OG 2020: Question No. 311
If r and s are positive numbers and θ is one of the operations, +, −, ×, or ÷, which operation is θ?
- If r = s, then r θ s = 0.
- If r ≠ s, then r θ s ≠ s θ r.
Steps 1 & 2: Understand Question and Draw Inferences
In this question, we are given
- The numbers r and s are positive
- Θ is one of the operations: +, or -, or x, or ÷
From the given information, we need to determine
- Out of the four given operations, which one is θ
As we have no other information available, let us now analyse the individual statements.
Step 3: Analyse Statement 1
As per the information given in statement 1, if r = s, then r θ s = 0.
We know that both r and s are positive numbers.
- Addition or multiplication or division of two positive numbers cannot be equal to 0.
- Also, if r = s, then r – s = r – r = 0
- Therefore, θ is definitely subtraction.
Hence, statement 1 is sufficient to answer the question.
Step 4: Analyse Statement 2
As per the information given in statement 2, if r ≠ s, then r θ s ≠ s θ r
|Input 1||Input 2||Operator (θ)||Final Result||Example (taking r = 4 and s = 2)|
|r||s||+||r + s = s + r||4 + 2 = 6 = 2 + 4|
|r||s||–||r – s ≠ s – r||4 – 2 = 2 2 – 4 = -2|
|r||s||x||r x s = s x r||4 x 2 = 8 = 2 x 4|
|r||s||÷||r ÷ s ≠ s ÷ r||4 ÷ 2 = 2 2 ÷ 4 = 0.5|
As we can see, θ can be either ‘-‘ or ‘÷’, but we cannot conclude definitely which operator is θ.
Hence, statement 2 is not sufficient to answer the question.
Step 5: Combine Both Statements Together (If Needed)
Since we can determine the answer from statement 1 individually, this step is not required.
Hence, the correct answer choice is option A.
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