The symbol ? represents one of the following operations: addition,…
2024
The symbol ? represents one of the following operations: addition, subtraction, multiplication, or division. What is the value of 3 ? 2?
(1) 0 ? 1 = 1
(2) 1 ? 0 = 1
- A.
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
- B.
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
- C.
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
- D.
EACH statement ALONE is sufficient.
Show answer & explanation
Correct answer: A
Concept
In Data Sufficiency, a statement is sufficient only when it pins down exactly one value for what is asked. Here, ? stands for one of four operations (addition, subtraction, multiplication, division); a statement is sufficient only if testing it against all four operations leaves exactly one operation standing — a statement consistent with more than one operation cannot fix the value of 3 ? 2.
Testing Statement (1): 0 ? 1 = 1
Operation | Test | Holds? |
|---|---|---|
Addition | 0 + 1 = 1 | Yes |
Subtraction | 0 − 1 = −1 | No |
Multiplication | 0 × 1 = 0 | No |
Division | 0 ÷ 1 = 0 | No |
Only addition satisfies 0 ? 1 = 1, so ? is uniquely fixed as addition, and 3 ? 2 = 3 + 2 can be evaluated. Statement (1) alone is sufficient.
Testing Statement (2): 1 ? 0 = 1
Operation | Test | Holds? |
|---|---|---|
Addition | 1 + 0 = 1 | Yes |
Subtraction | 1 − 0 = 1 | Yes |
Multiplication | 1 × 0 = 0 | No |
Division | 1 ÷ 0 = undefined | No |
Both addition and subtraction satisfy 1 ? 0 = 1, so ? could be either operation, giving two different values for 3 ? 2. Statement (2) alone is not sufficient.
Cross-check
Statement (1) narrows the four candidate operations to exactly one, while Statement (2) leaves two candidates standing — confirming that only the first statement, on its own, determines the value of 3 ? 2.
Conclusion
Statement (1) ALONE is sufficient, while Statement (2) alone is not sufficient.