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. If statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked;
• B. If statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked;
• C. If BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient;
• D. If EACH statement ALONE is sufficient to answer the question asked;
• E. If statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

Hint:

In Data Sufficiency problems, always check if the expression in the statement is a multiple or a fraction of the expression you are asked to find. This can often lead to a quick solution without needing to solve for the individual variables.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
This is a data sufficiency problem. We need to check if the information given in each statement, alone or together, is enough to uniquely determine the value of the required expression.

Step 2: Defining the Variables:
Let the price of one donut = \(d\).
Let the price of one bagel = \(b\).
We need to find: \[ 5d + 3b \]

Step 3: Analysis of Statement (1)
Statement (1): The cost of 10 donuts and 6 bagels is $12.90.
Equation: \[ 10d + 6b = 12.90 \] Factorizing: \[ 2(5d + 3b) = 12.90 \] \[ 5d + 3b = \frac{12.90}{2} = 6.45 \] We obtained a unique value.
Statement (1) alone is sufficient.

Step 4: Analysis of Statement (2)
Statement (2): A donut costs $0.15 less than a bagel.
Equation: \[ d = b - 0.15 \] Substitute into the expression: \[ 5d + 3b = 5(b - 0.15) + 3b = 8b - 0.75 \] Since the value of \(b\) is unknown, this does not give a unique answer.
Statement (2) alone is not sufficient.

Step 5: Combining Statements (1) and (2)
Statement (1) already provided a direct value of \(5d + 3b = 6.45\).
Adding Statement (2) does not change this.
Thus, combining is also sufficient (but unnecessary).

Step 6: Final Answer:
Since Statement (1) alone is sufficient and Statement (2) alone is not, the correct option is: (A) Statement (1) alone is sufficient.