts: 2326
Re: If 5 ≥ |x| ≥ 0, which of the following must be true?  [#permalink]

### Show Tags

12 Jun 2018, 14:26
EMPOWERgmatRichC wrote:
Hi Mo2men,

IF Roman Numeral 2 was changed to:

"II. x ≥ -5"

Then that statement would also always be true.

GMAT assassins aren't born, they're made,
Rich

Manager
Joined: 08 Sep 2016
Posts: 106
If 5 ≥ |x| ≥ 0, which of the following must be true?  [#permalink]

### Show Tags

12 Jun 2018, 14:49
We can quickly see that statement 1 and 2 are not always true.
Statement 1 - If X is 1 then yes, but if X is 100 then no
Statement 2 - If X is -4 then yes, but if X is 100 then no

Statement 3 is a bit tricky. You can't take the square root of a negative number so dividing the inequalities by 5 will give the following:

5 ≥ X^2/5≥-5

If X=5, then 5^2/5 = 5 which is sufficient
If X= -5, then -5^2/5 = 5 which is sufficient
All values in between 5 to 0 will still be in the range of satisfying the question

*remember - squaring a negative number will give you a positive value

Intern
Joined: 11 Feb 2016
Posts: 13
Re: If 5 ≥ |x| ≥ 0, which of the following must be true?  [#permalink]

### Show Tags

13 Jun 2018, 14:35
Mo2men wrote:
EMPOWERgmatRichC wrote:
Hi All,

This question can be solved by TESTing VALUES. Notice the specific inequalities that we're given to work with - based on the information in the prompt, we know that X can be any value from -5 to +5 INCLUSIVE. We're asked which of the following MUST be true.

I. x ≥ 0
II. x > -5

For Roman Numerals 1 and 2, you could consider X = -5. With that value, neither of those two Roman Numerals is true.
Eliminate Answers B, D and E.

III. 25 ≥ x^2 ≥ -25

Roman Numeral 3 asks us to think about SQUARED terms. With the given range of values that we have to work with, the range of the squared terms would be 0 through +25, inclusive. Regardless of the exact value that you choose for X, X^2 will fall into the range provided by Roman Numeral 3 every time, so Roman Numeral 3 IS true.

GMAT assassins aren't born, they're made,
Rich

Hi Rich,

Based on your solution above, Can Roman II be correct if it says that x ≥ -5 ??

I must say that I have a similar doubt. I thought that on "must to be true" questions, we need to pick those answers which if they are not, it will counter the initial equation.

In this case, we know that -5 <= x <= 5.

I thought that a "must to be true answer" will be anything that will make sure X is inside these constrains, say -3 < x < 3.

Reflecting uppon that, I figured out that an answer that "must to be true" whould hold for any value of x, say -10 < x. This must to be true... x has to be higher than -5, so it has to be higher than -10 as well.

Does this thought make sense? Would an alternative -10 < x be considered a true one?
Non-Human User
Joined: 09 Sep 2013
Posts: 12373
Re: If 5 ≥ |x| ≥ 0, which of the following must be true?  [#permalink]

### Show Tags

06 Aug 2019, 15:28
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 5 ≥ |x| ≥ 0, which of the following must be true?   [#permalink] 06 Aug 2019, 15:28

Go to page   Previous    1   2   [ 27 posts ]

Display posts from previous: Sort by