A 2 minute read

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.
SourceOG 2020
TypeData Sufficiency
TopicAlgebra
Sub-TopicOperators
DifficultyMedium

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 1Input 2Operator (θ)Final ResultExample (taking r = 4 and s = 2)
rs+r + s = s + r4 + 2 = 6 = 2 + 4
rsr – s ≠ s – r4 – 2 = 2 2 – 4 = -2
rsxr x s = s x r4 x 2 = 8 = 2 x 4
rs÷r ÷ s ≠ s ÷ r4 ÷ 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.

Did you know a 700+ GMAT Score can increase your chances to get into your dream business school? We can help you achieve that. Why don’t you try out our FREE Trial? We are the most reviewed online GMAT Preparation company in GMATClub with more than 2000 reviews as of February 2021.

People who read this article also read

Let's discuss further - What's your take?

Payal Tandon
Co-founder, e-GMAT
Welcome to e-GMAT Support!
I am Payal, Co-Founder of e-GMAT.
Feel free to ask any Query.
Thank you for your query.
We will be contacting you soon on