BTGmoderatorDC wrote:If a, b, c and d are distinct numbers, can b be the average of a, b, c and d?
(1) a + c = 2d
(2) b + d = 2c
If b is the average of a, b, c and d, then b = (a + b + c + d)/4
=> 3b = a + c + d
Let's take each statement one by one.
(1) a + c = 2d
Assuming that b is the average of a, b, c and d, then 3b = a + c + d
Replacing the value of Statement 1: a + c = 2d in 3b = a + c + d, we get b = d.
However, b = d is not possible since a, b, c and d are distinct numbers; thus, we can conclude that b is NOT the average of a, b, c and d. Sufficient.
(2) b + d = 2c
Case 1: Say a = -1, b = 2, c = 3, and d = 4; then b is the average; then answer is yes.
Case 2: Say a = 1, b = 2, c = 3, and d = 4; Average = 2.5; b is NOT the average; then answer is no.
No unique answer. Insufficient.
The correct answer:
A
Hope this helps!
-Jay
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