Understanding the Discount Percent Question

The question asks for the discount percent offered on the soap by the store. To find the discount percent, we generally need to know the amount of discount given and the original price of the item(s) purchased. The formula for discount percent is:

\\(\text{Discount Percent} = \left( \frac{\text{Discount Amount}}{\text{Original Price}} \right) \times 100 \\)

We need to evaluate whether each statement, independently or together, provides enough information to calculate this discount percent.

Analyzing Statement I: Free Soap Offer

Statement I says: "The store is giving 1 soap free on purchase of three."

Let's analyze this statement to see if it's sufficient to find the discount percent on the soap.

• This is a classic "Buy 3, Get 1 Free" offer.
• When you buy 3 soaps, you receive a total of \\(3 + 1 = 4\\) soaps.
• You pay the price of 3 soaps but get 4 soaps.
• The value of the 1 free soap is the discount you receive.

Let the original price of one soap be \\(P\\).

• The original price of the 4 soaps you receive is \\(4 \times P = 4P\\).
• The amount you pay is for 3 soaps, which is \\(3 \times P = 3P\\).
• The discount amount is the difference between the original price of what you received and what you paid: \\(4P - 3P = P\\).
• The discount percent is calculated on the original price of the items received (4 soaps).

Using the formula for discount percent:

\\(\text{Discount Percent} = \left( \frac{\text{Discount Amount}}{\text{Original Price of Items Received}} \right) \times 100 \\)

\\(\text{Discount Percent} = \left( \frac{P}{4P} \right) \times 100 \\)

Since \\(P\\) is the price of one soap, it cannot be zero. We can cancel out \\(P\\) from the numerator and the denominator.

\\(\text{Discount Percent} = \left( \frac{1}{4} \right) \times 100 = 25\% \\)

Statement I alone allows us to calculate a specific discount percent (25%). Therefore, Statement I alone is sufficient to answer the question about the discount percent offered on the soap.

Analyzing Statement II: Fixed Discount Amount

Statement II says: "Rs. 10 discount is offered on purchase of soap worth 36."

Let's analyze this statement to see if it's sufficient to find the discount percent on the soap.

• This statement directly gives us the discount amount and the original price for a specific purchase of soap.
• Discount Amount = Rs. 10
• Original Price = Rs. 36

Using the formula for discount percent:

\\(\text{Discount Percent} = \left( \frac{\text{Discount Amount}}{\text{Original Price}} \right) \times 100 \\)

\\(\text{Discount Percent} = \left( \frac{10}{36} \right) \times 100 \\)

We can simplify the fraction \(\\)\frac{10}{36}\$$ by dividing both numerator and denominator by 2:

\\(\frac{10}{36} = \frac{5}{18} \\)

So, the discount percent is:

\\(\text{Discount Percent} = \left( \frac{5}{18} \right) \times 100 = \frac{500}{18} = \frac{250}{9} \\)

The discount percent is approximately \\(27.78\%\\). Statement II alone allows us to calculate a specific discount percent. Therefore, Statement II alone is sufficient to answer the question about the discount percent offered on the soap.

Conclusion on Statement Sufficiency

Based on our analysis:

• Statement I alone is sufficient to determine the discount percent.
• Statement II alone is sufficient to determine the discount percent.

Since either statement by itself provides enough information to answer the question, the correct answer is that either statement I or statement II is sufficient.

Revision Table: Discount Calculations

Additional Information on Data Sufficiency Questions

Data sufficiency questions test your ability to determine if the given statements provide enough information to answer a question, rather than actually solving the question yourself. Here's a general approach:

• Read the question carefully to understand what needs to be determined.
• Analyze Statement I alone: Assume Statement II is false or not available. Can you find a unique answer to the question using only Statement I? If yes, Statement I is sufficient.
• Analyze Statement II alone: Assume Statement I is false or not available. Can you find a unique answer to the question using only Statement II? If yes, Statement II is sufficient.
• Analyze Statements I and II together: If neither statement alone is sufficient, consider if both statements combined provide enough information. If yes, both together are sufficient.
• If even both statements together are not enough, then the data is insufficient.

Common outcomes in data sufficiency problems:

• Statement I alone is sufficient (and II is not).
• Statement II alone is sufficient (and I is not).
• Either Statement I or Statement II alone is sufficient.
• Both statements together are sufficient (but neither alone is).
• Neither statement I nor Statement II is sufficient (even together).

In this specific soap discount question, both statements individually provided enough information to calculate the discount percent, leading to the conclusion that either statement is sufficient.