BTGmoderatorDC wrote: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 4 times the price of the scanner.

Let P = price of ONE printer
Let S = price of ONE scanner

Target question: What is the value of S?

Statement 1: The total price of the (3) printers and the (1) scanner was $1,300.
So, we can write: 3P + S = 1300
Does this provide enough information to determine the value of S?
No.
There are several cases that satisfy statement 1. Here are two:
Case a: P = 400 and S = 100. Notice that these values meet the condition that 3P + S = 1300. In this case, the answer to the target question is S = 100
Case b: P = 300 and S = 400. Notice that these values meet the condition that 3P + S = 1300. In this case, the answer to the target question is S = 400
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: The price of each printer was 4 times the price of the scanner.
So, we can write: P = 4S
There are several cases that satisfy statement 2. Here are two:
Case a: P = 400 and S = 100. Notice that these values meet the condition that P = 4S. In this case, the answer to the target question is S = 100
Case b: P = 800 and S = 200. Notice that these values meet the condition that P = 4S. In this case, the answer to the target question is S = 200
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that 3P + S = 1300
Statement 2 tells us that P = 4S
Since we COULD solve this system of equations for P and S, we COULD answer the target question (although we would NEVER waste our valuable time actually solving the system on test day.)
Since we COULD answer the target question with certainty, the combined statements are SUFFICIENT

Answer: C

ASIDE: If we solve the system, we get P = $400 and S = $100

Cheers,
Brent