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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 Instructor
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The median of a data set is x and its maximum is 40. The range of the  [#permalink]

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Updated on: 20 Aug 2018, 13:09
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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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"Only $99 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Originally posted by MathRevolution on 16 Aug 2018, 08:58. Last edited by MathRevolution on 20 Aug 2018, 13:09, edited 2 times in total.  Math Revolution Discount Codes Optimus Prep Discount Codes Magoosh Discount Codes 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 $$Range = Median+10 = x+10$$ $$Max_{set}=40$$ $$x+10 =40-Min_{set}$$ $$Min_{set}=40-(x+10)$$ $$Min_{set}=30-x$$ @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=40-m 40-m=2(40-x) m=2x-40 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=40-m [highlight]40-m=2(40-x)[\highlight] m=2x-40 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 40-30=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 40-30=35+10 Or, 10=45? PKN -- Yes You are Right Range = Max - Min R=x+10 x+10=40-Min Min = 40-x-10 Min = 30-x 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 GMAT 1: 760 Q51 V42 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 40-30=35+10 Or, 10=45? PKN -- Yes You are Right Range = Max - Min R=x+10 x+10=40-Min Min = 40-x-10 Min = 30-x 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 one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$99 for 3 month Online Course"
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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]

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17 Aug 2018, 13:14
1
Quote:

There is a different expression of 30 - x in the options.
It is 2x - 40.[/quote]

Noted.

So, the set is: {2x-40,.......,x,.......,40}
Range=40-(2x-40)=40-2x+40=80-2x
Given, Range of the set is 10 greater than the median.
So, 80-2x=x+10
Let me solve the above equation.
3x=70
or, x=$$70/3$$=median value
So, minimum value=2x-40=140/3-40=20/3
Range=80-2x=80-2*70/3=80-140/3=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 2x-40 is a different expression of 30-x ?

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
GMAT 1: 760 Q51 V42
GPA: 3.82
The median of a data set is x and its maximum is 40. The range of the  [#permalink]

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Updated on: 26 Aug 2018, 12:13
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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 $$x – ( 40 – x ) = 2x – 40$$.

_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only 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 Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Originally posted by MathRevolution on 19 Aug 2018, 18:45. Last edited by MathRevolution on 26 Aug 2018, 12:13, edited 1 time in total. 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: {2x-40,.......,x,.......,40} Range=40-(2x-40)=40-2x+40=80-2x Given, Range of the set is 10 greater than the median. So, 80-2x=x+10 Let me solve the above equation. 3x=70 or, x=$$70/3$$=median value So, minimum value=2x-40=140/3-40=20/3 Range=80-2x=80-2*70/3=80-140/3=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 2x-40 is a different expression of 30-x ? 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 1 PKN wrote: PKN wrote: Quote: MathRevolution There is a different expression of 30 - x in the options. It is 2x - 40. Noted. So, the set is: {2x-40,.......,x,.......,40} Range=40-(2x-40)=40-2x+40=80-2x Given, Range of the set is 10 greater than the median. So, 80-2x=x+10 Let me solve the above equation. 3x=70 or, x=$$70/3$$=median value So, minimum value=2x-40=140/3-40=20/3 Range=80-2x=80-2*70/3=80-140/3=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 2x-40 is a different expression of 30-x ? 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=30-x So when you took 2x-40 as minimum 2x-40=30-x....3x=70...X=70/3 So you got X as 70/3 and 2x-40 satisfied it. But the same case will be for other choices too.. For example A. x-20 So m=30-x=x-20....X=25.. now solve the way you had solved for 2x-40 and you will get your answer. So {x-20,.......X,.......40} 40-(x-20)=X+10.....40-x+20=X+10....X=25 Now min =x-20=25-20=5 Range =40-5=35 also range =X+10=25+10=35 _________________ 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 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=40-m 40-m=2(40-x) m=2x-40 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 40-x? 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 2 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 30-x 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 2x-40. I am sure MathRevolution will look into any typo that might have occurred. _________________ 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 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 30-x 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 2x-40. 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 Top Contributor 1 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 GMAT 1: 760 Q51 V42 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 one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$99 for 3 month Online Course"
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The median of a data set is x and its maximum is 40. The range of the &nbs [#permalink] 20 Aug 2018, 13:03
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