If a, b, c and d are distinct numbers, can b be the average

[BTGmoderatorDC]

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

[Jay@ManhattanReview]

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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