Question

The average (arithmetic mean) price of the 3 items that Kate purchased from a clothing store was $50.Iftherewasnosalestaxonanyitemthathadapriceoflessthan$80 and 6 percent sales tax on all other items, what was the total sales tax on the 3 items that Kate purchased?
(1) The price of the most expensive item that Kate purchased from the store was $100.
(2) The price of the least expensive item that Kate purchased from the store was $10.

• 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 A Statement (1) alone is sufficient, but statement (2) alone is not sufficient.

• It is given that the average of the $3$ prices is $\$50.$ Thus, it follows that the sum of the $3$prices is $\left(3\right)\times \left(\$50\right)=\$150.$ Now, one of the prices is $\$100$. Therefore, the sum of the $2$ remaining prices is $\$150–\$100=\$50$. Hence, each of the remaining items has a price that is less than $\$80$ and thus is not taxed. It follows that the total sales tax on the $3$ items is the sales tax on the $\$100$ item, which equals $\left(6\%\right)\times \left(\$100\right)=\$6$. Thus, statement 1 is sufficient.
• From statement 2, we have one of the prices as $\$10$. Therefore, the sum of the $2$ remaining prices is $\$150–\$10=\$140$. If the $2$ remaining prices are $\$70$ and $\$70$, then none of the items has a price greater than $\$80$, and hence the total sales tax on the $3$ items is $\$0$. If the $2$ remaining prices are $\$40$ and $\$100$, then the total sales tax on the $3$ items is $\left(6\%\right)\times \left(\$100\right)=\$6$. Thus, statement 2 is insufficient.