Bunuel 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.
DS37502.01
OG2020 NEW QUESTION
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 subtractionSince we can answer the
target question with certainty, statement 1 is SUFFICIENT
Statement 2: If r ≠ s, then r θ s ≠ s θ rLet'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