Carcass wrote:
If \(2^{a + 3} = 4^{a + 2} - 48\), then the value of a is
(A) \(\frac{-3}{2}\)
(B) -3
(C) -2
(D) 1
(E) 2
STRATEGY: As with all GRE Multiple Choice questions, we should immediately ask ourselves, Can I use the answer choices to my advantage?
In this case, all of the answers choices except A are easy to test.
Now we should give ourselves about 20 seconds to identify a faster approach.
In this case, we could try solving the equation, but that could take longer than testing values.
So, I'm going to test the answer choices, starting with the easiest ones (which are the two answer choices that are positive integers). (D) 1Plug in \(a = 1\), to get: \(2^{1 + 3} = 4^{1 + 2} - 48\)
Simplify: \(16 = 64 - 48\). WORKS!
Answer: D