Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 64318

If 5 ≥ x ≥ 0, which of the following must be true?
[#permalink]
Show Tags
02 Jan 2017, 04:26
Question Stats:
51% (01:31) correct 49% (01:37) wrong based on 762 sessions
HideShow timer Statistics
If 5 ≥ x ≥ 0, which of the following must be true? I. x ≥ 0 II. x > –5 III. 25 ≥ x^2 ≥ –25 A. None B. II only C. III only D. I and III only E. II and III only
Official Answer and Stats are available only to registered users. Register/ Login.
_________________




Senior Manager
Joined: 13 Oct 2016
Posts: 352
GPA: 3.98

Re: If 5 ≥ x ≥ 0, which of the following must be true?
[#permalink]
Show Tags
02 Jan 2017, 11:12
Bunuel wrote: If 5 ≥ x ≥ 0, which of the following must be true?
I. x ≥ 0 II. x > –5 III. 25 ≥ x^2 ≥ –25
A. None B. II only C. III only D. I and III only E. II and III only 0 ≤ x ≤ 5 or 5 ≤ x ≤ 0 I. Not always true because x can be negative. II. Not always true because x can be equal to 5. III. \(0 ≤ x^2 ≤ 5^2\) > \(0 ≤ x^2 ≤ 25\) \(x^2\) is always positive and ≤ 25. True Answer C




Director
Joined: 05 Mar 2015
Posts: 936

If 5 ≥ x ≥ 0, which of the following must be true?
[#permalink]
Show Tags
Updated on: 21 Jan 2017, 19:50
Bunuel wrote: If 5 ≥ x ≥ 0, which of the following must be true?
I. x ≥ 0 II. x > –5 III. 25 ≥ x^2 ≥ –25
A. None B. II only C. III only D. I and III only E. II and III only I. x could be 4 or 4....hence not must be true II. x could be 5 or 5 > 5 ........hence not must be true III. x^2 = 24 then x<5 (either x= 4.9 or x=4.9 say for instance..)..........TRue Ans C
Originally posted by rohit8865 on 02 Jan 2017, 09:44.
Last edited by rohit8865 on 21 Jan 2017, 19:50, edited 2 times in total.



Manager
Joined: 04 Sep 2016
Posts: 57
Location: Germany
GPA: 3

Re: If 5 ≥ x ≥ 0, which of the following must be true?
[#permalink]
Show Tags
21 Jan 2017, 16:59
Can someone please explain me how C is the correct answer. I chose A.
III. 25 ≥ x^2 ≥ –25
How can we apply square root to 25 and simplify it to 5 ≥ x ≥ –5



Math Expert
Joined: 02 Sep 2009
Posts: 64318

Re: If 5 ≥ x ≥ 0, which of the following must be true?
[#permalink]
Show Tags
22 Jan 2017, 03:32
Sanjeetgujrall wrote: Can someone please explain me how C is the correct answer. I chose A.
III. 25 ≥ x^2 ≥ –25
How can we apply square root to 25 and simplify it to 5 ≥ x ≥ –5 5 ≥ x ≥ 0 means that 5 ≥ x ≥ 0 or 0 ≥ x ≥ 5. For any x from these ranges, 25 ≥ x^2 ≥ –25 will be true.
_________________



Manager
Joined: 26 Jan 2016
Posts: 60
Location: India
GPA: 3.01

Re: If 5 ≥ x ≥ 0, which of the following must be true?
[#permalink]
Show Tags
22 May 2017, 19:31
Bunuel wrote: Sanjeetgujrall wrote: Can someone please explain me how C is the correct answer. I chose A.
III. 25 ≥ x^2 ≥ –25
How can we apply square root to 25 and simplify it to 5 ≥ x ≥ –5 5 ≥ x ≥ 0 means that 5 ≥ x ≥ 0 or 0 ≥ x ≥ 5. For any x from these ranges, 25 ≥ x^2 ≥ –25 will be true. Hi Bunuel, But in the term "25 ≥ x^2 ≥ –25" , doesn't the 25 imply that we cann't take the square root of 25 to simplify the inequality. ?



Retired Moderator
Joined: 21 Aug 2013
Posts: 1357
Location: India

Re: If 5 ≥ x ≥ 0, which of the following must be true?
[#permalink]
Show Tags
22 May 2017, 22:11
Given 0<= x <= 5 So absolute value of x can go from 0 to 5 (including both) So range of x becomes: 5 <= x <= 5 x can go from 5 to 5 (including both)
Now lets look at the given statements.
1. x >= 0 Its not necessary, because x can take negative values also from 5 <= x < 0, and still satisfy the given range
2. x > 5 Its not necessary because x can be = 5 also, and still satisfy the given range
3. 25 <= x^2 <= 25 If you pick any value in the range: 5 <= x <= 5, then it will always satisfy 0 <= x^2 <= 25 Which means it will still satisfy 25 <= x^2 <= 25 So this must be true.
Hence answer is C



Intern
Joined: 28 Jan 2017
Posts: 47

If 5 ≥ x ≥ 0, which of the following must be true?
[#permalink]
Show Tags
23 May 2017, 11:20
Bunuel wrote: If 5 ≥ x ≥ 0, which of the following must be true?
I. x ≥ 0 II. x > –5 III. 25 ≥ x^2 ≥ –25
A. None B. II only C. III only D. I and III only E. II and III only Hi Option "C" simply can't be correct choice here. Squire of a real number can never be ve. It can only be possible only if "x" is an imaginary number. However if "x" is an imaginary number then the condition mentioned in the question itself will not hold true. Hence option "ANone" should be the correct answer.



Math Expert
Joined: 02 Sep 2009
Posts: 64318

Re: If 5 ≥ x ≥ 0, which of the following must be true?
[#permalink]
Show Tags
23 May 2017, 11:28
ravi11 wrote: Bunuel wrote: If 5 ≥ x ≥ 0, which of the following must be true?
I. x ≥ 0 II. x > –5 III. 25 ≥ x^2 ≥ –25
A. None B. II only C. III only D. I and III only E. II and III only Hi Option "C" simply can't be correct choice here. Squire of a real number can never be ve. It can only be possible only if "x" is an imaginary number. However if "x" is an imaginary number then the condition mentioned in the question itself will not hold true. Hence option "ANone" should be the correct answer. You did not understand the question. I'll try to explain again: 5 ≥ x ≥ 0 means that 5 ≥ x ≥ 0 or 0 ≥ x ≥ 5. For example, x can be, among infinitely many other values, 0.1, 0.7, 1, 1.7, 4, 5 (because 5 ≥ x ≥ 0) as well as x can be 0.008, 0.4, 3.4, 4, 4.6, 5 (because 0 ≥ x ≥ 5). For ANY possible x, so for ANY x from 5 ≥ x ≥ 0 or 0 ≥ x ≥ 5, it will be true to say that 25 ≥ x^2 ≥ –25.
_________________



Intern
Joined: 28 Jan 2017
Posts: 47

If 5 ≥ x ≥ 0, which of the following must be true?
[#permalink]
Show Tags
Updated on: 23 May 2017, 12:13
Bunuel wrote: ravi11 wrote: Bunuel wrote: If 5 ≥ x ≥ 0, which of the following must be true?
I. x ≥ 0 II. x > –5 III. 25 ≥ x^2 ≥ –25
A. None B. II only C. III only D. I and III only E. II and III only Hi Option "C" simply can't be correct choice here. Squire of a real number can never be ve. It can only be possible only if "x" is an imaginary number. However if "x" is an imaginary number then the condition mentioned in the question itself will not hold true. Hence option "ANone" should be the correct answer. You did not understand the question. I'll try to explain again: 5 ≥ x ≥ 0 means that 5 ≥ x ≥ 0 or 0 ≥ x ≥ 5. For example, x can be, among infinitely many other values, 0.1, 0.7, 1, 1.7, 4, 5 (because 5 ≥ x ≥ 0) as well as x can be 0.008, 0.4, 3.4, 4, 4.6, 5 (because 0 ≥ x ≥ 5). For ANY possible x, so for ANY x from 5 ≥ x ≥ 0 or 0 ≥ x ≥ 5, it will be true to say that 25 ≥ x^2 ≥ –25. Thanks Bunuel for putting such a simplified explanation.However, I am still not convinced. 25 ≥ x^2 ≥ –25 means x^2 can be 24, 23, 22,21 etc as well. is there any number "x" for which x^2 can be ve value (25,24 etc) and satisfy 5 ≥ x ≥ 0 as well. Had the answer option been 25 ≥ x^2, I would have selected this as correct answer. Please let me know if I am missing an important concept here.



Math Expert
Joined: 02 Sep 2009
Posts: 64318

Re: If 5 ≥ x ≥ 0, which of the following must be true?
[#permalink]
Show Tags
23 May 2017, 12:11
ravi11 wrote: Thanks Bunuel for putting such a simplified explanation. I am still not convinced.
25 ≥ x^2 ≥ –25 means x^2 can be 24, 23, 22,21 etc as well. is there any number "x" for which x^2 can be ve value (25,24 etc) and satisfy 5 ≥ x ≥ 0 as well. Had the answer option been 25 ≥ x^2, I would have selected this as correct answer.
Please let me know if I am missing an important concept here. You are missing the point. The question asks: if 5 ≥ x ≥ 0 or 0 ≥ x ≥ 5, then which of the options must be true. So, if we choose any possible x from the given ranges (5 ≥ x ≥ 0 or 0 ≥ x ≥ 5) and substitute into the options, which option will be always true for any of the possible x's. Any possible x will satisfy 25 ≥ x^2 ≥ –25.
_________________



Intern
Joined: 28 Jan 2017
Posts: 47

Re: If 5 ≥ x ≥ 0, which of the following must be true?
[#permalink]
Show Tags
23 May 2017, 12:38
Bunuel wrote: ravi11 wrote: Thanks Bunuel for putting such a simplified explanation. I am still not convinced.
25 ≥ x^2 ≥ –25 means x^2 can be 24, 23, 22,21 etc as well. is there any number "x" for which x^2 can be ve value (25,24 etc) and satisfy 5 ≥ x ≥ 0 as well. Had the answer option been 25 ≥ x^2, I would have selected this as correct answer.
Please let me know if I am missing an important concept here. You are missing the point. The question asks: if 5 ≥ x ≥ 0 or 0 ≥ x ≥ 5, then which of the options must be true. So, if we choose any possible x from the given ranges (5 ≥ x ≥ 0 or 0 ≥ x ≥ 5) and substitute into the options, which option will be always true for any of the possible x's. Any possible x will satisfy 25 ≥ x^2 ≥ –25. Thanks Bunuel. I got the point. So basically all the options that have the question condition as subset of range will be valid.



Intern
Joined: 30 Mar 2017
Posts: 35
Location: United States (FL)

Re: If 5 ≥ x ≥ 0, which of the following must be true?
[#permalink]
Show Tags
31 May 2017, 02:08
For those that have difficulty with this question, do not underestimate the value of drawing a number line. It actually made the problem seem easy once I was able to visualize it better.



Intern
Joined: 02 Feb 2017
Posts: 15
Concentration: Entrepreneurship, Strategy

Re: If 5 ≥ x ≥ 0, which of the following must be true?
[#permalink]
Show Tags
05 Jun 2017, 05:36
laxpro2001 wrote: For those that have difficulty with this question, do not underestimate the value of drawing a number line. It actually made the problem seem easy once I was able to visualize it better. Just plug any number based on 5≥x≥5. It solved the questions.



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 16793
Location: United States (CA)

Re: If 5 ≥ x ≥ 0, which of the following must be true?
[#permalink]
Show Tags
21 Jan 2018, 12:33
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. Final Answer: GMAT assassins aren't born, they're made, Rich
_________________
Contact Rich at: Rich.C@empowergmat.comThe Course Used By GMAT Club Moderators To Earn 750+ souvik101990 Score: 760 Q50 V42 ★★★★★ ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★



Intern
Joined: 05 Dec 2017
Posts: 19
GMAT 1: 710 Q49 V38

If 5 ≥ x ≥ 0, which of the following must be true?
[#permalink]
Show Tags
11 Jun 2018, 10:02
Bunuel wrote: Sanjeetgujrall wrote: Can someone please explain me how C is the correct answer. I chose A.
III. 25 ≥ x^2 ≥ –25
How can we apply square root to 25 and simplify it to 5 ≥ x ≥ –5 5 ≥ x ≥ 0 means that 5 ≥ x ≥ 0 or 0 ≥ x ≥ 5. For any x from these ranges, 25 ≥ x^2 ≥ –25 will be true. I have a doubt here. Square root of 25 is an imaginary number, 5i. However that lies outside the range of values for x ( Which is [5,5] ) Doesn't that make StatementIII wrong as well?



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 16793
Location: United States (CA)

Re: If 5 ≥ x ≥ 0, which of the following must be true?
[#permalink]
Show Tags
11 Jun 2018, 10:20
Hi sssjav, Based on the information we're given at the beginning of the prompt, we know that X can be any value from 5 to +5 INCLUSIVE. That 'restriction' is what we have to work with when trying to determine which of the three Roman Numerals is ALWAYS TRUE. 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 ALWAYS 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
_________________
Contact Rich at: Rich.C@empowergmat.comThe Course Used By GMAT Club Moderators To Earn 750+ souvik101990 Score: 760 Q50 V42 ★★★★★ ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★



Math Expert
Joined: 02 Sep 2009
Posts: 64318

Re: If 5 ≥ x ≥ 0, which of the following must be true?
[#permalink]
Show Tags
11 Jun 2018, 10:20
sssjav wrote: Bunuel wrote: Sanjeetgujrall wrote: Can someone please explain me how C is the correct answer. I chose A.
III. 25 ≥ x^2 ≥ –25
How can we apply square root to 25 and simplify it to 5 ≥ x ≥ –5 5 ≥ x ≥ 0 means that 5 ≥ x ≥ 0 or 0 ≥ x ≥ 5. For any x from these ranges, 25 ≥ x^2 ≥ –25 will be true. I have a doubt here. Square root of 25 is an imaginary number, 5i. However that lies outside the range of values for x ( Which is [5,5] ) Doesn't that make StatementIII wrong as well? Numbers on the GMAT are real by default (GMAT deals with only real numbers), so no need to consider complex roots.
_________________



Intern
Joined: 05 Dec 2017
Posts: 19
GMAT 1: 710 Q49 V38

If 5 ≥ x ≥ 0, which of the following must be true?
[#permalink]
Show Tags
11 Jun 2018, 10:58
EMPOWERgmatRichC wrote: Hi sssjav,
Based on the information we're given at the beginning of the prompt, we know that X can be any value from 5 to +5 INCLUSIVE. That 'restriction' is what we have to work with when trying to determine which of the three Roman Numerals is ALWAYS TRUE.
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 ALWAYS 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 I agree to the points you've made, but my doubt remains unresolved. What you're saying is that for the concerned values of x ( [5,5] ), StatementIII will always be true  Even though the solution set of statementIII alone might include some values other than those with which we are concerned (All As are Bs, but all Bs are not As). so what you mean to say is that in a VennDiagramLanguage, the shape/circle representing [5,5] will lie enclosed within a bigger shape/circle of statementIII. (You can choose to ignore this statement if it it sounds confusing but you understood my point) However, by the above logic, even statementI and statementII will be true for the concerned values of x, even though the solution sets of the statements might include values other than the ones that belong to [5,5] and/or might not include some of the values from the set [5,5]. Now the questions asks us which of the given statements are "true"  according to me, there could only be two possible answers : if we go by the above logic, then all the three statements are true, and If we go by the logic that which of the statements truly represent the all the values of x, then none of the statements will be true. (as all of them represent some values which are either more or less than the concerned set) However, in another case, if it is asked, that which of the given statements will include ALL the concerned values of x, then statementIII is the best option available. I understand that this is what is meant to have been asked from the question. The thing that I need assistance with is understanding the language of the question  and narrow down on the correct meaning of the question. Where exactly did I interpret the question wrongly? Or what is it that I'm missing? EDIT : Just read bunuel's reply that gmat does not deal with imaginary number values, that clears up my doubt. Thanks to both of you for your resplies!



RSM Erasmus Moderator
Joined: 26 Mar 2013
Posts: 2445
Concentration: Operations, Strategy

Re: If 5 ≥ x ≥ 0, which of the following must be true?
[#permalink]
Show Tags
12 Jun 2018, 01:18
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. Final Answer: 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 ??




Re: If 5 ≥ x ≥ 0, which of the following must be true?
[#permalink]
12 Jun 2018, 01:18



Go to page
1 2
Next
[ 27 posts ]

