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# Which of the following is the best approximation for 11^{11}-9^9?

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Which of the following is the best approximation for 11^{11}-9^9?  [#permalink]

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21 Aug 2018, 02:38
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65% (hard)

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40% (01:16) correct 60% (01:39) wrong based on 93 sessions

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[Math Revolution GMAT math practice question]

Which of the following is the best approximation for $$11^{11}-9^9$$?

A. $$11^8$$
B. $$11^9$$
C. $$11^{10}$$
D. $$11^{11}$$
E. $$11^{12}$$

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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" Director Joined: 04 Aug 2010 Posts: 612 Schools: Dartmouth College Which of the following is the best approximation for 11^{11}-9^9? [#permalink] ### Show Tags Updated on: 21 Aug 2018, 07:20 1 1 MathRevolution wrote: [Math Revolution GMAT math practice question] Which of the following is the best approximation for $$11^{11}-9^9$$? A. $$11^8$$ B. $$11^9$$ C. $$11^{10}$$ D. $$11^{11}$$ E. $$11^{12}$$ Since the answer choices are very spread out, our approximation does not have to very exact. $$11^{11}-9^9 = 11^{11} - (11-2)^9 ≈ 11^{11} - 11^9 = 11^9(11^2 - 1) ≈ (11^9)(11^2) = 11^{11}$$ _________________ GMAT and GRE Tutor New York, NY Available for tutoring in NYC and long-distance. For more information, please email me at GMATGuruNY@gmail.com. Originally posted by GMATGuruNY on 21 Aug 2018, 03:43. Last edited by GMATGuruNY on 21 Aug 2018, 07:20, edited 1 time in total. Math Expert Joined: 02 Aug 2009 Posts: 8626 Which of the following is the best approximation for 11^{11}-9^9? [#permalink] ### Show Tags 21 Aug 2018, 04:01 MathRevolution wrote: [Math Revolution GMAT math practice question] Which of the following is the best approximation for $$11^{11}-9^9$$? A. $$11^8$$ B. $$11^9$$ C. $$11^{10}$$ D. $$11^{11}$$ E. $$11^{12}$$ answer would be $$11^{10}$$ if $$9^9>\frac{11^{11}}{2}$$, otherwise 11^{11}.. so lets see... $$\frac{11^{11}}{2} = \frac{11}{2}*11^{10}=5.5*11^{10}$$ This is much greater than $$9^9$$.. so you can neglect $$9^9$$ when compared to $$11^{11}$$ so answer is $$11^{11}$$ D _________________ Senior Manager Joined: 09 Jun 2014 Posts: 329 Location: India Concentration: General Management, Operations Re: Which of the following is the best approximation for 11^{11}-9^9? [#permalink] ### Show Tags 21 Aug 2018, 07:15 GMATGuruNY wrote: MathRevolution wrote: [Math Revolution GMAT math practice question] Which of the following is the best approximation for $$11^{11}-9^9$$? A. $$11^8$$ B. $$11^9$$ C. $$11^{10}$$ D. $$11^{11}$$ E. $$11^{12}$$ Since the answer choices are very spread out, our approximation does not have to very exact. $$11^{11}-9^9 = 11^{11} - (11-2)^{11} ≈ 11^{11} - 11^9 = 11^9(11^2 - 1) ≈ (11^9)(11^2) = 11^{11}$$ Have been your follower for a long time on beat the gmat!!Big fan of yours..cant afford so your posts are Bible .. good to have you here Sir. I think you mistyped the bold part .(just rewriting) . $$11^{11}-9^9 = 11^{11} - (11-2)^{09} ≈ 11^{11} - 11^9 = 11^9(11^2 - 1) ≈ (11^9)(11^2) = 11^{11}$$ Press Kudos if it helps!! Director Joined: 04 Aug 2010 Posts: 612 Schools: Dartmouth College Re: Which of the following is the best approximation for 11^{11}-9^9? [#permalink] ### Show Tags 21 Aug 2018, 07:47 1 prabsahi wrote: Have been your follower for a long time on beat the gmat!!Big fan of yours..cant afford so your posts are Bible .. good to have you here Sir. I think you mistyped the bold part .(just rewriting) . $$11^{11}-9^9 = 11^{11} - (11-2)^{09} ≈ 11^{11} - 11^9 = 11^9(11^2 - 1) ≈ (11^9)(11^2) = 11^{11}$$ Press Kudos if it helps!! Fixed! Thanks for catching the typo. Another way to approach this problem: 10¹¹ (100,000,000,000) is 100 TIMES the value of 10⁹ (1,000,000,000). Implication: 11¹¹ must be MORE THAN 100 TIMES the value of 9⁹. Since 9⁹ is so small when compared to 11¹¹, we can ignore the value of 9⁹ when we approximate: 11¹¹ - 9⁹ ≈ 11¹¹ _________________ GMAT and GRE Tutor New York, NY Available for tutoring in NYC and long-distance. For more information, please email me at GMATGuruNY@gmail.com. Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 9018 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: Which of the following is the best approximation for 11^{11}-9^9? [#permalink] ### Show Tags 23 Aug 2018, 01:12 => $$9^9$$ is much smaller than $$11^{11}$$. Thus, $$11^{11}-9^9$$ is closest to $$11^{11}.$$ 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$79 for 1 month Online Course"
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Which of the following is the best approximation for 11^{11}-9^9?  [#permalink]

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12 Jan 2019, 03:38
I think the easiest way goes like this

$$11^(11)-9^9 ≈ 10^(11)-10^9 = 10^9(10^2-1) = 10^9 (10-1) (10+1) ≈ 10^(11)$$
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Which of the following is the best approximation for 11^{11}-9^9?   [#permalink] 12 Jan 2019, 03:38