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20 Aug 2019, 02:15
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Difficulty:
35%
(medium)
Question Stats:
69% (01:55) correct
31%
(02:02)
wrong
based on 58
sessions
History
Date
Time
Result
Not Attempted Yet
Is \(3^m\) less than 2,000?
(1) \(3^{m + 1} > 2,000\)
(2) \(3^{m - 1} = 3^m - 486\)
(1) \(3^{m + 1} > 2,000\)
(2) \(3^{m - 1} = 3^m - 486\)
anbknaga
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20 Aug 2019, 03:15
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Bunuel
Is \(3^m\) less than 2,000?
(1) \(3^{m + 1} > 2,000\)
(2) \(3^{m - 1} = 3^m - 486\)
(1) \(3^{m + 1} > 2,000\)
(2) \(3^{m - 1} = 3^m - 486\)
Is \(3^m\) less than 2,000?
Statement 1: \(3^{m + 1} > 2,000\)
=> \(3^{m}*3 > 2000\)
=> \(3^{m} > 666\)
=> \(3^{6} = 729\) which is less than 2000 but m can be anything more than that which will greater than 2000
Therefore, statement 1 is INSUFFICIENT
Statement 2: \(3^{m - 1} = 3^m - 486\)
\(\frac{3^{m}}{3} = 3^m - 486\)
\(\frac{3^{m}}{3} - 3^m = -486\)
\(3^{m}*(\frac{1}{3} - 1) = -486\)
\(3^{m}*(\frac{-2}{3}) = -486\)
\(3^{m} = 729\) which is less than 2000. The answer is a clear NO.
Hence, Statement 2 is SUFFICIENT
The answer is B
Chethan92
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20 Aug 2019, 03:23
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\(3^7\) is 2187
\(3^6\) is 729
So, we need to find whether m is greater than or equal to 7.
From S1:
\(3^{m+1} > 2000\)
So, m is greater than or equal to 6.
If m is 6, then-No.
If m is 7 or any other integer, then Yes.
Insufficient.
From S2:
\(3^{m-1} = 3^m - 486\)
\(3^{m-1} = 3^m - 2^1*3^5\)
\(2*3^5 = 3^m-3^{m-1}\)
\(2*3^5 = 3^m[1-1/3]\)
\(2*3^5 = 3^m[2/3]\)
Solving gives m as 6.
So, \(3^m\) is not greater than 2000.
Sufficient.
B is the answer.
\(3^6\) is 729
So, we need to find whether m is greater than or equal to 7.
From S1:
\(3^{m+1} > 2000\)
So, m is greater than or equal to 6.
If m is 6, then-No.
If m is 7 or any other integer, then Yes.
Insufficient.
From S2:
\(3^{m-1} = 3^m - 486\)
\(3^{m-1} = 3^m - 2^1*3^5\)
\(2*3^5 = 3^m-3^{m-1}\)
\(2*3^5 = 3^m[1-1/3]\)
\(2*3^5 = 3^m[2/3]\)
Solving gives m as 6.
So, \(3^m\) is not greater than 2000.
Sufficient.
B is the answer.
