Author 
Message 
TAGS:

Hide Tags

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6219
GPA: 3.82

The median of a data set is x and its maximum is 40. The range of the
[#permalink]
Show Tags
Updated on: 20 Aug 2018, 13:09
Question Stats:
55% (01:38) correct 45% (02:08) wrong based on 94 sessions
HideShow timer Statistics
[ Math Revolution GMAT math practice question] The average of the maximum and the minimum of a data set is \(x\) and its maximum is \(40\). The range of the set is \(10\) greater than \(x\). What is the minimum of the set in terms of \(x\)? A. \(x  20\) B. \(2x  40\) C. \(2x\) D. \(20 – x\) E. \(40 – 2x\)
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The oneandonly World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only $99 for 3 month Online Course" "Free Resources30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons  try it yourself"





Manager
Joined: 18 Jun 2018
Posts: 154

Re: The median of a data set is x and its maximum is 40. The range of the
[#permalink]
Show Tags
16 Aug 2018, 11:03
MathRevolution wrote: [ Math Revolution GMAT math practice question] The median of a data set is \(x\) and its maximum is \(40\). The range of the set is \(10\) greater than the median. What is the minimum of the set in terms of \(x\)? A. \(x  20\) B. \(2x  40\) C. \(2x\) D. \(20 – x\) E. \(40 – 2x\) \(Range = Max_{set}Min_{set}\), where \(Max_{set}\) is maximum of set and \(Min_{set}\) is minimum of set Given \(Range = Median+10 = x+10\) \(Max_{set}=40\) \(x+10 =40Min_{set}\) \(Min_{set}=40(x+10)\) \(Min_{set}=30x\) @MathRevolution,Please recheck OA



VP
Joined: 07 Dec 2014
Posts: 1087

Re: The median of a data set is x and its maximum is 40. The range of the
[#permalink]
Show Tags
16 Aug 2018, 17:49
MathRevolution wrote: [ Math Revolution GMAT math practice question] The median of a data set is \(x\) and its maximum is \(40\). The range of the set is \(10\) greater than the median. What is the minimum of the set in terms of \(x\)? A. \(x  20\) B. \(2x  40\) C. \(2x\) D. \(20 – x\) E. \(40 – 2x\) let minimum=m range=40m 40m=2(40x) m=2x40 B



Senior Manager
Joined: 06 Jan 2015
Posts: 474
Location: India
Concentration: Operations, Finance
GPA: 3.35
WE: Information Technology (Computer Software)

Re: The median of a data set is x and its maximum is 40. The range of the
[#permalink]
Show Tags
16 Aug 2018, 19:09
MathRevolution wrote: [ Math Revolution GMAT math practice question] The median of a data set is \(x\) and its maximum is \(40\). The range of the set is \(10\) greater than the median. What is the minimum of the set in terms of \(x\)? A. \(x  20\) B. \(2x  40\) C. \(2x\) D. \(20 – x\) E. \(40 – 2x\) Let x=35 and max = 40, range =10, min =30 2(35)40 = 30 Only OPtion B satisfies Hence B
_________________
आत्मनॊ मोक्षार्थम् जगद्धिताय च
Resource: GMATPrep RCs With Solution



Director
Status: Learning stage
Joined: 01 Oct 2017
Posts: 852
WE: Supply Chain Management (Energy and Utilities)

Re: The median of a data set is x and its maximum is 40. The range of the
[#permalink]
Show Tags
16 Aug 2018, 19:49
gracie wrote: MathRevolution wrote: [ Math Revolution GMAT math practice question] The median of a data set is \(x\) and its maximum is \(40\). The range of the set is \(10\) greater than the median. What is the minimum of the set in terms of \(x\)? A. \(x  20\) B. \(2x  40\) C. \(2x\) D. \(20 – x\) E. \(40 – 2x\) let minimum=m range=40m [highlight]40m=2(40x)[\highlight] m=2x40 B Could you please explain the reasoning used in the highlighted portion? Thanking you in advance.
_________________
Regards,
PKN
Rise above the storm, you will find the sunshine



Director
Status: Learning stage
Joined: 01 Oct 2017
Posts: 852
WE: Supply Chain Management (Energy and Utilities)

Re: The median of a data set is x and its maximum is 40. The range of the
[#permalink]
Show Tags
16 Aug 2018, 20:14
NandishSS wrote: MathRevolution wrote: [ Math Revolution GMAT math practice question] The median of a data set is \(x\) and its maximum is \(40\). The range of the set is \(10\) greater than the median. What is the minimum of the set in terms of \(x\)? A. \(x  20\) B. \(2x  40\) C. \(2x\) D. \(20 – x\) E. \(40 – 2x\) Let x=35 and max = 40, range =10, min =30 2(35)40 = 30 Only OPtion B satisfies Hence B So, x(min)=30, x=median=35, x(max)=40 Set={x(min),.......,x(=median),.........,x(max)} Or, Set={30,....,35,....,40} Let's check whether it satisfies all the conditions given in the question. Range of the set is 10 greater than the median. Implies that 4030=35+10 Or, 10=45?
_________________
Regards,
PKN
Rise above the storm, you will find the sunshine



Senior Manager
Joined: 06 Jan 2015
Posts: 474
Location: India
Concentration: Operations, Finance
GPA: 3.35
WE: Information Technology (Computer Software)

Re: The median of a data set is x and its maximum is 40. The range of the
[#permalink]
Show Tags
16 Aug 2018, 20:27
PKN wrote: NandishSS wrote: MathRevolution wrote: [ Math Revolution GMAT math practice question] The median of a data set is \(x\) and its maximum is \(40\). The range of the set is \(10\) greater than the median. What is the minimum of the set in terms of \(x\)? A. \(x  20\) B. \(2x  40\) C. \(2x\) D. \(20 – x\) E. \(40 – 2x\) Let x=35 and max = 40, range =10, min =30 2(35)40 = 30 Only OPtion B satisfies Hence B So, x(min)=30, x=median=35, x(max)=40 Set={x(min),.......,x(=median),.........,x(max)} Or, Set={30,....,35,....,40} Let's check whether it satisfies all the conditions given in the question. Range of the set is 10 greater than the median. Implies that 4030=35+10 Or, 10=45? PKN  Yes You are Right Range = Max  Min R=x+10 x+10=40Min Min = 40x10 Min = 30x Not in options Bunuel Can you pls check this? MathRevolution
_________________
आत्मनॊ मोक्षार्थम् जगद्धिताय च
Resource: GMATPrep RCs With Solution



Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6219
GPA: 3.82

Re: The median of a data set is x and its maximum is 40. The range of the
[#permalink]
Show Tags
17 Aug 2018, 11:14
PKN wrote: NandishSS wrote: MathRevolution wrote: [ Math Revolution GMAT math practice question] The median of a data set is \(x\) and its maximum is \(40\). The range of the set is \(10\) greater than the median. What is the minimum of the set in terms of \(x\)? A. \(x  20\) B. \(2x  40\) C. \(2x\) D. \(20 – x\) E. \(40 – 2x\) Let x=35 and max = 40, range =10, min =30 2(35)40 = 30 Only OPtion B satisfies Hence B So, x(min)=30, x=median=35, x(max)=40 Set={x(min),.......,x(=median),.........,x(max)} Or, Set={30,....,35,....,40} Let's check whether it satisfies all the conditions given in the question. Range of the set is 10 greater than the median. Implies that 4030=35+10 Or, 10=45? PKN  Yes You are Right Range = Max  Min R=x+10 x+10=40Min Min = 40x10 Min = 30x Not in options Bunuel Can you pls check this? MathRevolution[/quote] There is a different expression of 30  x in the options. It is 2x  40.
_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The oneandonly World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only $99 for 3 month Online Course" "Free Resources30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons  try it yourself"



Director
Status: Learning stage
Joined: 01 Oct 2017
Posts: 852
WE: Supply Chain Management (Energy and Utilities)

Re: The median of a data set is x and its maximum is 40. The range of the
[#permalink]
Show Tags
17 Aug 2018, 13:14
Quote: There is a different expression of 30  x in the options. It is 2x  40.[/quote] Noted. So, the set is: {2x40,.......,x,.......,40} Range=40(2x40)=402x+40=802x Given, Range of the set is 10 greater than the median. So, 802x=x+10 Let me solve the above equation. 3x=70 or, x=\(70/3\)=median value So, minimum value=2x40=140/340=20/3 Range=802x=802*70/3=80140/3=100/3 Given, Range of the set is 10 greater than the median. So, 100/3=70/3+10=100/3 (Got it) But how to figure out that 2x40 is a different expression of 30x ? Do we have to check all the answer options? Thanking you.
_________________
Regards,
PKN
Rise above the storm, you will find the sunshine



Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6219
GPA: 3.82

The median of a data set is x and its maximum is 40. The range of the
[#permalink]
Show Tags
Updated on: 26 Aug 2018, 12:13
=> Attachment:
8.20.png [ 1.12 KiB  Viewed 675 times ]
The range of the set is \(2\) times \(40 – x\), since \(40 – x\) is the distance between \(x\) and the maximum. The minimum is the median minus the distance between the median and the maximum, which is \(x – ( 40 – x ) = 2x – 40\). Therefore, the answer is B. Answer : B
_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The oneandonly World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only $99 for 3 month Online Course" "Free Resources30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons  try it yourself"



Director
Status: Learning stage
Joined: 01 Oct 2017
Posts: 852
WE: Supply Chain Management (Energy and Utilities)

Re: The median of a data set is x and its maximum is 40. The range of the
[#permalink]
Show Tags
19 Aug 2018, 18:49
PKN wrote: Quote: There is a different expression of 30  x in the options. It is 2x  40. Noted. So, the set is: {2x40,.......,x,.......,40} Range=40(2x40)=402x+40=802x Given, Range of the set is 10 greater than the median. So, 802x=x+10 Let me solve the above equation. 3x=70 or, x=\(70/3\)=median value So, minimum value=2x40=140/340=20/3 Range=802x=802*70/3=80140/3=100/3 Given, Range of the set is 10 greater than the median. So, 100/3=70/3+10=100/3 (Got it) But how to figure out that 2x40 is a different expression of 30x ? Do we have to check all the answer options? Thanking you.[/quote] Hi chetan2u, Could you please explain ? I am not convinced with the official explanation. Thanking you in advance.
_________________
Regards,
PKN
Rise above the storm, you will find the sunshine



Math Expert
Joined: 02 Aug 2009
Posts: 6796

Re: The median of a data set is x and its maximum is 40. The range of the
[#permalink]
Show Tags
19 Aug 2018, 19:52
PKN wrote: PKN wrote: Quote: MathRevolutionThere is a different expression of 30  x in the options. It is 2x  40. Noted. So, the set is: {2x40,.......,x,.......,40} Range=40(2x40)=402x+40=802x Given, Range of the set is 10 greater than the median. So, 802x=x+10 Let me solve the above equation. 3x=70 or, x=\(70/3\)=median value So, minimum value=2x40=140/340=20/3 Range=802x=802*70/3=80140/3=100/3 Given, Range of the set is 10 greater than the median. So, 100/3=70/3+10=100/3 (Got it) But how to figure out that 2x40 is a different expression of 30x ? Do we have to check all the answer options? Thanking you. Hi chetan2u, Could you please explain ? I am not convinced with the official explanation. Thanking you in advance. Hi.. I can tell you that the method you have applied will be correct for all values and that is when the m=30x So when you took 2x40 as minimum 2x40=30x....3x=70...X=70/3 So you got X as 70/3 and 2x40 satisfied it. But the same case will be for other choices too.. For example A. x20 So m=30x=x20....X=25.. now solve the way you had solved for 2x40 and you will get your answer. So {x20,.......X,.......40} 40(x20)=X+10.....40x+20=X+10....X=25 Now min =x20=2520=5 Range =405=35 also range =X+10=25+10=35
_________________
1) Absolute modulus : http://gmatclub.com/forum/absolutemodulusabetterunderstanding210849.html#p1622372 2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html 3) effects of arithmetic operations : https://gmatclub.com/forum/effectsofarithmeticoperationsonfractions269413.html
GMAT online Tutor



Director
Status: Learning stage
Joined: 01 Oct 2017
Posts: 852
WE: Supply Chain Management (Energy and Utilities)

Re: The median of a data set is x and its maximum is 40. The range of the
[#permalink]
Show Tags
19 Aug 2018, 20:30
Thank you Sir. I have to verify each of the answer options since the direct method don't work here. I thought there must be some easy way out.
_________________
Regards,
PKN
Rise above the storm, you will find the sunshine



Manager
Joined: 09 Oct 2015
Posts: 222

Re: The median of a data set is x and its maximum is 40. The range of the
[#permalink]
Show Tags
19 Aug 2018, 20:45
gracie wrote: MathRevolution wrote: [ Math Revolution GMAT math practice question] The median of a data set is \(x\) and its maximum is \(40\). The range of the set is \(10\) greater than the median. What is the minimum of the set in terms of \(x\)? A. \(x  20\) B. \(2x  40\) C. \(2x\) D. \(20 – x\) E. \(40 – 2x\) let minimum=m range=40m 40m=2(40x) m=2x40 B Can you explain how you got the rhs of the eq? Posted from my mobile device



Manager
Joined: 09 Oct 2015
Posts: 222

Re: The median of a data set is x and its maximum is 40. The range of the
[#permalink]
Show Tags
19 Aug 2018, 20:46
MathRevolution wrote: => Attachment: 8.20.png The range of the set is \(2\) times \(40 – x\), since \(40 – x\) is the distance between the median and the maximum. The minimum is the median minus the distance between the median and the maximum, which is \(x – ( 40 – x ) = 2x – 40\). Therefore, the answer is B. Answer : B How do we know range is 2 times 40x? Posted from my mobile device



Math Expert
Joined: 02 Aug 2009
Posts: 6796

Re: The median of a data set is x and its maximum is 40. The range of the
[#permalink]
Show Tags
19 Aug 2018, 21:01
PKN wrote: Thank you Sir. I have to verify each of the answer options since the direct method don't work here. I thought there must be some easy way out. What I meant was that all choices will fit in unless X>40... So our answer should be 30x in present state. May be the question is missing something like all elements are equally spaced that is it is an AP. Then answer would be 2x40. I am sure MathRevolution will look into any typo that might have occurred.
_________________
1) Absolute modulus : http://gmatclub.com/forum/absolutemodulusabetterunderstanding210849.html#p1622372 2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html 3) effects of arithmetic operations : https://gmatclub.com/forum/effectsofarithmeticoperationsonfractions269413.html
GMAT online Tutor



Director
Status: Learning stage
Joined: 01 Oct 2017
Posts: 852
WE: Supply Chain Management (Energy and Utilities)

Re: The median of a data set is x and its maximum is 40. The range of the
[#permalink]
Show Tags
19 Aug 2018, 21:41
chetan2u wrote: PKN wrote: Thank you Sir. I have to verify each of the answer options since the direct method don't work here. I thought there must be some easy way out. What I meant was that all choices will fit in unless X>40... So our answer should be 30x in present state. May be the question is missing something like all elements are equally spaced that is it is an AP. Then answer would be 2x40. I am sure MathRevolution will look into any typo that might have occurred. Thank you sir for your time. The question may be modified in either of the following ways: 1) The elements of the set are evenly spaced. Or, 2) Which of the following COULD be the minimum of the set in terms of x? This is my understanding in succinct in order to arrive at the given correct answer option.
_________________
Regards,
PKN
Rise above the storm, you will find the sunshine



CEO
Joined: 12 Sep 2015
Posts: 2864
Location: Canada

Re: The median of a data set is x and its maximum is 40. The range of the
[#permalink]
Show Tags
20 Aug 2018, 07:30
MathRevolution wrote: The range of the set is \(2\) times \(40 – x\), since \(40 – x\) is the distance between the median and the maximum. The minimum is the median minus the distance between the median and the maximum, which is \(x – ( 40 – x ) = 2x – 40\).
Therefore, the answer is B.
Answer : B The only time the range = 2(maximum value  median) is when the median is the average of the minimum and maximum value. For example, in the set {1, 9, 17}, the range = 17  1 = 16, which is equal to 2(maximum value  median) However, the rule, range = 2(maximum value  median), does not work when the median is NOT the average of the minimum and maximum value. For example, the set {9, 39, 40} satisfies the given information Here, x = 39, the maximum value is 40, and the range (of 49) is 10 greater than the median (39) In this case, minimum value (9) does NOT equal 2x  40 Cheers, Brent
_________________
Brent Hanneson – GMATPrepNow.com
Sign up for our free Question of the Day emails



Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6219
GPA: 3.82

The median of a data set is x and its maximum is 40. The range of the
[#permalink]
Show Tags
20 Aug 2018, 13:03
GMATPrepNow wrote: MathRevolution wrote: The range of the set is \(2\) times \(40 – x\), since \(40 – x\) is the distance between the median and the maximum. The minimum is the median minus the distance between the median and the maximum, which is \(x – ( 40 – x ) = 2x – 40\).
Therefore, the answer is B.
Answer : B The only time the range = 2(maximum value  median) is when the median is the average of the minimum and maximum value. For example, in the set {1, 9, 17}, the range = 17  1 = 16, which is equal to 2(maximum value  median) However, the rule, range = 2(maximum value  median), does not work when the median is NOT the average of the minimum and maximum value. For example, the set {9, 39, 40} satisfies the given information Here, x = 39, the maximum value is 40, and the range (of 49) is 10 greater than the median (39) In this case, minimum value (9) does NOT equal 2x  40 Cheers, Brent You are right. The question should be changed to the following. It is fixed now. The average of the maximum and the minimum of a data set is \(x\) and its maximum is \(40\). The range of the set is \(10\) greater than \(x\). What is the minimum of the set in terms of \(x\)?
_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The oneandonly World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only $99 for 3 month Online Course" "Free Resources30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons  try it yourself"




The median of a data set is x and its maximum is 40. The range of the &nbs
[#permalink]
20 Aug 2018, 13:03






