Bunuel wrote:
A merchant discounted the sale price of a coat and the sale price of a sweater. Was the discount in dollars on the coat greater than that on the sweater?
(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: Was the discount in dollars on the coat greater than that on the sweater? Statement 1: The percent discount on the coat was 2 percentage points greater than the percent discount on the sweater No information about the PRICES before the discount.
NOT SUFFICIENT
Statement 2: Before the discounts, the sale price of the coat was $10 less than the sale price of the sweaterNo information about the PERCENT DISCOUNTS.
NOT SUFFICIENT
Statements 1 and 2 combined Let
x = the PRE-DISCOUNT price of a coat
So,
x + 10 = the PRE-DISCOUNT price of a sweater
Let
p= the percent discount on a sweater
So,
p + 2 = the percent discount on a coat
So, the dollar discount on the sweater = (
p/100)(
x + 10 )
And the dollar discount on the coat = [
(p + 2)/100](
x)
So, the question becomes:
"Is [(p + 2)/100](x) > (p/100)(x + 10 )?"Multiply both sides by 100 to get: Is (p + 2)(x) > (p)(x + 10)?
Expand both sides to get: Is px + 2x > px + 10p?
Subtract px from both sides to get: Is 2x > 10p?
And for kicks, let's divide both sides by 2 to get: Is x > 5p?
In other words, Is the PRE-DISCOUNT price of a coat
greater than 5 times the percent discount on a sweater?
Since we can't answer this question with certainty, the correct answer is E.
If you're not convinced, check out these two possible cases:
Case a: The pre-discount coat price is $100, and there a 4% discount on the coat. Total discount = 4% of $100 = $4.00
The pre-discount sweater price $110, and there a 2% discount on the coat. Total discount = 2% of $110 = $2.20. In this case, the answer to the target question is
YES, the coat discount IS greater than the sweater discountCase b: The pre-discount coat price is $1, and there a 3% discount on the coat. Total discount = 3% of $1 = $0.03
The pre-discount sweater price $11, and there a 1% discount on the coat. Total discount = 1% of $11 = $0.11. In this case, the answer to the target question is
NO, the coat discount is NOT greater than the sweater discountSince we cannot answer the
target question with certainty, the combined statements are NOT SUFFICIENT
Answer: E
Cheers,
Brent