Which of the following is equivalent to 4^(2n - 1)/2^(3n + 1)?

Question

Which of the following is equivalent to \frac{4^{2n - 1}}{2^{3n + 1}} ? A. 2^{n-3} B. 2^{n-1} C. 2^{-n+2} D. 2^{-n} E. 2^{-n-2} 2024-01-29_00-20-10.png

Bunuel · Answer

\frac{4^{2n - 1}}{2^{3n + 1}}=

=\frac{(2^2)^{2n - 1}}{2^{3n + 1}}=

=\frac{2^{2(2n - 1)}}{2^{3n + 1}}=

=2^{2(2n - 1) - (3n + 1)}=

=2^{n - 3}

Answer: A.

DanTheGMATMan · Answer

Keep it simple:
 https://www.youtube.com/watch?v=oNHn1-d_bEQ

SageGMATtutor · Answer

Simplifying the algebra by using a common base is a good strategy here, but it's not the only way. If you look at a problem like this and think "I don't know how to do the algebra here", then another approach is to pick an example. If we pick a value for n, we should get the same result for the expression in the question and in the correct answer.

Start with a simple value, n=1. Then the question becomes (4)/2^4 = 4/16 = 1/4. Next, test the answers:
(A) 2^-2 = 1/4
(B) 2^0 = 1 wrong
(C) 2^1 = 2 wrong
(D) 2^-2 = 1/4
(E) 2^-3 = 1/8 wrong

Even though we haven't completed the problem, we've made progress. To decide between answers A and D, pick another value for n. We could pick n=2, but that gives higher values and creates more work than choosing n=0, which gives the expression (4^-1)/2 = 1/8. Then test answers A and D:
(A) 2^-3 = 1/8
(D) 2^0 = 1 wrong

So the correct answer is A.

Which of the following is equivalent to 4^(2n - 1)/2^(3n + 1)?

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Which of the following is equivalent to 4^(2n - 1)/2^(3n + 1)?

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

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