## 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.

Source | OG 2020 |

Type | Data Sufficiency |

Topic | Algebra |

Sub-Topic | Operators |

Difficulty | Medium |

### Solution

__Steps 1 & 2: Understand Question and Draw Inferences__

__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__

__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__

__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)__

__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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