The median of a data set is x and its maximum is 40. The range of the

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

Bismarck · Answer

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

gracie · Answer

let minimum=m
range=40-m
40-m=2(40-x)
m=2x-40
B

NandishSS · Answer

Let x=35 and max = 40, range =10, min =30

2(35)-40 = 30

Only OPtion B satisfies

Hence B

PKN · Answer

Could you please explain the reasoning used in the highlighted portion?
Thanking you in advance.

PKN · Answer

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?

NandishSS · Answer

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

MathRevolution · Answer

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

PKN · Answer

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.

MathRevolution · Answer

=> 8.20.png 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

PKN · Answer

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.

chetan2u · Answer

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

PKN · Answer

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.

rahulkashyap · Answer

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

Posted from my mobile device

rahulkashyap · Answer

How do we know range is 2 times 40-x?

Posted from my mobile device

chetan2u · Answer

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.

PKN · Answer

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.

BrentGMATPrepNow · Answer

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

MathRevolution · Answer

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 ?

kanishaksharma · Answer

This is the question I can see, whereas the solution is discussed for a different problem. According to this question answer must be x/2 - 5, which is not there in options.

The median of a data set is x and its maximum is 40. The range of the

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

The median of a data set is x and its maximum is 40. The range of the

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards