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9^9 - 9^2 is approximation of which of the following?

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Math Revolution GMAT Instructor
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9^9 - 9^2 is approximation of which of the following?  [#permalink]

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New post 03 Mar 2016, 18:25
00:00
A
B
C
D
E

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9^9 - 9^2 is approximation of which of the following?

A. 9^7
B. 9^8
C. 9^9
D. 9^11
E. 9^10


* A solution will be posted in two days.

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Re: 9^9 - 9^2 is approximation of which of the following?  [#permalink]

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New post 03 Mar 2016, 20:00
MathRevolution wrote:
9^9 - 9^2 is approximation of which of the following?

A. 9^7
B. 9^8
C. 9^9
D. 9^11
E. 9^10


* A solution will be posted in two days.



It can be straight way seen from the equation that 9^9 is much higher than 9^2 and addition or subtraction of 9^2 from 9^9 will not make much difference..
so \(9^9 - 9^2\) should be nearly equal to C\(9^9\)..

Other way would be factorization..
\(9^9 - 9^2=9^2(9^7-1)..\) ..
1 is way too small quantity in comparison to 9^7..
so (9^7-1)=9^7..
so \(9^9 - 9^2=9^2(9^7-1)=9^2*9^7=9^9
ans C..\)

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Re: 9^9 - 9^2 is approximation of which of the following?  [#permalink]

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New post 06 Mar 2016, 03:51
9^9 - 9^2 is approximation of which of the following?

A. 9^7
B. 9^8
C. 9^9
D. 9^11
E. 9^10

=> Since 9^2 is a small number compared to 9^9, it can be disregarded. Thus, 9^9-9^2=9^9 is derived and the answer is C.
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Re: 9^9 - 9^2 is approximation of which of the following?  [#permalink]

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New post 02 May 2017, 16:52
1
MathRevolution wrote:
9^9 - 9^2 is approximation of which of the following?

A. 9^7
B. 9^8
C. 9^9
D. 9^11
E. 9^10


We can simplify the given expression:

9^9 - 9^2

9^2(9^7 - 1)

Since 9^7 - 1 is almost the same as 9^7, we have:

9^2 x 9^7 = 9^9.

Answer: C
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Re: 9^9 - 9^2 is approximation of which of the following?  [#permalink]

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Re: 9^9 - 9^2 is approximation of which of the following?   [#permalink] 05 Feb 2019, 01:13
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