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06 Mar 2023, 02:30
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D
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Difficulty:
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Question Stats:
47% (01:38) correct
53%
(02:03)
wrong
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Which of the following is the best approximation for \(11^{11}-9^9\)?
A. \(11^8\)
B. \(11^9\)
C. \(11^{10}\)
D. \(11^{11}\)
E. \(11^{12}\)
A. \(11^8\)
B. \(11^9\)
C. \(11^{10}\)
D. \(11^{11}\)
E. \(11^{12}\)
15 Mar 2023, 14:10
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avggmatstudent23
My line of thinking would be similar to the explanations given in the previous posts. The crucial idea is that 9^9 is significantly smaller than 11^11, and subtracting it from 11^11 would have a negligible effect on the result. In fact, even if we had 11^9 instead of 9^9, the result would still be very close to 11^11:
- \(11^{11}-11^9 = 11^9(11^2-1)\approx 11^9*11^2=11^{11}\).
Therefore, \(11^{11}-9^9\) will be even closer to 11^11 than \(11^{11}-11^9\).
Answer: D.
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General Discussion
10 Mar 2023, 13:11
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Bunuel
Given that the section is called Quantitative REASONING, let's get the right answer without doing the math. 9^9 is tiny compared to 11^11. Less than 1%, since 11^11 is more than 11*11*(9^9). We surely are not subtracting enough to decrease by a power of 11.
Answer choice D.
