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10 Feb 2014, 04:33
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Bunuel
Yup. Thanks for your patience though.
06 Nov 2015, 05:41
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Is \(10^m<5000\)?
(1) \(10^{m+1}>9000\) --> \(10^m>900\). If \(10^m\) is in the range \(900<10^m<{5000}\) (for instance if \(m=3\)) then the answer to the question will be YES, but if \(10^m\geq{5000}\) (for instance if \(m=4\)) then the answer to the question will be NO. Not sufficient.
To elaborate more: \(10^m>900\) means \(m>log_{10}900\approx{2.95}\).
(2) \(10^{m-1}=10^m-900\) --> we can calculate \(m\), so we can answer to the question whether \(10^m<5000\). Sufficient.
To show how it can be done: \(900=10^m(1-\frac{1}{10})\) --> \(10^m=1000<5000\) (\(m=3\)).
Answer: B.[/quote]
Dear Bunuel,
I tried solving it this way :
10^m < 5,000
i.e 10^1 = 10
10^2 = 100
10^3 = 1,000
10^4 = 10,000
Therefore, I concluded 3<m<4.
Now, using the data points given :
(1) 10^m+1 > 9,000
assuming m=3, m+1 = 4.
Therefore, 10^4 = 10,000 > 9,000........SUFFICIENT.
(2) 10^m-1 = 10^m - 900
assuming m=3, m-1 = 2.
Therefore, 10^2 = 100 = 10^3 - 900.....SUFFICIENT.
Thus, answer becomes D.
Please let me know where I am going wrong.
(1) \(10^{m+1}>9000\) --> \(10^m>900\). If \(10^m\) is in the range \(900<10^m<{5000}\) (for instance if \(m=3\)) then the answer to the question will be YES, but if \(10^m\geq{5000}\) (for instance if \(m=4\)) then the answer to the question will be NO. Not sufficient.
To elaborate more: \(10^m>900\) means \(m>log_{10}900\approx{2.95}\).
(2) \(10^{m-1}=10^m-900\) --> we can calculate \(m\), so we can answer to the question whether \(10^m<5000\). Sufficient.
To show how it can be done: \(900=10^m(1-\frac{1}{10})\) --> \(10^m=1000<5000\) (\(m=3\)).
Answer: B.[/quote]
Dear Bunuel,
I tried solving it this way :
10^m < 5,000
i.e 10^1 = 10
10^2 = 100
10^3 = 1,000
10^4 = 10,000
Therefore, I concluded 3<m<4.
Now, using the data points given :
(1) 10^m+1 > 9,000
assuming m=3, m+1 = 4.
Therefore, 10^4 = 10,000 > 9,000........SUFFICIENT.
(2) 10^m-1 = 10^m - 900
assuming m=3, m-1 = 2.
Therefore, 10^2 = 100 = 10^3 - 900.....SUFFICIENT.
Thus, answer becomes D.
Please let me know where I am going wrong.
09 Apr 2016, 07:14
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shekar123
stmt-1
10^m * 10 > 9000
10^m > 9 * 10^2
if m =3 then yes else no insuff.
stmt-2
10^m / 10 = 10^m - 900
10^m = 10^(m+1) - 9000
10^(m+1) - 10^m = 9000
10^m (10-1) = 9000
10^m * 9 = 9 * 10^3
m = 3, sufficient.
