# If r and s are positive numbers and θ is one of the operations, +, −, ×, or ÷, which operation is θ? – OG 2020 Question #311 with Solution

## OG 2020: Question No. 311

If r and s are positive numbers and θ is one of the operations, +, −, ×, or ÷, which operation is θ?

1. If r = s, then r θ s = 0.
2. If r ≠ s, then r θ s ≠ s θ r.

### Solution

#### 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

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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