Since \(x < y < z\), we can see that the median of the set must be y. So Quantity B = y

We have:
Quantity A: \(\frac{x + y + z}{3}\)

Quantity B: \(y\)


Multiply both quantities by 3 to get:
Quantity A: \(x + y + z\)
Quantity B: \(3y\)


Subtract \(y\) from both quantities to get
Quantity A: \(x + z\)
Quantity B: \(2y\)


GIVEN: The average (arithmetic mean) of x and z is greater than y

We can write: \(\frac{x + y}{2} > y\)

Multiply both sides of the inequality by 2 to get: \(x + y > 2y\)

Perfect! This last bit of information tells us that Quantity A must be greater

Answer: A

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