The average of x and y is 30. The average of x, y, and z is 40. What is the average of x, y, and 2z?

Correct — C.
Turn each average into a total.

x + y = 2 × 30 = 60
x + y + z = 3 × 40 = 120
Subtract: z = 120 − 60 = 60

x + y + 2z = 60 + 2 × 60 = 180
Average of the three = 180 ÷ 3 = 60 → option (c)

Why the others are wrong

• (a)
  50 — 50 raises the old average of 40 by only 10. Doubling z adds one more z = 60 to a total of three terms, so the average rises by 60 ÷ 3 = 20.
• (b)
  55 — 55 would need x + y + 2z = 165, which makes z = 52.5. The two averages fix z at 120 − 60 = 60.
• (d)
  65 — 65 would need x + y + 2z = 195, which makes z = 67.5. The two averages fix z at exactly 60.

Average × count = total. Averages cannot be added or doubled directly, but totals can.

Once z is known, x + y + 2z is the old total plus one more z: 120 + 60 = 180.

The divisor stays 3. The question averages three quantities, x, y and 2z, even though z's value enters twice.

Key facts

• Sum = average × number of terms
• x + y = 60 and x + y + z = 120 give z = 60
• Replacing z by 2z adds z to the total, so the average of three rises by z ⁄ 3 = 20

Common traps

• Dividing 180 by 4 because z appears twice, when x, y and 2z are still three terms
• Repeating the rise from 30 to 40 and answering 50, when doubling z raises the average by z ⁄ 3 = 20

No directly related past PYQ was found.