Question

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.

• A. Statement (1) alone is sufficient, but statement (2) alone is not sufficient.
• B. Statement (2) alone is sufficient, but statement (1) alone is not sufficient.
• C. Both statements together are sufficient, but neither statement alone is sufficient.
• D. Each statement alone is sufficient.
• E. Statements (1) and (2) together are not sufficient.

Answer 1

The correct option is E Statements (1) and (2) together are not sufficient.

1. Given that the discount on the coat was 2 percentage points greater than the discount on the sweater, the sweater could have been discounted by the greater dollar amount ($30sweaterwith10$3; $20coatwith12$2.40) and the coat could have been discounted by the greater dollar amount ($110sweaterwith10$11; $100coatwith12$12). Thus, statement 1 is insufficient.
2. Given that the coat’s sale price was $10 less than the sweater’s sale price, the same examples used to show that (1) is not sufficient can be used for (2). Thus, not sufficient.

• Taking (1) and (2) together is of no more help than either (1) or (2) taken separately because the same examples used to show that (1) is not sufficient also show that (2) is not sufficient.
  
• The correct answer is E; both statements together are still not sufficient.