metallicafan wrote:If the average (arithmetic mean) of 4 different numbers is 30, how many of the numbers are less than 30?
(1) The median of the numbers is 30.
(2) The largest and smallest of the numbers are odd, and the two middle numbers are even.
We can combine some logic with the some number picking.
Target question:
How many of the numbers are less than 30?
Given: If the average (arithmetic mean) the 4 numbers is is 30
So, the sum of all 4 numbers must = (4)(30) = 120
For the ease of an explanation, let's say that if we arrange the 4 numbers in ascending order we get a, b, c, d
In other words, a < b < c < d
Statement 1: The median of the numbers is 30.
Since there are 4 numbers, the median (30) must equal the mean of the 2 middlemost numbers.
So, the mean of b and c must equal 30
This means that b +c must equal 60.
Since the two numbers cannot be equal, b must be less than 30 and c must be greater than 30.
In other words b < 30 < c
When we add a and d, we get a < b < 30 < c < d
So,
2 of the numbers are less than 30
Since we can answer the
target question with certainty, statement 1 is SUFFICIENT
Statement 2: The largest and smallest of the numbers are odd, and the two middle numbers are even.
There are several sets of numbers that meet this condition. Here are two:
Case a: the numbers are {1, 2, 4, 113} in which case
3 of the numbers are less than 30
Case b: the numbers are {27, 28, 32, 33} in which case
2 of the numbers are less than 30
Since we
cannot answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Answer =
A
Cheers,
Brent
