Question

A company bought 3 printers and 1 scanner. What was the price of the scanner?
(1) The total price of the printers and the scanner was \$1,300.
(2) The price of each printer was \$300.

Hint:

When you see a word problem that can be translated into a system of linear equations, count your variables and your equations. To find a unique solution, you typically need the same number of independent equations as you have variables.

Answer 1

Step 1: Understanding the Concept:
This is a Data Sufficiency problem. We are asked to find the price of a scanner.
Let \(P\) be the price of one printer and \(S\) be the price of the scanner.
The question is: What is the value of S?
Step 2: Detailed Explanation:
Evaluating Statement (1) Alone:
"The total price of the printers and the scanner was \$1,300."
Since the company bought 3 printers and 1 scanner, this translates to the equation:
\[ 3P + S = 1300 \] This is one equation with two unknown variables. We cannot determine the value of S. For example, if P=\$100, S=\$1000. If P=\$200, S=\$700. Not sufficient.
Evaluating Statement (2) Alone:
"The price of each printer was \$300."
This gives us a value for P: \(P = 300\).
However, this statement provides no information about the scanner's price, S. Not sufficient.
Evaluating Statements (1) and (2) Together:
From statement (1), we have the equation: \(3P + S = 1300\).
From statement (2), we have the value: \(P = 300\).
We can substitute the value of P from statement (2) into the equation from statement (1):
\[ 3(300) + S = 1300 \] \[ 900 + S = 1300 \] \[ S = 1300 - 900 = 400 \] We can find a single, unique value for S. Therefore, the statements together are sufficient.
Step 3: Final Answer:
Neither statement alone is sufficient, but the two statements together are sufficient. This corresponds to option (C). (Note: The value for statement (2) was inferred from context, as it was cut off in the image).