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# Which of the following is the approximation of

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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Which of the following is the approximation of  [#permalink]

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12 Dec 2016, 00:27
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45% (medium)

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65% (02:12) correct 35% (02:15) wrong based on 87 sessions

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Which of the following is the approximation of $$(4^4+8^6)/(4^8+16^8$$)?

A. $$2^-^1^2$$
B. $$2^-^1^4$$
C. $$2^-^1^6$$
D. $$2^1^2$$
E. $$2^1^4$$

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MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
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"Only $79 for 1 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Target Test Prep Representative Status: Founder & CEO Affiliations: Target Test Prep Joined: 14 Oct 2015 Posts: 10566 Location: United States (CA) Re: Which of the following is the approximation of [#permalink] ### Show Tags 13 Dec 2016, 16:46 1 MathRevolution wrote: Which of the following is the approximation of $$(4^4+8^6)/(4^8+16^8$$)? A. $$2^-^1^2$$ B. $$2^-^1^4$$ C. $$2^-^1^6$$ D. $$2^1^2$$ E. $$2^1^4$$ We can start by prime factorizing each term in the given expression: 4^4 = (2^2)^4 = 2^8 8^6 = (2^3)^6 = 2^18 4^8 = (2^2)^8 = 2^16 16^8 = (2^4)^8 = 2^32 Putting these values back into the given expression, we have: (2^8 + 2^18)/(2^16 + 2^32) We can factor out a 2^8 from the numerator and a 2^16 from the denominator, and we have: [2^8(1 + 2^10)]/[2^16(1 + 2^16)] (1 + 2^10)/[2^8(1 + 2^16)] Since the 1s are quite small compared to the other values, we can ignore them, and we have: 2^10/(2^8 x 2^16) = 2^10/2^24 = 2^-14 Answer: B _________________ # Scott Woodbury-Stewart Founder and CEO Scott@TargetTestPrep.com 202 Reviews 5-star rated online GMAT quant self study course See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews If you find one of my posts helpful, please take a moment to click on the "Kudos" button. Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 8992 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: Which of the following is the approximation of [#permalink] ### Show Tags 14 Dec 2016, 00:29 ==> Because of the word “approximation”, you get $$(4^4+8^6)/(4^8+16^8)= 8^6/16^8$$. Also, from $$8^6/16^8 =(2^3)^6/(2^4)^8=2^1^8/2^3^2=2^1^8^-^3^2=2^-^1^4$$, the answer is B. Answer: B _________________ 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$79 for 1 month Online Course"
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Re: Which of the following is the approximation of   [#permalink] 14 Dec 2016, 00:29