annaleroy wrote:
Henry purchased three items during a sale. He received a 20% discount on the regular price of the most expensive of the 3 items and a 10 percent discount on the regular price of each of the other two items. What was the total amount of the 3 discounts?
(1) the average (arithmetic mean) of the regular prices of the 3 items was $30.
(2) the regular price of the most expensive of the 3 items was $50
Let's say that X is the most expensive item.
and the prices of items purchased are in this order: X>Y>Z
So the actual price of the 3 items: X+Y+Z
Discount he got on item X: 0.2X
Price he paid for the item X: 0.8X
Discount he got on item Y: 0.1Y
Price he paid for the item Y: 0.9Y
Discount he got on item Z: 0.9Z
Price he paid for the item Z: 0.9Z
Total discount he got: 0.2X+0.1Y+0.1Z =
0.2X + 0.1 (Y+Z)Statement A: the average (arithmetic mean) of the regular prices of the 3 items was $30
\(\frac{X+Y+Z}{3} = 30\)
X+Y+Z = 90
Clearly NOT Sufficient
Statement B: the regular price of the most expensive of the 3 items was $50
X = 50
Discount on X: 0.2X = 0.2x50 = $10
No information about Y and Z.
Not Sufficient
Together:
X+Y+Z = 90
X = 50
Y+Z = 40
0.2X = $10
0.1 (Y+Z) = 0.1 x 40 = $4
Total Discount: $10+$4 = $14
Sufficient