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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8017
GMAT 1: 760 Q51 V42 GPA: 3.82
Which of the following is closest to 11^5*9^5–7*10^7?  [#permalink]

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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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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]

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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)
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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]

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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.

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Math Revolution GMAT Instructor V
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]

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=>

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.

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Concentration: Entrepreneurship, Finance
Re: Which of the following is closest to 11^5*9^5–7*10^7?  [#permalink]

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$$11^5×9^5 = (11×9)^5 ≈ 100^5 = 10^{10}$$

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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