karthikpandian19 wrote:Margo purchased 3 items at a Labor Day sale. She received discounts off the regular prices of items according to the following: 40 percent off the most expensive item and 20 percent off the others. Was the total amount of the three discounts Margo received greater than 30 percent of the sum of the regular prices of the items?
The regular price of the most expensive item was 100 $, and the regular price of the next most expensive item was 40 $.
The regular price of the least expensive item was 30$.
Very little math is needed if we understand how weighted averages work.
If the sum of the regular prices of the two least expensive items (each purchased at a 20% discount) is EQUAL to the regular price of the most expensive item (purchased at a 40% discount), then the total amount of the discount will be 30% -- HALFWAY BETWEEN 20% and 40%.
To illustrate:
Let the regular price of the two least expensive items = 25 and the regular price of the most expensive item = 50, for a total cost of 100.
Discount received = .2(25+25) + .4(50) = 30, a discount of 30%.
Thus, for the total discount to EXCEED 30%, the regular price of the most expensive item -- which receives the GREATER discount -- must be GREATER than the sum of the regular prices of the two least expensive items.
Question rephrased: Is the regular price of the most expensive item GREATER than the sum of the regular prices of the two least expensive items?
Statement 1: The regular price of the most expensive item was $100, and the regular price of the next most expensive item was $40.
Thus, the regular price of the most expensive item (100) is greater than the maximum possible sum of the regular prices of the two least expensive items (40+40=80).
SUFFICIENT.
Statement 2: The regular price of the least expensive item was $30.
No information about the regular price of the most expensive item.
INSUFFICIENT.
The correct answer is
A.
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