AbeNeedsAnswers wrote: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.
Given: r and s are positive numbers and θ is one of the operations, +, −, ×, or ÷
Target question: Which operation is θ ?
Statement 1: If r = s, then r θ s = 0
Keep in mind that r and s are POSITIVE
So, we have POSITIVE θ POSITIVE = 0
POSITIVE + POSITIVE ≠0 So, θ cannot represent addition
POSITIVE - POSITIVE = 0 So, θ COULD represent subtraction
POSITIVE × POSITIVE ≠0 So, θ cannot represent multiplication
POSITIVE ÷ POSITIVE ≠0 So, θ cannot represent division
The answer to the target question is
θ represents subtraction
Since we can answer the
target question with certainty, statement 1 is SUFFICIENT
Statement 2: If r ≠s, then r θ s ≠s θ r
Let's test some values for each possible operation.
1 ≠2, yet 1 + 2 = 2 + 1. So, θ cannot be addition
1 ≠2, yet 1 x 2 = 2 x 1. So, θ cannot be multiplication
If r and s are DIFFERENT positive numbers, then r - s will never equal s - r. So,
θ COULD represent subtraction
If r and s are DIFFERENT positive numbers, then r ÷ s will never equal s ÷ r. So,
θ COULD represent division
Since we cannot answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Answer: A
Cheers,
Brent
