Question

If the total cost of 5 pencils and 3 erasers is \$3.75, and the total cost of 4 pencils and 5 erasers is \$3.50, what is the price of one pencil?
(1) The price of an eraser is \$0.25.
(2) The price of 5 pencils and 3 erasers is \$3.75.

• A. Statement (1) alone is sufficient.
• B. Statement (2) alone is sufficient.
• C. Both statements together are sufficient.
• D. Each statement alone is not sufficient.

Hint:

In Data Sufficiency, focus on whether a unique answer can be found, not on the actual calculation. If a statement gives you a solvable system of equations (e.g., n equations for n variables), it is sufficient.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
This question is formatted as a Data Sufficiency problem. We must determine if the information in the statements is sufficient to answer the question. The text in the main question stem is unusually detailed and appears to be poorly formatted, likely intended as context or potentially replacing the statements themselves. The most logical interpretation is to treat this as a standard Data Sufficiency question where the question is "What is the price of one pencil?" and we evaluate the numbered statements.
Step 2: Analyzing the Question and Statements:
Let \(p\) be the price of a pencil and \(e\) be the price of an eraser.
The question is: What is the value of \(p\)?
Evaluating Statement (1) Alone:
"The price of an eraser is \$0.25."
This gives us \(e = 0.25\). However, we have no information about the price of a pencil, \(p\).
Therefore, Statement (1) alone is not sufficient.
Evaluating Statement (2) Alone:
"The price of 5 pencils and 3 erasers is \$3.75."
This gives us one equation with two variables: \(5p + 3e = 3.75\). We cannot determine a unique value for \(p\) from this single equation.
Therefore, Statement (2) alone is not sufficient.
Evaluating Statements (1) and (2) Together:
From Statement (1), we have \(e = 0.25\).
From Statement (2), we have the equation \(5p + 3e = 3.75\).
We can substitute the value of \(e\) from Statement (1) into the equation from Statement (2):
\[ 5p + 3(0.25) = 3.75 \] \[ 5p + 0.75 = 3.75 \] \[ 5p = 3.75 - 0.75 \] \[ 5p = 3.00 \] \[ p = \frac{3.00}{5} = 0.60 \] We can find a single, unique value for \(p\).
Therefore, both statements together are sufficient.
Step 3: Final Answer:
Neither statement alone is sufficient, but together they are sufficient. This corresponds to option (C). (Note: The information in the question stem is contradictory to the statements and should be disregarded as it makes the question unsolvable as written.)