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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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Originally posted by MathRevolution on 16 Aug 2018, 07:58.
Last edited by MathRevolution on 20 Aug 2018, 12:09, edited 2 times in total.
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Re: The median of a data set is x and its maximum is 40. The range of the  [#permalink]

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New post 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 \(Range = Median+10 = x+10\)
\(Max_{set}=40\)
\(x+10 =40-Min_{set}\)
\(Min_{set}=40-(x+10)\)
\(Min_{set}=30-x\)
@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  [#permalink]

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New post 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=40-m
40-m=2(40-x)
m=2x-40
B
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Re: The median of a data set is x and its maximum is 40. The range of the  [#permalink]

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New post 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  [#permalink]

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New post 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=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.
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Re: The median of a data set is x and its maximum is 40. The range of the  [#permalink]

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New post 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 40-30=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  [#permalink]

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New post 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 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
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Re: The median of a data set is x and its maximum is 40. The range of the  [#permalink]

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New post 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 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.
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Re: The median of a data set is x and its maximum is 40. The range of the  [#permalink]

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New post 17 Aug 2018, 12:14
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.
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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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New post Updated on: 26 Aug 2018, 11:13
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=>

Attachment:
8.20.png
8.20.png [ 1.12 KiB | Viewed 854 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
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Originally posted by MathRevolution on 19 Aug 2018, 17:45.
Last edited by MathRevolution on 26 Aug 2018, 11:13, edited 1 time in total.
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Re: The median of a data set is x and its maximum is 40. The range of the  [#permalink]

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New post 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: {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.
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Re: The median of a data set is x and its maximum is 40. The range of the  [#permalink]

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New post 19 Aug 2018, 18:52
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
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New post 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  [#permalink]

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New post 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=40-m
40-m=2(40-x)
m=2x-40
B


Can you explain how you got the rhs of the eq?

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

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New post 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 40-x?

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

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New post 19 Aug 2018, 20:01
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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.
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Re: The median of a data set is x and its maximum is 40. The range of the  [#permalink]

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New post 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 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.
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Re: The median of a data set is x and its maximum is 40. The range of the  [#permalink]

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New post 20 Aug 2018, 06:30
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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  [#permalink]

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New post 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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