MathRevolution wrote:
Is (r²)x>0?
1) r⁵ = 1
2) x > 0
*An answer will be posted in 2 days.
Target question: Is (r²)(x) > 0? Statement 1: r⁵ = 1 This tells us that r = 1, however we don't know the value of x.
Let's TEST some values.
Case a: r = 1 and x = 1, in which case (r²)(x) = (1²)(1) = 1. Here,
(r²)(x) is GREATER than 0Case b: r = 1 and x = -1, in which case (r²)(x) = (1²)(-1) = -1. Here,
(r²)(x) is NOT GREATER than 0Since we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: x > 0 Okay, x is POSITIVE, however we don't know the value of r.
Let's TEST some values.
Case a: r = 1 and x = 1, in which case (r²)(x) = (1²)(1) = 1. Here,
(r²)(x) is GREATER than 0Case b: r = 0 and x = 1, in which case (0²)(x) = (0²)(1) = 0. Here,
(r²)(x) is NOT GREATER than 0Since we cannot answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined Statement 1 tells us that r = 1, which means
r² = 1Statement 2 tells us that x is POSITIVE
This means that (r²)(x) = (
1³)(POSITIVE) = SOME POSITVE #. In other words,
(r²)(x) is GREATER than 0Since we can answer the
target question with certainty, the combined statements are SUFFICIENT
Answer =
Cheers,
Brent
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