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# Which of the following is closest to 11^5*9^5–7*10^7?

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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GMAT 1: 760 Q51 V42
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Which of the following is closest to 11^5*9^5–7*10^7?  [#permalink]

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21 Feb 2018, 01:07
00:00

Difficulty:

55% (hard)

Question Stats:

56% (01:31) correct 44% (02:07) wrong based on 56 sessions

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[GMAT math practice question]

Which of the following is closest to $$11^5*9^5–7*10^7?$$

$$A. 10^2$$
$$B. 10^7$$
$$C. 10^8$$
$$D. 10^9$$
$$E. 10^{10}$$

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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" Current Student Joined: 07 Jan 2016 Posts: 1086 Location: India GMAT 1: 710 Q49 V36 Re: Which of the following is closest to 11^5*9^5–7*10^7? [#permalink] ### Show Tags 21 Feb 2018, 03:31 MathRevolution wrote: [GMAT math practice question] Which of the following is closest to $$11^5*9^5–7*10^7?$$ $$A. 10^2$$ $$B. 10^7$$ $$C. 10^8$$ $$D. 10^9$$ $$E. 10^{10}$$ 11^5*9^5–7*10^7 = (10+1)^5(10-1)^5 - 7*10^7 = (10^10 -1) - 7*10^7 (a+b)(a-b0 = a^2-b^2 10^10-10^7 = 10^7(10^3 -1 ) = 10^10 (E) Current Student Joined: 12 Aug 2015 Posts: 2567 Schools: Boston U '20 (M) GRE 1: Q169 V154 Re: Which of the following is closest to 11^5*9^5–7*10^7? [#permalink] ### Show Tags 21 Feb 2018, 03:42 APPROXIMATION TECHNIQUE :- Here is what I did on this one -> $$11^{5} * 9^{5}– 7*10^{7} = 99^{5} -7*10^{7}$$ Now, lets approximate. Lets say time is running out and we have 30 seconds to get to the correct answer. $$99^{5} - 7*10^{7} = 100^{5} - 7*10^{7} = 10^{10} - 7*10^{7}$$ Notice that $$10^{10}$$ is extremely large as compared to $$7*10^{7}$$ Hence the value would be close to $$10^{10}$$ Smash that E. _________________ Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 8017 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: Which of the following is closest to 11^5*9^5–7*10^7? [#permalink] ### Show Tags 25 Feb 2018, 18:40 => Since $$11$$ is close to $$10$$ and $$9$$ is close to $$10, 11^5*9^5$$ is close to $$10^5*10^5 = 10^{10}.$$ Since $$7*10^7$$ is a relatively small number compared with $$10^{10}, 11^5*9^5 – 7*10^7$$ is approximately equal to $$10^{10}$$. Therefore, the answer is E. Answer: E _________________ 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 closest to 11^5*9^5–7*10^7?  [#permalink]

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25 Feb 2018, 20:22
$$11^5×9^5 = (11×9)^5 ≈ 100^5 = 10^{10}$$

Now, $$10^{10}-7×10^7 = 10^7(10^3-7)$$

Since 7 is very tiny and hence can be ignored as we only need approx value.

$$10^7×10^3 = 10^{10}$$
Re: Which of the following is closest to 11^5*9^5–7*10^7?   [#permalink] 25 Feb 2018, 20:22
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# Which of the following is closest to 11^5*9^5–7*10^7?

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