GWD19-32

xiongxiong88

Q32:

A certain list consists of 3 different numbers. Does the median of the 3 numbers equal the average (arithmetic mean) of the 3 numbers?

(1) The range of the 3 numbers is equal to twice the difference between the greatest number and the median.

(2) The sum of the 3 numbers is equal to 3 times one of the numbers.

key is D ?... why 2 is correct??

THANKS

dingzhiyin19

Let the list be {a, b, c} where a > b > c so median = b
question: (a+b+c)/3 ? b
conditon 2: a+b+c = 3* one of the numbers.
=> 3*a > a+b+c (because a>b>c)
=> 3*c < a+b+c (because c<b<a)
"one of the numbers" has to be b => (a+b+c)/3 = b