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Math Revolution GMAT Instructor V
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Which of the following is the best approximation for 11^{11}-9^9?  [#permalink]

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Difficulty:   65% (hard)

Question Stats: 38% (01:18) correct 62% (01:40) wrong based on 88 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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Which of the following is the best approximation for 11^{11}-9^9?  [#permalink]

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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.
$$11^{11}-9^9 = 11^{11} - (11-2)^9 ≈ 11^{11} - 11^9 = 11^9(11^2 - 1) ≈ (11^9)(11^2) = 11^{11}$$

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Originally posted by GMATGuruNY on 21 Aug 2018, 04:43.
Last edited by GMATGuruNY on 21 Aug 2018, 08:20, edited 1 time in total.
Math Expert V
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Which of the following is the best approximation for 11^{11}-9^9?  [#permalink]

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

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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)

.
$$11^{11}-9^9 = 11^{11} - (11-2)^{09} ≈ 11^{11} - 11^9 = 11^9(11^2 - 1) ≈ (11^9)(11^2) = 11^{11}$$

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

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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

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

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=>

$$9^9$$ is much smaller than $$11^{11}$$.
Thus, $$11^{11}-9^9$$ is closest to $$11^{11}.$$

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

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I think the easiest way goes like this

$$11^(11)-9^9 ≈ 10^(11)-10^9 = 10^9(10^2-1) = 10^9 (10-1) (10+1) ≈ 10^(11)$$
_________________ Which of the following is the best approximation for 11^{11}-9^9?   [#permalink] 12 Jan 2019, 04:38
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