If the average (arithmetic mean) of 4 numbers is 30, how many of the numbers are greater than 30 ?
(1) Two of the numbers are equal to 20.
(2) None of the numbers are equal to 30.
When it is given that the average of 4 nos is 30, we can ASSUME that each no is equal to 30.
Thus, we can represent the nos as 30,30,30,30.Note that if we reduce any one of the quantity, say 30 by 10, we will have to redistribute that same quantity amongst the other 3 nos to keep the same average.
From F.S 1, two of the nos are equal to 20. Thus, this could either lead to 20,20,30,50 OR 20,20,40,40. In both the scenarios, we get different answers for # greater than 30. Insufficient.
From F.S 2, the given set can be represented as 29,29,31,31 OR 28,28,28,36. Again, Insufficient.
Taking both together also, we can have either 20,20,31,49 OR 20,20,25,55. Insufficient.
All that is equal and not-Deep Dive In-equality
Hit and Trial for Integral Solutions