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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]  24 May 2008, 11:33
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Difficulty:

25% (medium)

Question Stats:

63% (01:29) correct 37% (00:51) wrong based on 108 sessions
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, 00:23, edited 2 times in total.
Renamed the topic, edited the question and added the OA.
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Re: closest value [#permalink]  24 May 2008, 11:53
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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]  24 May 2008, 15:24
1
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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]  26 Nov 2009, 12:37
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]  09 May 2010, 22:30
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]  09 May 2010, 22:50
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]  10 May 2010, 15:40
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Expert's post
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]  25 Feb 2014, 19:58
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]  26 Feb 2014, 00:25
Expert's post
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Re: Which of the following is closest to 9^9 - 9^2? [#permalink]  02 Apr 2014, 01:19
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 to 9^9 - 9^2?   [#permalink] 02 Apr 2014, 01:19
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