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Which of the following is closest to (1+2^18)/(2^4+2^10)?

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Which of the following is closest to (1+2^18)/(2^4+2^10)?  [#permalink]

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New post 16 Oct 2017, 01:57
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A
B
C
D
E

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  25% (medium)

Question Stats:

69% (00:57) correct 31% (01:29) wrong based on 72 sessions

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[GMAT math practice question]

Which of the following is closest to \(\frac{(1+2^{18})}{(2^4+2^{10})}\)?

A. \(2^5\)
B. \(2^6\)
C. \(2^7\)
D. \(2^8\)
E. \(2^9\)

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Re: Which of the following is closest to (1+2^18)/(2^4+2^10)?  [#permalink]

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New post 16 Oct 2017, 02:53
MathRevolution wrote:
[GMAT math practice question]

Which of the following is closest to \(\frac{(1+2^{18})}{(2^4+2^{10})}\)?

A. \(2^5\)
B. \(2^6\)
C. \(2^7\)
D. \(2^8\)
E. \(2^9\)



Hi..

Since the answer asked is in Approximation, we can remove inconsequential parts


\(\frac{(1+2^{18})}{(2^4+2^{10})}\)...
1 is very small in 1+2^18 and 2^4 in 2^4+2^10 but let's just remove 1..
\(\frac{(2^{18})}{2^4(1+2^{6})}=\frac{2^{18-4}}{1+2^6}=2^14-2^6=2^8\)
D
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Re: Which of the following is closest to (1+2^18)/(2^4+2^10)?  [#permalink]

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New post 17 Oct 2017, 11:54
MathRevolution wrote:
[GMAT math practice question]

Which of the following is closest to \(\frac{(1+2^{18})}{(2^4+2^{10})}\)?

A. \(2^5\)
B. \(2^6\)
C. \(2^7\)
D. \(2^8\)
E. \(2^9\)


Since 1 is a lot less than 2^18 in the numerator, we can approximate the numerator as 2^18. Similarly, since 2^4 is a lot less than 2^10 in the denominator, we can approximate the denominator as 2^10. Thus, we have:

(1 + 2^18)/(2^4 + 2^10) ≈ 2^18/2^10 = 2^8

Answer: D
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Re: Which of the following is closest to (1+2^18)/(2^4+2^10)?  [#permalink]

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New post 18 Oct 2017, 03:19
=>

\(\frac{(1+2^{18})}{(2^4+2^{10})}\) = \(\frac{(1+2^{18})}{(2^4(1+2^6))}\) = \(\frac{(1+2^6)(1-2^6+2^{12})}{(2^4(1+2^6))}\)
= \(\frac{(1-2^6+2^{12})}{2^4}\)≒ \(2^8\)

Therefore, the answer is D.

Answer: D
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Re: Which of the following is closest to (1+2^18)/(2^4+2^10)? &nbs [#permalink] 18 Oct 2017, 03:19
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