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

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6386
GMAT 1: 760 Q51 V42
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Which of the following is closest to (1+2^18)/(2^4+2^10)?  [#permalink]

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16 Oct 2017, 01:57
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Difficulty:

25% (medium)

Question Stats:

72% (01:34) correct 28% (02:00) wrong based on 74 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. $$2^9$$

_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $99 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Math Expert Joined: 02 Aug 2009 Posts: 6959 Re: Which of the following is closest to (1+2^18)/(2^4+2^10)? [#permalink] ### Show Tags 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 _________________ 1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372 2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html 3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html GMAT online Tutor Target Test Prep Representative Status: Founder & CEO Affiliations: Target Test Prep Joined: 14 Oct 2015 Posts: 3886 Location: United States (CA) Re: Which of the following is closest to (1+2^18)/(2^4+2^10)? [#permalink] ### Show Tags 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 _________________ Scott Woodbury-Stewart Founder and CEO GMAT Quant Self-Study Course 500+ lessons 3000+ practice problems 800+ HD solutions Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6386 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: Which of the following is closest to (1+2^18)/(2^4+2^10)? [#permalink] ### Show Tags 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 _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$99 for 3 month Online Course"
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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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