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What is the value of (2^{2020} + 2^{2018}) / (2^{2020}-2^{2018})?

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Math Revolution GMAT Instructor
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What is the value of (2^{2020} + 2^{2018}) / (2^{2020}-2^{2018})?  [#permalink]

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New post 15 Feb 2019, 01:22
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A
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Difficulty:

  5% (low)

Question Stats:

88% (01:01) correct 12% (01:00) wrong based on 42 sessions

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[GMAT math practice question]

What is the value of \(\frac{(2^{2020} + 2^{2018})}{(2^{2020}-2^{2018}})?\)

\(A. \frac{3}{5}\)
\(B. \frac{5}{3}\)
\(C. 2^{2018}\)
\(D. 2^{2019}\)
\(E. 2^{2020}\)

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What is the value of (2^{2020} + 2^{2018}) / (2^{2020}-2^{2018})?  [#permalink]

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New post 15 Feb 2019, 01:41
MathRevolution wrote:
[GMAT math practice question]

What is the value of \(\frac{(2^{2020} + 2^{2018})}{(2^{2020}-2^{2018}})?\)

\(A. \frac{3}{5}\)
\(B. \frac{5}{3}\)
\(C. 2^{2018}\)
\(D. 2^{2019}\)
\(E. 2^{2020}\)


Take \(2^{2020}\) common from both numerator and denominator, and even cancel them out to get

{1+1/4} / {1-1/4}

5/4 * 4/3

\(\frac{5}{3}\)

B
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Re: What is the value of (2^{2020} + 2^{2018}) / (2^{2020}-2^{2018})?  [#permalink]

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New post 15 Feb 2019, 06:13
2
MathRevolution wrote:
[GMAT math practice question]

What is the value of \(\frac{(2^{2020} + 2^{2018})}{(2^{2020}-2^{2018}})?\)

\(A. \frac{3}{5}\)
\(B. \frac{5}{3}\)
\(C. 2^{2018}\)
\(D. 2^{2019}\)
\(E. 2^{2020}\)


\(\frac{2^{2020} + 2^{2018}}{2^{2020}-2^{2018}}\)

= \(\frac{2^{2018}(2^2+1)}{2^{2018}(2^2-1)}\)

=\(\frac{5}{3}\)


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Math Revolution GMAT Instructor
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GPA: 3.82
Re: What is the value of (2^{2020} + 2^{2018}) / (2^{2020}-2^{2018})?  [#permalink]

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New post 17 Feb 2019, 18:37
=>

\(\frac{(2^{2020} + 2^{2018})}{(2^{2020}-2^{2018})}\)
\(= \frac{(2^22^{2018} + 2^{2018})}{(2^22^{2018}-2^{2018})}\)
\(= \frac{(2^{2018})(2^2+1)}{(2^{2018})(2^2-1)} = \frac{(2^2+1)}{(2^2-1)}\)
\(= \frac{5}{3}\)

Therefore, the answer is B.
Answer: B
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Re: What is the value of (2^{2020} + 2^{2018}) / (2^{2020}-2^{2018})?  [#permalink]

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New post 18 Feb 2019, 16:52
I tried this out a different way by giving the same scenario to more manageable numbers.

(2^5+2^3) / (2^5 +2^3) = (32 + 8) / (32 - 8) = 40 / 24 = 5/3
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Re: What is the value of (2^{2020} + 2^{2018}) / (2^{2020}-2^{2018})?   [#permalink] 18 Feb 2019, 16:52
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