Is 3^m less than 2000 ?
1. 3^m+1 > 2000
2. 3^m-1 = 3^m-486
Standard DS options follow.
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adthedaddy
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Matt@VeritasPrep
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S1::
3��¹ = 3� * 3, so we have
3� * 3 > 2000, or
3� > (2000/3)
Assuming integers -- NOT a reasonable assumption here, but I'm guessing the author intended this -- this gives m ≥ 6. If m = 6, then 3� < 2000. If m ≥ 7, then 3� > 2000. NOT SUFFICIENT.
S2::
I'm assuming you mean
3��¹ = 3� - 486
which is
486 = 3� - 3��¹, or
486 = 3��¹ * (3 - 1), or
243 = 3��¹
So (m - 1) = 5, and m = 6. This gives us one and only one value, so it is sufficient to answer the question (YES, 3� = 729, which is < 2000.)
3��¹ = 3� * 3, so we have
3� * 3 > 2000, or
3� > (2000/3)
Assuming integers -- NOT a reasonable assumption here, but I'm guessing the author intended this -- this gives m ≥ 6. If m = 6, then 3� < 2000. If m ≥ 7, then 3� > 2000. NOT SUFFICIENT.
S2::
I'm assuming you mean
3��¹ = 3� - 486
which is
486 = 3� - 3��¹, or
486 = 3��¹ * (3 - 1), or
243 = 3��¹
So (m - 1) = 5, and m = 6. This gives us one and only one value, so it is sufficient to answer the question (YES, 3� = 729, which is < 2000.)
