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Is 3^m less than 2,000? (1) 3^(m + 1) > 2,000 (2) 3^(m - 1) = 3^m -

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Bunuel
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Is 3^m less than 2,000? (1) 3^(m + 1) > 2,000 (2) 3^(m - 1) = 3^m - [#permalink] New post   20 Aug 2019, 02:15
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Is \(3^m\) less than 2,000?

(1) \(3^{m + 1} > 2,000\)

(2) \(3^{m - 1} = 3^m - 486\)
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B
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Re: Is 3^m less than 2,000? (1) 3^(m + 1) > 2,000 (2) 3^(m - 1) = 3^m - [#permalink] New post   20 Aug 2019, 03:15
Bunuel wrote:
Is \(3^m\) less than 2,000?

(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
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Re: Is 3^m less than 2,000? (1) 3^(m + 1) > 2,000 (2) 3^(m - 1) = 3^m - [#permalink] New post   20 Aug 2019, 03:23
\(3^7\) 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.
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Re: Is 3^m less than 2,000? (1) 3^(m + 1) > 2,000 (2) 3^(m - 1) = 3^m - [#permalink] New post   20 Aug 2019, 04:04
Bunuel wrote:
Is \(3^m\) less than 2,000?

(1) \(3^{m + 1} > 2,000\)

(2) \(3^{m - 1} = 3^m - 486\)


#1
\(3^{m + 1} > 2,000\)
m=6, yes and yes for condition Is \(3^m\) less than 2,000?
m=yes and no for condition
insufficient
#2
\(3^{m - 1} = 3^m - 486\)[/quote]
solve the expression we get m=6
sufficeint
IMO B
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Re: Is 3^m less than 2,000? (1) 3^(m + 1) > 2,000 (2) 3^(m - 1) = 3^m - [#permalink] New post   20 Aug 2019, 05:17
Bunuel wrote:
Is \(3^m\) less than 2,000?

(1) \(3^{m + 1} > 2,000\)

(2) \(3^{m - 1} = 3^m - 486\)


Asked: Is \(3^m\) less than 2,000?

(1) \(3^{m + 1} > 2,000\)
3^m > 2000/3 = 666.67
NOT SUFFICIENT

(2) \(3^{m - 1} = 3^m - 486\)
3^m - 3^{m-1} = 486
3^m = 486 * 3/2 = 729 is NOT >2,000
SUFFICIENT

IMO B
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Re: Is 3^m less than 2,000? (1) 3^(m + 1) > 2,000 (2) 3^(m - 1) = 3^m - [#permalink] New post   19 Sep 2019, 02:16
Expert Reply
Bunuel wrote:
Is \(3^m\) less than 2,000?

(1) \(3^{m + 1} > 2,000\)

(2) \(3^{m - 1} = 3^m - 486\)


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Re: Is 3^m less than 2,000? (1) 3^(m + 1) > 2,000 (2) 3^(m - 1) = 3^m - [#permalink]
19 Sep 2019, 02:16
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