Question

By what percent was the price of a certain Tab discounted for a sale?
(1) The price of the tab was sold with a discount of 50.
(2) The price of the tab before it was discounted for the sale was 25 percent greater than the discounted price.

• A. Statement 1 alone is sufficient but statement 2 alone is not sufficient to answer the question asked.
• B. Statement 2 alone is sufficient but statement 1 alone is not sufficient to answer the question asked.
• C. Both statements 1 and 2 together are sufficient to answer the question but neither statement is sufficient alone.
• D. Each statement alone is sufficient to answer the question.
• E. Statements 1 and 2 are not sufficient to answer the question asked and additional data is needed to answer the statements.

Hint:

When working with percentage-based problems, always identify what is being compared (e.g., discount amount to original price) and use simple equations to solve.

Answer 1

The Correct Option is C

Step 1: Analyze Statement 1.
Statement 1 tells us that the price of the tab was sold with a discount of \$50. However, this does not provide enough information to determine the original price or the discount percentage. So, statement 1 alone is not sufficient.
Step 2: Analyze Statement 2.
Statement 2 tells us that the price of the tab before it was discounted for the sale was 25 percent greater than the discounted price. Let the discounted price be \( p \). The original price is then \( 1.25p \). However, this also does not give us any specific information about the discount in terms of dollar amount or percentage. Thus, statement 2 alone is not sufficient.
Step 3: Combine Both Statements.
Combining both statements, we know the amount of the discount (\$50), and we also know that the original price is 25% greater than the discounted price. Thus, we can calculate the original price and the discount percentage: Let the original price be \( 1.25p \), and the discounted price be \( p \). We are told the discount is \$50, so: \[ 1.25p - p = 50 \] \[ 0.25p = 50 \] \[ p = \frac{50}{0.25} = 200 \] Thus, the original price is \( 1.25 \times 200 = 250 \). The discount percentage is: \[ \frac{50}{250} \times 100 = 20% \] Therefore, the correct answer is (C).