kook44 wrote:
If the average (arithmetic mean) of four different numbers is 30, how many of the numbers are greater than 30?
(1) None of the four numbers is greater than 60.
(2) Two of the four numbers are 9 and 10, respectively.
Sum of the 4 numbers = (quantity)(average) = 4*30 = 120.
Statement 1:
Case 1: The four numbers are 32, 31, 30, 27
In this case, two of the numbers are greater than 30.
Case 2: The four numbers are 33, 32, 31, 24
In this case, three of the numbers are greater than 30.
INSUFFICENT.
Statement 2:
Case 1: The four numbers are 9, 10, 31, 70
In this case, two of the numbers are greater than 30.
Case 2: The four numbers are 9, 10, 30, 71
In this case, one of the numbers is greater than 30.
INSUFFICENT.
Statements combined:
Since the sum of the four numbers = 120, and two of the numbers are 9 and 10, the sum of the other two numbers = 120-9-10 = 101.
Since neither of the two remaining numbers may exceed 60, a sum of 101 is possible only if each of the two remaining numbers is greater than 30.
Thus, two of the numbers must be greater than 30.
SUFFICIENT.
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