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BTGmoderatorDC
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Question: Is x a positive number?BTGmoderatorDC wrote:Is x a positive number?
(1) (x - 2)^2 > 2
(2) 2^x > 3^x
Let's take each statement one by one.
(1) (x - 2)^2 > 2
x can take any value: positive, 0, or negative. Insufficient.
Say, x = 0, then (x - 2)^2 > 2 => (0 - 2)^2 > 2 => 4 > 2.
Say, x = 4, then (x - 2)^2 > 2 => (4 - 2)^2 > 2 => 4 > 2.
Say, x = -1, then (x - 2)^2 > 2 => (-1 - 2)^2 > 2 => 9 > 2.
(2) 2^x > 3^x
We see that x cannot be 0 since at x = 0, 2^x > 3^x => 2^0 > 3^0 => 1 = 1. Not valid.
We note that the base (2) of the number 2^x is less than the base (3) of the number 3^x, while the exponents are the same, x each. For 2^x to be greater than 3^x, x must be negative. Let's take an example.
Say x = -2, then 2^x > 3^x => 2^(-1) > 3^(-1) => 1/4 > 1/9
You may test this with any positive number between 0 and 1.
Say x = 1/2, then 2^x > 3^x => 2^(1/2) > 3^(1/2) => 1.414 < 1.732. Not valid.
The correct answer: B
Hope this helps!
-Jay
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