Bunuel 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 = 1300Does 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 = 100Case 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 = 400Since 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 = 4SThere 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 = 100Case 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 = 200Since 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 = 1300Statement 2 tells us that
P = 4SSince 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 = $100Cheers,
Brent
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