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
A. 9^9
B. 9^8
C. 9^7
D. 9^6
E. 9^5
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9^9-9^2=
9^2(9^7-1)
what do i do for next step?
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9^9-9^2
Source: Beat The GMAT — Problem Solving |
(9^7 -1) is closest to 9^7
therefore expression in paranthesis ~ 9^7
9^7 * 9^2 = 9^9
hope this helps.
therefore expression in paranthesis ~ 9^7
9^7 * 9^2 = 9^9
hope this helps.
9^9 - 9^2
Like Just do it said Take 9^2 the common factor out
9^2 (9^7 - 1)
So 9^2 (9^7 - 1)
= 9^2 (9 ^ 7) (since 9 ^ 7 - 1 is very close to 9 ^ 7)
=9^2(9^7)
=9^9
Like Just do it said Take 9^2 the common factor out
9^2 (9^7 - 1)
So 9^2 (9^7 - 1)
= 9^2 (9 ^ 7) (since 9 ^ 7 - 1 is very close to 9 ^ 7)
=9^2(9^7)
=9^9
The approximation works since the questions asks for the closet value.
9^7 - 1 would be closest to 9 ^ 7
9^7 - 1 would be closest to 9 ^ 7
I also did the same way as suggested by other members.
Another way to look at it is,
9^9 would result in such a huge number that 9^2, i.e. 81 would be insignificant. Hence, answer would be 9^9.
As I said, this struck me after I had solved. :roll:
Another way to look at it is,
9^9 would result in such a huge number that 9^2, i.e. 81 would be insignificant. Hence, answer would be 9^9.
As I said, this struck me after I had solved. :roll:
