Last Updated on May 10, 2023
GMAT OFFICIAL GUIDE DS
Solution:
We must determine whether the coat or the sweater was discounted by a greater amount.
Statement One Alone:
The percent discount on the coat was 2 percentage points greater than the percent discount on the sweater.
Using the information in statement one we know that the discount on the coat was 2 percentage points greater than the percent discount on the sweater; however, because we do not know the original price of either item, we cannot determine which item was discounted by a greater amount. A larger percentage difference is not the same as a larger dollar difference. Statement one alone is not sufficient to answer the question. We can eliminate answer choices A and D.
Statement Two Alone:
Before the discounts, the sale price of the coat was $10 less than the sale price of the sweater.
Using the information in statement two we know that the sale price of the coat was $10 less than the sale price of the sweater; however, we still do not know the original price of either the coat or sweater, nor do we know the discounts applied to those items. Statement two alone is not sufficient to answer the question. We can eliminate answer choice B.
Statements One and Two Together:
Using the information from statements one and two we know that the percent discount on the coat was 2 percentage points greater than the percent discount on the sweater and that before the discounts, the sale price of the coat was $10 less than the sale price of the sweater. Although we may think we have enough information to determine the answer, we must remember that we are not provided with any actual numerical values for the prices of either the coat or the sweater nor the percentage discount on either of the items. Without that information, we cannot determine whether the coat or the sweater had the larger discount. If this is hard to see, let’s use some sample numbers below.
Scenario 1:
Price of coat = 20
% discount of coat = 4%
Discount on coat = 20 x 0.04 = 0.80
Price of sweater = 30
% discount of sweater = 2%
Discount on sweater = 30 x 0.02 = 0.60
discount on sweater < discount on coat
Scenario 2:
Price of coat = 90
% discount of coat = 30%
Discount on coat = 90 x 0.30 = 27
Price of sweater = 100
% discount of sweater = 28%
Discount on sweater = 100 x 0.28 = 28
discount on sweater> discount on coat
Answer: E
