A merchant discounted the sale price of a coat and the sale price of a sweater. Which of the two articles of clothing

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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.

Answer: E

Source: Official Guide

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Gmat_mission wrote:
Wed Sep 29, 2021 8:36 am
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.

Answer: E

Source: Official Guide
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 discount

Case 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 discount

Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer: E

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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