List A consists of 30 integers. If each integer in the list is more th

Question

List A consists of 30 integers. If each integer in the list is more than or equal to 3, what is the median of the list?

(1) Each integer in the list is less than or equal to 6

(2) The sum of the integer in the list is 104

What is the median of 30 numbers? Each of the numbers is greater more or equal to 3.
1) Each number <=6
2) The sum of the numbers is 104

rocky620 · Answer

Median will be (15th term+16th term)/2

(1) Each integer in the list is less than or equal to 6
 
All terms can be 3, 4, 5, or 6. the median will change accordingly
  Insufficient

(2) The sum of the integer in the list is 104 
Since all numbers are integers (lets minimize all numbers)
  Case-1  -Lets assume that all numbers are 3
so total = 90, difference = 104-90 = 14
That means there are 16 3's and 14 4's
Median = 3

Case-2  -Lets assume that all numbers are 4
so total = 120, difference = 104-20 = -16
Again, it means there are 16 3's and 14 4's (back to case 1)
Median = 3

If we increase the numbers the count of 3's will increase, but the median will remain 3 only.
  Sufficient

Option B

Tonkotsu · Answer

Hi  rocky620 , may I get some help with the method you used?
I'm not able to grasp how keeping all the numbers constant would help with solving this problem.

rocky620 · Answer

Hi  Tonkotsu 
We are keeping it constant to arrive at a benchmark for the sum of all terms. We can see that the minimum sum of all terms will be 90 and the maximum sum will be 180. Also, we are given that sum of all terms is 104.

Sum if all the terms are constant:
3 = 90
4 = 120
5 = 150
6 = 180

104 is between 90 & 120. The distance of 104 from 90 is 14, and from 120 is 16. So there must be more number of 3's than 4's (this is the least possible scenario). 
Lets us assume that there is a 5/6 in the set, so to balance the total sum we will have to increase the number of 3's in the set , but the median will remain same as we already have established that the 15th & 16th terms will be 3 only.

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List A consists of 30 integers. If each integer in the list is more th

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