docabuzar wrote:
Henry purchased 3 items during a sale. He received a 20 percent discount off the regular price of the most expensive item and a 10 percent discount off the regular price of each of the other 2 items. Was the total amount of the 3 discounts greater than 15 percent of the sum of the regular prices of the 3 items?
(1) The regular price of the most expensive item was $50, and the regular price of the next most expensive item was $20
(2) The regular price of the least expensive item was $15
We can treat this as a MIXTURE PROBLEM.
How can we combine a 20% solution (the higher discount) with a 10% solution (the lower discount) to yield a mixture that is more than 15% (the total discount)?
If we use EQUAL amounts of 20% solution and 10% solution, the resulting solution will be exactly 15%.
Implication:
To yield a solution that is MORE THAN 15%, we must use MORE OF the 20% solution and LESS OF the 10% solution.
In other words:
The price of the most expensive item (the 20% solution) must be greater than the total cost of the two cheaper items (the 10% solution).:
Question stem, rephrased:
Is the price of the most expensive item greater than the total cost of the two cheaper items?
Statement 1: The regular price of the most expensive item was $50, and the regular price of the next most expensive item was $20.Maximum total cost of the two cheaper items = 20+20 = 40.
Since the price of the most expensive item ($50) is greater than the maximum total cost of the 2 cheaper items ($40), the answer to the rephrased question stem is YES.
SUFFICIENT.
Statement 2: The regular price of the least expensive item was $15.No way to determine whether the price of the most expensive item is greater than the total cost of the 2 cheaper items.
INSUFFICIENT.
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