carcass wrote:
If \(x^2 = 2^x\), what is the value of x ?
(1) \(2x = (\frac{x}{2})^3\)
(2) \(x = 2^{x-2}\)
Given: \(x^2 = 2^x\) Strategy: There aren't many solutions to this given equation, so let's spend a little bit of time up front listing all possible cases. It turns out there are only two possible cases:
Case i: \(x = 2\)
Case ii: \(x = 4\)
In other words, the given information is telling us that
x is either 2 or 4.
With this in mind, it'll be super easy to check each statement.
Target question: What is the value of x? Statement 1: \(2x = (\frac{x}{2})^3\) Rather than solve this equation, we can just test the two possible x-values.
Test \(x =2\), to get: \(2(2) = (\frac{2}{2})^3\), which we can simplify to get: \(4 = 1\). FALSE.
So, \(x \neq 2\), which means it must be the case that
\(x = 4\)Since we can answer the
target question with certainty, statement 1 is SUFFICIENT
Statement 2: \(x = 2^{x-2}\)Once again, we'll test the two possible x-values.
Test \(x =2\), to get: \(2 = 2^{2-2}\), which we can simplify to get: \(2 = 1\). FALSE.
So, \(x \neq 2\), which means it must be the case that
\(x = 4\)Since we can answer the
target question with certainty, statement 2 is SUFFICIENT
Answer: D
Cheers,
Brent
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Brent Hanneson – Creator of gmatprepnow.com
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