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# Which of the following is closest in value to (9^9)-(9^2)?

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Which of the following is closest in value to (9^9)-(9^2)? [#permalink]

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24 May 2008, 12:33
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Which of the following is closest in value to (9^9)-(9^2)?

A. 9^9
B. 9^8
C. 9^7
D. 9^6
E. 9^5
[Reveal] Spoiler: OA

Last edited by Bunuel on 26 Feb 2014, 01:23, edited 2 times in total.
Renamed the topic, edited the question and added the OA.

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Re: closest value [#permalink]

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24 May 2008, 12:53
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I think the answer is going to be A. The reason is that subtracting 81 from 9^9 is not going to subtract enough to get it anywhere close to 9^8. 9^8 is going to be such a huge number that when you multiply it by 9 again to get 9^9, subtracting 81 (i.e., 9^2) from it, the result will still be must closer to 9^9 than any of the others.

puma wrote:
Which of the following is closest in value to (9^9)-(9^2)?

a) 9^9
b) 9^8
c) 9^7
d) 9^6
e) 9^5

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Re: closest value [#permalink]

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24 May 2008, 16:24
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i would say A as well ... i just simplified out to 9^2*(9^7 - 1) ... and the 1 is pretty much negligible ... so we go back down to 9^9 ...

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Re: closest value [#permalink]

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26 Nov 2009, 13:37
gmat620 wrote:
isn't there any algebraic solution ?

We need to get approximate answer. I'm pretty sure exact number is unreachable w/o Excel spreadsheets.

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Which of the following is closest to 9^9 - 9^2? [#permalink]

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09 May 2010, 23:30
Which of the following is closest to 9^9 - 9^2?

A. 9^9
B. 9^8
C. 9^7
D. 9^6
E. 9^5

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Re: quick qs [#permalink]

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09 May 2010, 23:50
bibha wrote:
1. which of the following is closest to 9^9 - 9^2?
9^9
9^8
9^7
9^6
9^5

What is the trick?>>???

IMO A, whats the OA?

clearly 9^8 <9^9 - 9^2 < 9^9
now 9^9 - 9^2 will be closer to 9^9 if 9^9 - 9^2? lies between $$\frac{(9^9+9^8)}{2}$$ and 9^9 else 9^8
$$\frac{(9^9+9^8)}{2}$$ = $$9^8*\frac{(9+1)}{2} = 9^{8} * 5$$

$$9^9 - 9^2 = 9^8( 9 - 9^{-6}) > 9^8 * 8 > 9^8*5$$

since 9^9 - 9^2 is greater than $$\frac{(9^9+9^8)}{2}$$ i.e $$9^{8} * 5$$

This lies closer to 9^9
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Re: quick qs [#permalink]

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10 May 2010, 16:40
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bibha wrote:
1. which of the following is closest to 9^9 - 9^2?
9^9
9^8
9^7
9^6
9^5

What is the trick?>>???

Easier way: $$9^9 - 9^2=9^2(9^7-1)$$. Now $$9^7-1$$ is very close to $$9^7$$, hence $$9^9 - 9^2=9^2(9^7-1)\approx{9^2*9^7=9^9}$$.

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Re: Which of the following is closest in value to (9^9)-(9^2)? [#permalink]

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25 Feb 2014, 20:58
puma wrote:
Which of the following is closest in value to (9^9)-(9^2)?

a) 9^9
b) 9^8
c) 9^7
d) 9^6
e) 9^5

9^9 is way too high compared to 9^2
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Re: Which of the following is closest in value to (9^9)-(9^2)? [#permalink]

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26 Feb 2014, 01:25
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Re: Which of the following is closest to 9^9 - 9^2? [#permalink]

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02 Apr 2014, 02:19
$$9^9$$ is way too high than $$9^2$$

$$So answer = A = 9^9$$
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Re: Which of the following is closest in value to (9^9)-(9^2)? [#permalink]

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26 Jun 2015, 08:56
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Re: Which of the following is closest in value to (9^9)-(9^2)? [#permalink]

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17 Sep 2016, 05:12
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Re: Which of the following is closest in value to (9^9)-(9^2)?   [#permalink] 17 Sep 2016, 05:12
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# Which of the following is closest in value to (9^9)-(9^2)?

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