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The median of a data set is x and its maximum is 40. The range of the
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[ 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. \(40 – 2x\)
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Re: The median of a data set is x and its maximum is 40. The range of the
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16 Aug 2018, 10:03
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



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Re: The median of a data set is x and its maximum is 40. The range of the
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16 Aug 2018, 16:49
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



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Re: The median of a data set is x and its maximum is 40. The range of the
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16 Aug 2018, 18:09
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
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Re: The median of a data set is x and its maximum is 40. The range of the
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16 Aug 2018, 18:49
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.
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Re: The median of a data set is x and its maximum is 40. The range of the
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16 Aug 2018, 19:14
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?
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Re: The median of a data set is x and its maximum is 40. The range of the
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16 Aug 2018, 19:27
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
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Re: The median of a data set is x and its maximum is 40. The range of the
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17 Aug 2018, 10:14
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.
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Re: The median of a data set is x and its maximum is 40. The range of the
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17 Aug 2018, 12:14
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.
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The median of a data set is x and its maximum is 40. The range of the
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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
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Re: The median of a data set is x and its maximum is 40. The range of the
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19 Aug 2018, 17:49
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.
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Re: The median of a data set is x and its maximum is 40. The range of the
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19 Aug 2018, 18:52
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
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Re: The median of a data set is x and its maximum is 40. The range of the
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19 Aug 2018, 19:30
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.
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Re: The median of a data set is x and its maximum is 40. The range of the
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19 Aug 2018, 19:45
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



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Re: The median of a data set is x and its maximum is 40. The range of the
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19 Aug 2018, 19:46
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



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Re: The median of a data set is x and its maximum is 40. The range of the
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19 Aug 2018, 20:01
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.
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Re: The median of a data set is x and its maximum is 40. The range of the
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19 Aug 2018, 20:41
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.
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Re: The median of a data set is x and its maximum is 40. The range of the
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20 Aug 2018, 06:30
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
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The median of a data set is x and its maximum is 40. The range of the
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20 Aug 2018, 12:03
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 \(x\)?
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