Question

By what percent was the price of a certain Tab discounted for a sale?
I. The price of the tab was sold with a discount of \$50.
II. The price of the tab before it was discounted for the sale was 25 percent greater than the discounted price.

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

Hint:

In percentage-based Data Sufficiency, statements that provide a relative relationship (like Statement II) are often sufficient, while statements that provide an absolute value (like Statement I) are often insufficient unless another value is known.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
This is a Data Sufficiency question about percentages. To find the discount percent, we need to know the relationship between the discount amount and the original price. The formula is: \[ \text{Discount Percent} = \left( \frac{\text{Discount Amount}}{\text{Original Price}} \right) \times 100% \] Let \(P_O\) be the original price, \(P_D\) be the discounted price, and \(D\) be the discount amount. So, \(D = P_O - P_D\). We need to find \(\frac{D}{P_O}\).
Step 2: Detailed Explanation:
Analyze Statement I: "The price of the tab was sold with a discount of \$50."
This tells us that the discount amount, \(D = \$50\). However, we do not know the original price, \(P_O\). Without the original price, we cannot calculate the discount percentage. For example, if the original price was \$100, the discount is 50%. If the original price was \$200, the discount is 25%. Statement I alone is not sufficient.
Analyze Statement II: "The price of the tab before it was discounted for the sale was 25 percent greater than the discounted price."
This gives us a relationship between the original price (\(P_O\)) and the discounted price (\(P_D\)). \[ P_O = P_D + 0.25 \times P_D = 1.25 \times P_D \] Now let's express the discount percent in terms of one variable. We know \(D = P_O - P_D\). Substituting \(P_O = 1.25 P_D\): \[ D = 1.25 P_D - P_D = 0.25 P_D \] The discount percent is \(\frac{D}{P_O}\): \[ \frac{D}{P_O} = \frac{0.25 P_D}{1.25 P_D} \] The variable \(P_D\) cancels out: \[ \frac{0.25}{1.25} = \frac{25}{125} = \frac{1}{5} = 0.20 \] To express this as a percentage, we multiply by 100: \(0.20 \times 100% = 20%\). Since we found a unique value for the discount percentage, Statement II alone is sufficient.
Step 3: Final Answer:
Statement II alone is sufficient, but Statement I alone is not. This corresponds to option (B).