Bunuel wrote:
If \(4^{(2x + 1)} + 4^{(x+1)} = 80\), what is the value of x ?
(A) -5
(B) 0
(C) 1
(D) 4
(E) 5
STRATEGY: Upon reading any GMAT Problem Solving question, we should always ask, Can I use the answer choices to my advantage?
In this case, we can easily test the answer choices.
In fact, if I apply a little bit of number sense, I can quickly rule out answer choices D and E, since \(4^{(2x + 1)}\) and \(4^{(x+1)}\) would each evaluate to be much greater than 80.
From here, I'd typically give myself up to 20 seconds to identify a faster approach, but I can already see that testing the answer choices will be super fast.
Let's start by testing answer choice B, \(x = 0\).
When we plug \(x = 0\) into the given equation we get: \(4^{(2(0) + 1)} + 4^{(0+1)} = 80\)
Simplify to get: \(4^{1} + 4^{1} = 80\)
Evaluate to get: \(4 + 4 = 80\). Doesn't work!
So, we can eliminate answer choice B .
More importantly, we can see that we need the exponents to be bigger in order to get a sum of 80.
So let's now test answer choice C, \(x = 1\).
We get: \(4^{(2(1) + 1)} + 4^{(1+1)} = 80\)
Simplify to get: \(4^{3} + 4^{2} = 80\)
Evaluate to get: \(64 + 16 = 80\)
Works!!
Answer: C
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Brent Hanneson – Creator of gmatprepnow.com
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