BTGmoderatorDC wrote:Is x a positive number?
(1) (x - 2)^2 > 2
(2) 2^x > 3^x
Target question: Is x a positive number?
Statement 1: (x - 2)^2 > 2
Let's TEST some values.
There are several values of x that satisfy statement 1. Here are two:
Case a: x = 4 works, since (4 - 2)^2 > 2. In this case, the answer to the target question is
YES, x is positive
Case b: x = -1 works, since (-1 - 2)^2 > 2. In this case, the answer to the target question is
NO, x is not positive
Since we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: 2^x > 3^x
Since 2^x is always positive, we can safely divide both sides of the inequality by 2^x to get: 1 < (3^x)/(2^x)
Simplify to get: 1 < (3/2)^x
Now notice that, when x = 0, (3/2)^x
equals 1
When x is a NEGATIVE integer, then (3/2)^x will be
less than 1
And, when x is a POSITIVE integer, then (3/2)^x will be
greater than 1
So, x must be positive.
In other words, the answer to the target question is
YES, x is positive
Since we can answer the
target question with certainty, statement 2 is SUFFICIENT
Answer: B
Cheers,
Brent
