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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.

Source	OG 2020
Type	Data Sufficiency
Topic	Algebra
Sub-Topic	Operators
Difficulty	Medium

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

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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