Bunuel wrote:
A merchant discounted the sale price of a coat and the sale price of a sweater. Which of the two articles of clothing was discounted by the greater dollar amount?
(1) The percent discount on the coat was 2 percentage points greater than the percent discount on the sweater.
(2) Before the discounts, the sale price of the coat was $10 less than the sale price of the sweater.
Target question: Which of the two articles of clothing was discounted by the greater dollar amount?Let's jump straight to....
Statements 1 and 2 combined Let p = percent discount on SWEATER
So, p+2 = percent discount on COAT
Let x = price of SWEATER
before discount
Let x - 10 = price of COAT
before discount
Now let's calculate the discount for each item.
Discount on SWEATER = (p/100)(x)
Discount on COAT = (p+2/100)(x - 10)
Let's make things easier on ourselves by multiplying both values by 100 to get:
Discount on SWEATER = (p)(x)
Discount on COAT = (p + 2)(x - 10)
So, which value is greater?
Is (p)(x) greater than (p + 2)(x - 10)? Or is (p + 2)(x - 10) greater than (p)(x)?
Let's test some values.
Case a: p = 8 and x = 11.
In this case, (p)(x) = (8)(11) = 88 (= discount on SWEATER)
And (p + 2)(x - 10) = (8 + 2)(11 - 10) = (10)(1) = 10 (= discount on COAT)
So, the answer to the target question is
the SWEATER has the greater discountCase a: p = 8 and x = 110.
In this case, (p)(x) = (8)(110) = 880 (= discount on SWEATER)
And (p + 2)(x - 10) = (8 + 2)(110 - 10) = (10)(100) = 1000 (= discount on COAT)
So, the answer to the target question is
the COAT has the greater discountSince we cannot answer the
target question with certainty, the combined statements are NOT SUFFICIENT
Answer: E
Cheers,
Brent