GMATPrepNow wrote:
The symbols $ and # each represent one of the following operations: addition, subtraction, multiplication or division. What is the value of 1 $ 1 # 1?
1) 2 $ 2 # 2 = 3
2) 3 $ 2 # 1 = 5
Target question: What is the value of 1 $ 1 # 1? Statement 1: 2 $ 2 # 2 = 3 There are two possible cases in which 2 $ 2 # 2 = 3
Case a: $ represents
+, and # represents
÷. We get 2
+ 2
÷ 2 = 3, which works. In this case, the answer to the target question is
1 $ 1 # 1 = 1 + 1 ÷ 1 = 2Case b: $ represents
÷, and # represents
+. We get 2
÷ 2
+ 2 = 3, which works. In this case, the answer to the target question is
1 $ 1 # 1 = 1 ÷ 1 + 1 = 2Since, we get the SAME answer to the target question (
1 $ 1 # 1 = 2) in both cases, it MUST be the case that
1 $ 1 # 1 = 2Since we can answer the
target question with certainty, statement 1 is SUFFICIENT
Statement 2: 3 $ 2 # 1 = 5There are three possible cases in which 3 $ 2 # 1 = 5. Here are two such cases:
Case a: $ represents
+, and # represents
÷. We get 3
+ 2
÷ 1 = 5, which works. In this case, the answer to the target question is
1 $ 1 # 1 = 1 + 1 ÷ 1 = 2Case b: $ represents
x, and # represents
-. We get 3
x 2
- 1 = 5, which works. In this case, the answer to the target question is
1 $ 1 # 1 = 1 x 1 - 1 = 0Since we cannot answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Answer: A
Cheers,
Brent