Question

By what percentage was the price of a certain television set discounted for a sale?
(1) The price of the television set before it was discounted for the sale was 25 percent greater than the discounted price.
(2) The price of the television set was discounted by $60 for the sale.

• 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

Answer: (A)

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

• Let B represent the price, in dollars, for the television before the sale and let D represent the discounted price, in dollars. The percent by which B was discounted to obtain D can be determined if the value of can be determined.
• From statement 1, it indicates that B is $25\%$ greater than $D$ or that $B=1.25D$. Then, i.e $20\%$. Thus, statement 1 is sufficient.
• Considering statement 2, it indicates that $D=B–60$, but B is unknown. So, statement 2 is insufficient.