Question

What was the range of the selling prices of the 30 wallets sold by a certain store yesterday?
(1) $\frac{1}{3}$ of the wallets had a selling price of $24 each
(2) The lowest selling price of the wallets wast the highest selling price of the wallets.

• A. Statement I alone is sufficient to answer the problem.
• B. Statement II alone is sufficient to answer the problem.
• C. Statement I and II both are needed.
• D. Either of the statement I or II is sufficient alone.
• E. Statement I and II both are not sufficient.

Answer 1

The correct option is E Statement I and II both are not sufficient.

Arithmetic Statistics

Since the range of a data set is the greatest value in the data set minus the least value in the data set, this problem can be solved if the least selling price and the greatest selling price of the wallets sold by the store yesterday can be determined.

(1) This indicates that 10 of the wallets had a selling price of $24 each, but does not indicate the least selling price or the greatest selling price of the wallets sold by the store yesterday; NOT sufficient.

(2) This indicates that $L=\frac{1}{3}G$, where L represents the least selling price and G represents the greatest selling price, but does not give enough information to determine G - L; NOT sufficient.

Taking (1) and (2) together, the least and greatest selling prices of the wallets sold by the store yesterday could be $10and$30 for a range of $30-$10 = $20,ortheleastandgreatestsellingpricesofthewalletssoldbythestoreyesterdaycouldbe$20 and $60forarangeof$60 -$20=$40.

The correct answer is E; both statements together are still not sufficient.