Question

At a bakery, all donuts are priced equally and all bagels are priced equally. What is the total price of 5 donuts and 3 bagels at the bakery?
(1) At the bakery, the total price of 10 donuts and 6 bagels is $12.90.
(2) At the bakery, the price of a donut is $0.15 less than the price of a bagel.

• 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.

Let x be the price, in dollars, of each donut and let y be the price, in dollars, of each bagel. We have to find the value of 5x + 3y.

1. Given that , 10x + 6y = 12.90 then , it follows that . Thus, sufficient.
2. Given that x = y - 0.15, then 5x + 3y = 5(y - 0.15) + 3y = 8y - 0.75, which varies as y varies; NOT sufficient.

• The correct answer is A; statement 1 alone is sufficient.