The median of 5 numbers is 50, and their range is 40. If the median of

Question

The median of 5 numbers is 50, and their range is 40. If the median of the 3 smallest numbers is 40, which of the following could represent the range of the 3 largest numbers?

I. 0
II. 20
III. 40

A. I only
B. II only
C. I and II only
D.I and III only
E. I, II and III

Source: Math Revolution

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paragw · Answer

Let the numbers be 
a ≤ 40 ≤ 50 ≤ d ≤ a+40

I. 0
Possible case: 10, 40, 50, 50, 50

II. 20
Possible case: 30, 40, 50, 50, 70

III. 40
Not possible coz max value of "e" can be 80

Hence,  C

dhart · Answer

the range of 40 for last 3 numbers is too high to achieve if the median is 50 and range is 40 , so only options 1 and 2

findingmyself · Answer

Let the smallest be Y, The largest hence becomes Y+40
From this we can infer that Y should be greater or equal to 10 and maximum of Y is 40 (If y becomes less than 10, then median will not be 50 and if Y become more than 40, the median of lowest three will be less than 40)

Let the numbers be:
Y, 40,50, Unknown, Y+40

Option 1: Zero: This is possible when Y=10
Option 2: 20: This is possible when Y=30
Option 3: 40, Not possible, Lets give Y its maximum value which is 40, then largest becomes 80 and range of largest three will be 80-50=30

sachin0411 · Answer

I thought this way.
_ 40 50 _ _ This is given
smallest number can not be less than 10, otherwise Range of 5 numbers will become more than 40
Hence,
10 40 50 50 50 -- Here Range of 5 is 40 and Range of last 3 is 0
Largest number can not be more than 80, otherwise Range of 5 numbers will become more than 40
Hence, 
40 40 50 80 80 -- here Range of 5 is 40 and Range of last 3 is 30
Hence Range of Last 3 numbers will be --> 0 ≤ Range ≤ 30

So Answer will be C

TheAdmissionHub · Answer

We have 5 numbers with 50 as median (ordered from greatest to smallest):  a,\: b,\: 50,\: d,\: e\:

Range:  a-e=40   ⭢  a=40+e

Median of the three smallest numbers is 40 ⭢  d=40

Therefore, our set is:  40+e,\: b,\: 50,\: 40,\: e\:

We have to find the range of the three gratest numbers, which is  a-50 .

(I) If  a-50=0  ⭢  a=50 .
Set will be:  50,\: 50,\: 50,\: 40,\: 10 
 Possible

(II)  If a-50=20  ⭢  a=70  
 Set will be:  70,\: b,\: 50,\: 40,\: 30\: , with  b   that can be any number between 50 and 70. 
 Possible

(III)  If a-50=40   ⭢  a=90  
 Set will be:  90,\: b,\: 50,\: 40,\: 50\:  ⭢  e   cannot be 50 because it has to be the smallest number. 
 Not possible

Answer: C

The median of 5 numbers is 50, and their range is 40. If the median of

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The median of 5 numbers is 50, and their range is 40. If the median of

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