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

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by Max@Math Revolution » Thu Mar 03, 2016 5:25 pm
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


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by Brent@GMATPrepNow » Fri Mar 04, 2016 8:30 am
Max@Math Revolution 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
This is a case of relative sizes.
9^9 is a VERY BIG number (10^9 = 1,000,000,000 so 9^9 is very big also)
In comparison to 9^9, we can see that 9^2 (81) is negligible.

So, 9^9 - 9^2 is still VERY CLOSE to 9^9
Answer: C

Another way to look at it:
9^9 - 9^2 = 9^2(9^7 - 1) [notice that 9^7 - 1 is very close to 9^7]
≈ 9^2(9^7)
≈ 9^9
Answer: C

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by Max@Math Revolution » Sun Mar 06, 2016 2:52 am
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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by Scott@TargetTestPrep » Thu Dec 14, 2017 6:08 am
Max@Math Revolution 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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