A certain list consists of 3 different numbers…
We are given that a certain list contains three different numbers. Let’s label these three numbers.
a = smallest number
b = middle number
c = largest number
Since b is the middle number, it is also the median. We must determine whether the median is equal to the average of the three numbers. Using the formula average = sum/number, we have:
b = (a+b+c)/3 ?
3b = a + b + c ?
2b = a + c ?
Statement One Alone:
The range of the three numbers is equal to twice the difference between the greatest number and the median.
Using the information from statement one, we can create the following equation:
c – a = 2(c – b)
c – a = 2c – 2b
2b = c + a
Statement one alone is sufficient to answer the question. We can eliminate answer choices B, C, and E.
Statement Two Alone:
The sum of the three numbers is equal to 3 times one of the numbers.
So we could have a + b + c = 3a OR a + b + c = 3b OR a + b + c = 3c.
However, under closer inspection, the first case is not possible. If it were, then a + b + c = 3a would mean b + c = 2a, but we know both b and c are greater than a, so there is no way b + c = 2a. Similarly, the last case is also not possible. If it were, then a + b + c = 3c would mean a + b = 2c, but we know both a and b are less than c, so there is no way a + b = 2c.
Thus, only the second case is possible: a + b + c = 3b and from this, we see that a + c = 2b. Statement two alone is also sufficient to answer the question.